Chapter 5 from Textbook Rs Aggrawal 2020 2021 for Class 6 MATHS

Question 1:

Answer:

(i) The shaded portion is 3 parts of the whole figure
     $∴$ $\frac{3}{4}$
(ii) The shaded portion is 1 parts of the whole figure
     $∴$ $\frac{1}{4}$
(iii) The shaded portion is 2 parts of the whole figure.
     $∴$ $\frac{2}{3}$
(iv) The shaded portion is 3 parts of the whole figure.
     $∴$ $\frac{3}{10}$
(v)The shaded portion is 4 parts of the whole figure.
     $∴$ $\frac{4}{9}$
(vi) The shaded portion is 3 parts of the whole figure.
   $∴$ $\frac{3}{8}$

Question 2:

(i) The shaded portion is 3 parts of the whole figure
     $∴$ $\frac{3}{4}$
(ii) The shaded portion is 1 parts of the whole figure
     $∴$ $\frac{1}{4}$
(iii) The shaded portion is 2 parts of the whole figure.
     $∴$ $\frac{2}{3}$
(iv) The shaded portion is 3 parts of the whole figure.
     $∴$ $\frac{3}{10}$
(v)The shaded portion is 4 parts of the whole figure.
     $∴$ $\frac{4}{9}$
(vi) The shaded portion is 3 parts of the whole figure.
   $∴$ $\frac{3}{8}$

Answer:

Question 3:

Answer:

The given rectangle is not divided into four equal parts.

Thus, the shaded region is not equal to $\frac{1}{4}$ of the whole.

Question 4:

The given rectangle is not divided into four equal parts.

Thus, the shaded region is not equal to $\frac{1}{4}$ of the whole.

Answer:

(i) $\frac{3}{4}$ (ii) $\frac{4}{7}$ (iii) $\frac{2}{5}$ (iv) $\frac{3}{10}$ (v) $\frac{1}{8}$
(vi) $\frac{5}{6}$ (vii) $\frac{8}{9}$ (viii) $\frac{7}{12}$

Question 5:

(i) $\frac{3}{4}$ (ii) $\frac{4}{7}$ (iii) $\frac{2}{5}$ (iv) $\frac{3}{10}$ (v) $\frac{1}{8}$
(vi) $\frac{5}{6}$ (vii) $\frac{8}{9}$ (viii) $\frac{7}{12}$

Answer:

Numerator Denominator
(i) 4       9
(ii) 6 11
(iii) 8    15
(iv) 12 17
(v) 5    1

Question 6:

Numerator Denominator
(i) 4       9
(ii) 6 11
(iii) 8    15
(iv) 12 17
(v) 5    1

Answer:

(i) $\frac{3}{8}$ (ii) $\frac{5}{12}$ (iii) $\frac{7}{16}$ (iv) $\frac{8}{15}$

Question 7:

(i) $\frac{3}{8}$ (ii) $\frac{5}{12}$ (iii) $\frac{7}{16}$ (iv) $\frac{8}{15}$

Answer:

(i) two-thirds
(ii) four $-$ ninths
(iii) two $-$ fifths
(iv) seven $-$ tenths
(v) one $-$ thirds
(vi) three $-$ fourths
(vii) three $-$ eighths
(viii) nine $-$ fourteenths
(ix) five $-$ elevenths
(x) six $-$ fifteenths

Question 8:

(i) two-thirds
(ii) four $-$ ninths
(iii) two $-$ fifths
(iv) seven $-$ tenths
(v) one $-$ thirds
(vi) three $-$ fourths
(vii) three $-$ eighths
(viii) nine $-$ fourteenths
(ix) five $-$ elevenths
(x) six $-$ fifteenths

Answer:

We know: 1 hour = 60 minutes
∴ The required fraction = $\frac{24}{60} = \frac{2}{5}$

Question 9:

We know: 1 hour = 60 minutes
∴ The required fraction = $\frac{24}{60} = \frac{2}{5}$

Answer:

There are total 9 natural numbers from 2 to 10. They are 2, 3, 4, 5, 6, 7, 8, 9, 10.
Out of these natural numbers, 2, 3, 5, 7 are the prime numbers.
∴ The required fraction = $\frac{4}{9}$ .

Question 10:

There are total 9 natural numbers from 2 to 10. They are 2, 3, 4, 5, 6, 7, 8, 9, 10.
Out of these natural numbers, 2, 3, 5, 7 are the prime numbers.
∴ The required fraction = $\frac{4}{9}$ .

Answer:

(i) $\frac{2}{3}$ of 15 pens = $(\frac{2}{3_{1}} \times \frac{15^{5}}{1}) = 10 pens$
(ii) $\frac{2}{3}$ of 27 balls = $(\frac{2}{3_{1}} \times \frac{27^{9}}{1}) = 18 balls$
(iii) $\frac{2}{3}$ of 36 balloons = â€‹ $(\frac{2}{3_{1}} \times \frac{36^{12}}{1}) = 24 balloons$

Question 11:

(i) $\frac{2}{3}$ of 15 pens = $(\frac{2}{3_{1}} \times \frac{15^{5}}{1}) = 10 pens$
(ii) $\frac{2}{3}$ of 27 balls = $(\frac{2}{3_{1}} \times \frac{27^{9}}{1}) = 18 balls$
(iii) $\frac{2}{3}$ of 36 balloons = â€‹ $(\frac{2}{3_{1}} \times \frac{36^{12}}{1}) = 24 balloons$

Answer:

(i) $\frac{3}{4}$ of 16 cups = $(\frac{3}{4_{1}} \times \frac{16^{4}}{1}) = 12 cups$
(ii) $\frac{3}{4}$ of 28 rackets = $(\frac{3}{4_{1}} \times \frac{28^{7}}{1}) = 21 rackets$
(iii) $\frac{3}{4}$ of 32 books = $(\frac{3}{4_{1}} \times \frac{32^{8}}{1}) = 24 books$

Question 12:

(i) $\frac{3}{4}$ of 16 cups = $(\frac{3}{4_{1}} \times \frac{16^{4}}{1}) = 12 cups$
(ii) $\frac{3}{4}$ of 28 rackets = $(\frac{3}{4_{1}} \times \frac{28^{7}}{1}) = 21 rackets$
(iii) $\frac{3}{4}$ of 32 books = $(\frac{3}{4_{1}} \times \frac{32^{8}}{1}) = 24 books$

Answer:

Neelam gives $\frac{4}{5}$ of 25 pencils to Meena.
$(\frac{4}{5_{1}} \times \frac{25^{5}}{1}) = 20 Pencils$
Thus, Meena gets 20 pencils.
∴ Number of pencils left with Neelam = 25 $-$ 20 = 5 pencils
Thus, 5 pencils are left with Neelam.

Question 13:

Neelam gives $\frac{4}{5}$ of 25 pencils to Meena.
$(\frac{4}{5_{1}} \times \frac{25^{5}}{1}) = 20 Pencils$
Thus, Meena gets 20 pencils.
∴ Number of pencils left with Neelam = 25 $-$ 20 = 5 pencils
Thus, 5 pencils are left with Neelam.

Answer:

Draw a 0 to 1 on a number line. Label point 1 as A and mark the starting point as 0.

(i) Divide the number line from 0 to 1 into 8 equal parts and take out 3 parts from it to reach point P.

(ii) Divide the number line from 0 to 1 into 9 equal parts and take out 5 parts from it to reach point P

.

(iii) Divide the number line from 0 to 1 into 7 equal parts and take out 4 parts from it to reach point P.

(Iv) Divide the number line from 0 to 1 into 5 equal parts and take out 2 parts from it to reach point P.

(v) Divide the number line from 0 to 1 into 4 equal parts and take out 1 part from it to reach point P.

Question 1:

Draw a 0 to 1 on a number line. Label point 1 as A and mark the starting point as 0.

(i) Divide the number line from 0 to 1 into 8 equal parts and take out 3 parts from it to reach point P.

(ii) Divide the number line from 0 to 1 into 9 equal parts and take out 5 parts from it to reach point P

.

(iii) Divide the number line from 0 to 1 into 7 equal parts and take out 4 parts from it to reach point P.

(Iv) Divide the number line from 0 to 1 into 5 equal parts and take out 2 parts from it to reach point P.

(v) Divide the number line from 0 to 1 into 4 equal parts and take out 1 part from it to reach point P.

Answer:

$\frac{1}{2}, \frac{3}{5}, \frac{10}{11}$

Question 2:

$\frac{1}{2}, \frac{3}{5}, \frac{10}{11}$

Answer:

A fraction whose numerator is greater than or equal to its denominator is called an improper fraction. Hence, $\frac{3}{2}, \frac{9}{4}, \frac{8}{8}, \frac{27}{16}, \frac{19}{18} and \frac{26}{26}$ are improper fractions.

Question 3:

A fraction whose numerator is greater than or equal to its denominator is called an improper fraction. Hence, $\frac{3}{2}, \frac{9}{4}, \frac{8}{8}, \frac{27}{16}, \frac{19}{18} and \frac{26}{26}$ are improper fractions.

Answer:

Clearly, $\frac{6}{5}, \frac{7}{5}, \frac{8}{5}, \frac{9}{5}, \frac{11}{5} and \frac{12}{5}$ are improper fractions, each with 5 as the denominator.

Question 4:

Clearly, $\frac{6}{5}, \frac{7}{5}, \frac{8}{5}, \frac{9}{5}, \frac{11}{5} and \frac{12}{5}$ are improper fractions, each with 5 as the denominator.

Answer:

Clearly, $\frac{13}{2}, \frac{13}{3}, \frac{13}{4}, \frac{13}{5}, \frac{13}{6}, \frac{13}{7}$ are improper fractions, each with 13 as the numerator.

Question 5:

Clearly, $\frac{13}{2}, \frac{13}{3}, \frac{13}{4}, \frac{13}{5}, \frac{13}{6}, \frac{13}{7}$ are improper fractions, each with 13 as the numerator.

Answer:

We have:
(i) $5 \frac{5}{7} = \frac{(5 \times 7) + 5}{7} = \frac{40}{7}$

(ii) $9 \frac{3}{8} = \frac{(9 \times 8) + 3}{8} = \frac{75}{8}$

(iii) $6 \frac{3}{10} = \frac{(6 \times 10) + 3}{10} = \frac{63}{10}$

(iv) $3 \frac{5}{11} = \frac{(3 \times 11) + 5}{11} = \frac{38}{11}$

(v) $10 \frac{9}{14} = \frac{(10 \times 14) + 9}{14} = \frac{149}{14}$

(vi) $12 \frac{7}{15} = \frac{(12 \times 15) + 7}{15} = \frac{187}{15}$

(vii) $8 \frac{8}{13} = \frac{(8 \times 13) + 8}{13} = \frac{112}{13}$

(viii) $51 \frac{2}{3} = \frac{(51 \times 3) + 2}{3} = \frac{155}{3}$

Question 6:

We have:
(i) $5 \frac{5}{7} = \frac{(5 \times 7) + 5}{7} = \frac{40}{7}$

(ii) $9 \frac{3}{8} = \frac{(9 \times 8) + 3}{8} = \frac{75}{8}$

(iii) $6 \frac{3}{10} = \frac{(6 \times 10) + 3}{10} = \frac{63}{10}$

(iv) $3 \frac{5}{11} = \frac{(3 \times 11) + 5}{11} = \frac{38}{11}$

(v) $10 \frac{9}{14} = \frac{(10 \times 14) + 9}{14} = \frac{149}{14}$

(vi) $12 \frac{7}{15} = \frac{(12 \times 15) + 7}{15} = \frac{187}{15}$

(vii) $8 \frac{8}{13} = \frac{(8 \times 13) + 8}{13} = \frac{112}{13}$

(viii) $51 \frac{2}{3} = \frac{(51 \times 3) + 2}{3} = \frac{155}{3}$

Answer:

(i) On dividing 17 by 5, we get:
Quotient = 3
    Remainder = 2
∴ $\frac{17}{5} = 3 + \frac{2}{5} = 3 \frac{2}{5}$

(ii) On dividing 62 by 7, we get:
Quotient = 8
    Remainder = 6
∴ $\frac{62}{7} = 8 + \frac{6}{7} = 8 \frac{6}{7}$

(iii) On dividing 101 by 8, we get:
Quotient = 12
    Remainder = 5
∴ $\frac{101}{8} = 12 + \frac{5}{8} = 12 \frac{5}{8}$

(iv) On dividing 95 by 13, we get:
Quotient = 7
    Remainder = 4
∴ $\frac{95}{13} = 7 + \frac{4}{13} = 7 \frac{4}{13}$

(v) On dividing 81 by 11, we get:
Quotient = 7
    Remainder = 4
∴ $\frac{81}{11} = 7 + \frac{4}{11} = 7 \frac{4}{11}$

(vi) On dividing 87 by 16, we get:
Quotient = 5
    Remainder = 7
∴ $\frac{87}{16} = 5 + \frac{7}{16} = 5 \frac{7}{16}$

(vii) On dividing 103 by 12, we get:
Quotient = 8
    Remainder = 7
∴ $\frac{103}{12} = 8 + \frac{7}{12} = 8 \frac{7}{12}$

(viii) On dividing 117 by 20, we get:
Quotient = 5
    Remainder = 17
∴ $\frac{117}{20} = 5 + \frac{17}{20} = 5 \frac{17}{20}$

Question 7:

(i) On dividing 17 by 5, we get:
Quotient = 3
    Remainder = 2
∴ $\frac{17}{5} = 3 + \frac{2}{5} = 3 \frac{2}{5}$

(ii) On dividing 62 by 7, we get:
Quotient = 8
    Remainder = 6
∴ $\frac{62}{7} = 8 + \frac{6}{7} = 8 \frac{6}{7}$

(iii) On dividing 101 by 8, we get:
Quotient = 12
    Remainder = 5
∴ $\frac{101}{8} = 12 + \frac{5}{8} = 12 \frac{5}{8}$

(iv) On dividing 95 by 13, we get:
Quotient = 7
    Remainder = 4
∴ $\frac{95}{13} = 7 + \frac{4}{13} = 7 \frac{4}{13}$

(v) On dividing 81 by 11, we get:
Quotient = 7
    Remainder = 4
∴ $\frac{81}{11} = 7 + \frac{4}{11} = 7 \frac{4}{11}$

(vi) On dividing 87 by 16, we get:
Quotient = 5
    Remainder = 7
∴ $\frac{87}{16} = 5 + \frac{7}{16} = 5 \frac{7}{16}$

(vii) On dividing 103 by 12, we get:
Quotient = 8
    Remainder = 7
∴ $\frac{103}{12} = 8 + \frac{7}{12} = 8 \frac{7}{12}$

(viii) On dividing 117 by 20, we get:
Quotient = 5
    Remainder = 17
∴ $\frac{117}{20} = 5 + \frac{17}{20} = 5 \frac{17}{20}$

Answer:

An improper fraction is greater than 1. Hence, it is always greater than a proper fraction, which is less than 1.
(i) $\frac{1}{2} < 1$

(ii) $\frac{3}{4} < 1$

(iii) $1 > \frac{6}{7}$

(iv) $\frac{6}{6} = 1$

(v) $\frac{3016}{3016} = 1$

(vi) $\frac{11}{5} > 1$

Question 8:

An improper fraction is greater than 1. Hence, it is always greater than a proper fraction, which is less than 1.
(i) $\frac{1}{2} < 1$

(ii) $\frac{3}{4} < 1$

(iii) $1 > \frac{6}{7}$

(iv) $\frac{6}{6} = 1$

(v) $\frac{3016}{3016} = 1$

(vi) $\frac{11}{5} > 1$

Answer:

(i) Draw a number line. Mark 0 as the starting point and 1 as the ending point.
Then, divide 0 to 1 in four equal parts, where each part is equal to 1/4.
Show the consecutive parts as 1/4, 1/2, 3/4 and at 1 show 4/4 = 1.

(ii) Draw 0 to 1 on a number line. Divide the segment into 8 equal parts, each part corresponds to 1/8. Show the consecutive parts as 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 and 8/8. Highlight the required ones only.

(iii) Draw 0 to 2 on a number line. Divide the segment between 0 and 1 into 5 equal parts, where each part is equal to 1/5.
Show 2/5, 3/5, 4/5 and 8/5 3 parts away from 1 towards 2. (1 < 8/5 < 2)

Question 1:

(i) Draw a number line. Mark 0 as the starting point and 1 as the ending point.
Then, divide 0 to 1 in four equal parts, where each part is equal to 1/4.
Show the consecutive parts as 1/4, 1/2, 3/4 and at 1 show 4/4 = 1.

(ii) Draw 0 to 1 on a number line. Divide the segment into 8 equal parts, each part corresponds to 1/8. Show the consecutive parts as 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 and 8/8. Highlight the required ones only.

(iii) Draw 0 to 2 on a number line. Divide the segment between 0 and 1 into 5 equal parts, where each part is equal to 1/5.
Show 2/5, 3/5, 4/5 and 8/5 3 parts away from 1 towards 2. (1 < 8/5 < 2)

Answer:

(i) $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{2 \times 3}{3 \times 3} = \frac{2 \times 4}{3 \times 4} = \frac{2 \times 5}{3 \times 5} = \frac{2 \times 6}{3 \times 6}$

∴ $\frac{2}{3} = \frac{4}{6} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} = \frac{12}{18}$

Hence, the five fractions equivalent to $\frac{2}{3}$ are $\frac{4}{6}, \frac{6}{9}, \frac{8}{12}, \frac{10}{15} and \frac{12}{18}$ .

(ii) â€‹ $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{4 \times 3}{5 \times 3} = \frac{4 \times 4}{5 \times 4} = \frac{4 \times 5}{5 \times 5} = \frac{4 \times 6}{5 \times 6}$

∴ $\frac{4}{5} = \frac{8}{10} = \frac{12}{15} = \frac{16}{20} = \frac{20}{25} = \frac{24}{30}$

Hence, the five fractions equivalent to $\frac{4}{5}$ are $\frac{8}{10}, \frac{12}{15}, \frac{16}{20}, \frac{20}{25} and \frac{24}{30}$ .

(iii) â€‹ $\frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{5 \times 3}{8 \times 3} = \frac{5 \times 4}{8 \times 4} = \frac{5 \times 5}{8 \times 5} = \frac{5 \times 6}{8 \times 6}$

∴ $\frac{5}{8} = \frac{10}{16} = \frac{15}{24} = \frac{20}{32} = \frac{25}{40} = \frac{30}{48}$

Hence, the five fractions equivalent to $\frac{5}{8}$ are $\frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40} and \frac{30}{48}$ .

(iv) â€‹ $\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{7 \times 3}{10 \times 3} = \frac{7 \times 4}{10 \times 4} = \frac{7 \times 5}{10 \times 5} = \frac{7 \times 6}{10 \times 6}$

∴ $\frac{7}{10} = \frac{14}{20} = \frac{21}{30} = \frac{28}{40} = \frac{35}{50} = \frac{42}{60}$

Hence, the five fractions equivalent to $\frac{7}{10}$ are $\frac{14}{20}, \frac{21}{30}, \frac{28}{40}, \frac{35}{50} and \frac{42}{60}$ .

(v) â€‹â€‹ $\frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{3 \times 3}{7 \times 3} = \frac{3 \times 4}{7 \times 4} = \frac{3 \times 5}{7 \times 5} = \frac{3 \times 6}{7 \times 6}$

∴ $\frac{3}{7} = \frac{6}{14} = \frac{9}{21} = \frac{12}{28} = \frac{15}{35} = \frac{18}{42}$

Hence, the five fractions equivalent to $\frac{3}{7}$ are $\frac{6}{14}, \frac{9}{21}, \frac{12}{28}, \frac{15}{35} and \frac{18}{42}$ .

(vi) â€‹ $\frac{6}{11} = \frac{6 \times 2}{11 \times 2} = \frac{6 \times 3}{11 \times 3} = \frac{6 \times 4}{11 \times 4} = \frac{6 \times 5}{11 \times 5} = \frac{6 \times 6}{11 \times 6}$

∴ $\frac{6}{11} = \frac{12}{22} = \frac{18}{33} = \frac{24}{44} = \frac{30}{55} = \frac{36}{66}$

Hence, the five fractions equivalent to $\frac{6}{11}$ are $\frac{12}{22}, \frac{18}{33}, \frac{24}{44}, \frac{30}{55} and \frac{36}{66}$ .

(vii) $\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{7 \times 3}{9 \times 3} = \frac{7 \times 4}{9 \times 4} = \frac{7 \times 5}{9 \times 5} = \frac{7 \times 6}{9 \times 6}$

∴ $\frac{7}{9} = \frac{14}{18} = \frac{21}{27} = \frac{28}{36} = \frac{35}{45} = \frac{42}{54}$

Hence, the five fractions equivalent to $\frac{7}{9}$ are $\frac{14}{18}, \frac{21}{27}, \frac{28}{36}, \frac{35}{45} and \frac{42}{54}$ .

(viii) $\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{5 \times 3}{12 \times 3} = \frac{5 \times 4}{12 \times 4} = \frac{5 \times 5}{12 \times 5} = \frac{5 \times 6}{12 \times 6}$

∴ $\frac{5}{12} = \frac{10}{24} = \frac{15}{36} = \frac{20}{48} = \frac{25}{60} = \frac{30}{72}$

Hence, the five fractions equivalent to $\frac{5}{12}$ are $\frac{10}{24}, \frac{15}{36}, \frac{20}{48}, \frac{25}{60} and \frac{30}{72}$ .

Question 2:

(i) $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{2 \times 3}{3 \times 3} = \frac{2 \times 4}{3 \times 4} = \frac{2 \times 5}{3 \times 5} = \frac{2 \times 6}{3 \times 6}$

∴ $\frac{2}{3} = \frac{4}{6} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} = \frac{12}{18}$

Hence, the five fractions equivalent to $\frac{2}{3}$ are $\frac{4}{6}, \frac{6}{9}, \frac{8}{12}, \frac{10}{15} and \frac{12}{18}$ .

(ii) â€‹ $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{4 \times 3}{5 \times 3} = \frac{4 \times 4}{5 \times 4} = \frac{4 \times 5}{5 \times 5} = \frac{4 \times 6}{5 \times 6}$

∴ $\frac{4}{5} = \frac{8}{10} = \frac{12}{15} = \frac{16}{20} = \frac{20}{25} = \frac{24}{30}$

Hence, the five fractions equivalent to $\frac{4}{5}$ are $\frac{8}{10}, \frac{12}{15}, \frac{16}{20}, \frac{20}{25} and \frac{24}{30}$ .

(iii) â€‹ $\frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{5 \times 3}{8 \times 3} = \frac{5 \times 4}{8 \times 4} = \frac{5 \times 5}{8 \times 5} = \frac{5 \times 6}{8 \times 6}$

∴ $\frac{5}{8} = \frac{10}{16} = \frac{15}{24} = \frac{20}{32} = \frac{25}{40} = \frac{30}{48}$

Hence, the five fractions equivalent to $\frac{5}{8}$ are $\frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40} and \frac{30}{48}$ .

(iv) â€‹ $\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{7 \times 3}{10 \times 3} = \frac{7 \times 4}{10 \times 4} = \frac{7 \times 5}{10 \times 5} = \frac{7 \times 6}{10 \times 6}$

∴ $\frac{7}{10} = \frac{14}{20} = \frac{21}{30} = \frac{28}{40} = \frac{35}{50} = \frac{42}{60}$

Hence, the five fractions equivalent to $\frac{7}{10}$ are $\frac{14}{20}, \frac{21}{30}, \frac{28}{40}, \frac{35}{50} and \frac{42}{60}$ .

(v) â€‹â€‹ $\frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{3 \times 3}{7 \times 3} = \frac{3 \times 4}{7 \times 4} = \frac{3 \times 5}{7 \times 5} = \frac{3 \times 6}{7 \times 6}$

∴ $\frac{3}{7} = \frac{6}{14} = \frac{9}{21} = \frac{12}{28} = \frac{15}{35} = \frac{18}{42}$

Hence, the five fractions equivalent to $\frac{3}{7}$ are $\frac{6}{14}, \frac{9}{21}, \frac{12}{28}, \frac{15}{35} and \frac{18}{42}$ .

(vi) â€‹ $\frac{6}{11} = \frac{6 \times 2}{11 \times 2} = \frac{6 \times 3}{11 \times 3} = \frac{6 \times 4}{11 \times 4} = \frac{6 \times 5}{11 \times 5} = \frac{6 \times 6}{11 \times 6}$

∴ $\frac{6}{11} = \frac{12}{22} = \frac{18}{33} = \frac{24}{44} = \frac{30}{55} = \frac{36}{66}$

Hence, the five fractions equivalent to $\frac{6}{11}$ are $\frac{12}{22}, \frac{18}{33}, \frac{24}{44}, \frac{30}{55} and \frac{36}{66}$ .

(vii) $\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{7 \times 3}{9 \times 3} = \frac{7 \times 4}{9 \times 4} = \frac{7 \times 5}{9 \times 5} = \frac{7 \times 6}{9 \times 6}$

∴ $\frac{7}{9} = \frac{14}{18} = \frac{21}{27} = \frac{28}{36} = \frac{35}{45} = \frac{42}{54}$

Hence, the five fractions equivalent to $\frac{7}{9}$ are $\frac{14}{18}, \frac{21}{27}, \frac{28}{36}, \frac{35}{45} and \frac{42}{54}$ .

(viii) $\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{5 \times 3}{12 \times 3} = \frac{5 \times 4}{12 \times 4} = \frac{5 \times 5}{12 \times 5} = \frac{5 \times 6}{12 \times 6}$

∴ $\frac{5}{12} = \frac{10}{24} = \frac{15}{36} = \frac{20}{48} = \frac{25}{60} = \frac{30}{72}$

Hence, the five fractions equivalent to $\frac{5}{12}$ are $\frac{10}{24}, \frac{15}{36}, \frac{20}{48}, \frac{25}{60} and \frac{30}{72}$ .

Answer:

The pairs of equivalent fractions are as follows:
(i) $\frac{5}{6} and \frac{20}{24} (\frac{20}{24} = \frac{5 \times 4}{6 \times 4})$
(ii) $\frac{3}{8} and \frac{15}{40} (\frac{15}{40} = \frac{3 \times 5}{8 \times 5})$
(iv) $\frac{2}{9} and \frac{14}{63} (\frac{14}{63} = \frac{2 \times 7}{9 \times 7})$

Question 3:

The pairs of equivalent fractions are as follows:
(i) $\frac{5}{6} and \frac{20}{24} (\frac{20}{24} = \frac{5 \times 4}{6 \times 4})$
(ii) $\frac{3}{8} and \frac{15}{40} (\frac{15}{40} = \frac{3 \times 5}{8 \times 5})$
(iv) $\frac{2}{9} and \frac{14}{63} (\frac{14}{63} = \frac{2 \times 7}{9 \times 7})$

Answer:

(i) Let $\frac{3}{5} = \frac{}{30}$
Clearly, 30 = 5 $\times$ 6
So, we multiply the numerator by 6.

∴ â€‹ $\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$
Hence, the required fraction is $\frac{18}{30}$ .
(ii) â€‹Let $\frac{3}{5} = \frac{24}{}$
Clearly, 24 = 3 $\times$ 8
So, we multiply the denominator by 8.

∴ â€‹ $\frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40}$
Hence, the required fraction is $\frac{24}{40}$ .

Question 4:

(i) Let $\frac{3}{5} = \frac{}{30}$
Clearly, 30 = 5 $\times$ 6
So, we multiply the numerator by 6.

∴ â€‹ $\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$
Hence, the required fraction is $\frac{18}{30}$ .
(ii) â€‹Let $\frac{3}{5} = \frac{24}{}$
Clearly, 24 = 3 $\times$ 8
So, we multiply the denominator by 8.

∴ â€‹ $\frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40}$
Hence, the required fraction is $\frac{24}{40}$ .

Answer:

(i) Let $\frac{5}{9} = \frac{}{54}$
Clearly, 54 = 9 $\times$ 6
So, we multiply the numerator by 6.
∴ â€‹ $\frac{5}{9} = \frac{5 \times 6}{9 \times 6} = \frac{30}{54}$
Hence, the required fraction is $\frac{30}{54}$ .
(ii) â€‹Let $\frac{5}{9} = \frac{35}{}$
Clearly, 35 = 5 $\times$ 7
So, we multiply the denominator by 7.
∴ â€‹ $\frac{5}{9} = \frac{5 \times 7}{9 \times 7} = \frac{35}{63}$
Hence, the required fraction is $\frac{35}{63}$ .

Question 5:

(i) Let $\frac{5}{9} = \frac{}{54}$
Clearly, 54 = 9 $\times$ 6
So, we multiply the numerator by 6.
∴ â€‹ $\frac{5}{9} = \frac{5 \times 6}{9 \times 6} = \frac{30}{54}$
Hence, the required fraction is $\frac{30}{54}$ .
(ii) â€‹Let $\frac{5}{9} = \frac{35}{}$
Clearly, 35 = 5 $\times$ 7
So, we multiply the denominator by 7.
∴ â€‹ $\frac{5}{9} = \frac{5 \times 7}{9 \times 7} = \frac{35}{63}$
Hence, the required fraction is $\frac{35}{63}$ .

Answer:

(i) Let $\frac{6}{11} = \frac{}{77}$
Clearly, 77 = 11 $\times$ 7
So, we multiply the numerator by 7.

∴ â€‹ $\frac{6}{11} = \frac{6 \times 7}{11 \times 7} = \frac{42}{77}$
Hence, the required fraction is $\frac{42}{77}$ .
(ii) â€‹Let $\frac{6}{11} = \frac{60}{}$
Clearly, 60 = 6 $\times$ 10
So, we multiply the denominator by 10.

∴ â€‹ $\frac{6}{11} = \frac{6 \times 10}{11 \times 10} = \frac{60}{110}$
Hence, the required fraction is $\frac{60}{110}$ .

Question 6:

(i) Let $\frac{6}{11} = \frac{}{77}$
Clearly, 77 = 11 $\times$ 7
So, we multiply the numerator by 7.

∴ â€‹ $\frac{6}{11} = \frac{6 \times 7}{11 \times 7} = \frac{42}{77}$
Hence, the required fraction is $\frac{42}{77}$ .
(ii) â€‹Let $\frac{6}{11} = \frac{60}{}$
Clearly, 60 = 6 $\times$ 10
So, we multiply the denominator by 10.

∴ â€‹ $\frac{6}{11} = \frac{6 \times 10}{11 \times 10} = \frac{60}{110}$
Hence, the required fraction is $\frac{60}{110}$ .

Answer:

Let $\frac{24}{30} = \frac{4}{}$
Clearly, 4 = 24 $\div$ 6
So, we divide the denominator by 6.
∴ â€‹ $\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}$
Hence, the required fraction is $\frac{4}{5}$ .

Question 7:

Let $\frac{24}{30} = \frac{4}{}$
Clearly, 4 = 24 $\div$ 6
So, we divide the denominator by 6.
∴ â€‹ $\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}$
Hence, the required fraction is $\frac{4}{5}$ .

Answer:

(i) Let $\frac{36}{48} = \frac{9}{}$
Clearly, 9 = 36 $\div$ 4
So, we divide the denominator by 4.
∴ â€‹ $\frac{36}{48} = \frac{36 \div 4}{48 \div 4} = \frac{9}{12}$
Hence, the required fraction is $\frac{9}{12}$ .
(ii) â€‹Let $\frac{36}{48} = \frac{}{4}$
Clearly, 4 = 48 $\div$ 12
So, we divide the numerator by 12.
∴ â€‹ $\frac{36}{48} = \frac{36 \div 12}{48 \div 12} = \frac{3}{4}$
Hence, the required fraction is $\frac{3}{4}$ .

Question 8:

(i) Let $\frac{36}{48} = \frac{9}{}$
Clearly, 9 = 36 $\div$ 4
So, we divide the denominator by 4.
∴ â€‹ $\frac{36}{48} = \frac{36 \div 4}{48 \div 4} = \frac{9}{12}$
Hence, the required fraction is $\frac{9}{12}$ .
(ii) â€‹Let $\frac{36}{48} = \frac{}{4}$
Clearly, 4 = 48 $\div$ 12
So, we divide the numerator by 12.
∴ â€‹ $\frac{36}{48} = \frac{36 \div 12}{48 \div 12} = \frac{3}{4}$
Hence, the required fraction is $\frac{3}{4}$ .

Answer:

(i) Let $\frac{56}{70} = \frac{4}{}$
Clearly, 4 = 56 $\div$ 14
So, we divide the denominator by 14.
∴ â€‹ $\frac{56}{70} = \frac{56 \div 14}{70 \div 14} = \frac{4}{5}$
Hence, the required fraction is $\frac{4}{5}$ .
(ii) â€‹Let $\frac{56}{70} = \frac{}{10}$
Clearly, 10 = 70 $\div$ 7
So, we divide the numerator by 7.
∴ â€‹ $\frac{56}{70} = \frac{56 \times 7}{70 \times 7} = \frac{8}{10}$
Hence, the required fraction is $\frac{8}{10}$ .

Question 9:

(i) Let $\frac{56}{70} = \frac{4}{}$
Clearly, 4 = 56 $\div$ 14
So, we divide the denominator by 14.
∴ â€‹ $\frac{56}{70} = \frac{56 \div 14}{70 \div 14} = \frac{4}{5}$
Hence, the required fraction is $\frac{4}{5}$ .
(ii) â€‹Let $\frac{56}{70} = \frac{}{10}$
Clearly, 10 = 70 $\div$ 7
So, we divide the numerator by 7.
∴ â€‹ $\frac{56}{70} = \frac{56 \times 7}{70 \times 7} = \frac{8}{10}$
Hence, the required fraction is $\frac{8}{10}$ .

Answer:

(i) Here, numerator = 9 and denominator = 15
Factors of 9 are 1, 3 and 9.
Factors of 15 are 1, 3, 5 and 15.
Common factors of 9 and 15 are 1 and 3.
H.C.F. of 9 and 15 is 3.
∴ $\frac{9}{15} = \frac{9 \div 3}{15 \div 3} = \frac{3}{5}$
Hence, the simplest form of $\frac{9}{15} is \frac{3}{5}$ .

(ii) Here, numerator = 48 and denominator = 60
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Common factors of 48 and 60 are 1, 2, 3, 4, 6 and 12.
H.C.F. of 48 and 60 is 12.
∴ $\frac{48}{60} = \frac{48 \div 12}{60 \div 12} = \frac{4}{5}$
Hence, the simplest form of $\frac{48}{60} is \frac{4}{5}$ .

(iii) Here, numerator = 84 and denominator = 98
Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 42 and 84.
Factors of 98 are 1, 2, 7, 14, 49 and 98.
Common factors of 84 and 98 are 1, 2, 7 and 14.
H.C.F. of 84 and 98 is 14.
∴ $\frac{84}{98} = \frac{84 \div 14}{98 \div 14} = \frac{6}{7}$
Hence, the simplest form of $\frac{84}{98} is \frac{6}{7}$ .

(iv) Here, numerator = 150 and denominator = 60
Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75 and 150.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Common factors of 150 and 60 are 1, 2, 3, 5, 6, 10, 15 and 30.
H.C.F. of 150 and 60 is 30.
∴ $\frac{150}{60} = \frac{150 \div 30}{60 \div 30} = \frac{5}{2}$
Hence, the simplest form of $\frac{150}{60} is \frac{5}{2}$ .

(v) â€‹Here, numerator = 72 and denominator = 90
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
Common factors of 72 and 90 are 1, 2, 3, 6, 9 and 18.
H.C.F. of 72 and 90 is 18.
∴ $\frac{72}{90} = \frac{72 \div 18}{90 \div 18} = \frac{4}{5}$
Hence, the simplest form of $\frac{72}{90} is \frac{4}{5}$ .

Question 10:

(i) Here, numerator = 9 and denominator = 15
Factors of 9 are 1, 3 and 9.
Factors of 15 are 1, 3, 5 and 15.
Common factors of 9 and 15 are 1 and 3.
H.C.F. of 9 and 15 is 3.
∴ $\frac{9}{15} = \frac{9 \div 3}{15 \div 3} = \frac{3}{5}$
Hence, the simplest form of $\frac{9}{15} is \frac{3}{5}$ .

(ii) Here, numerator = 48 and denominator = 60
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Common factors of 48 and 60 are 1, 2, 3, 4, 6 and 12.
H.C.F. of 48 and 60 is 12.
∴ $\frac{48}{60} = \frac{48 \div 12}{60 \div 12} = \frac{4}{5}$
Hence, the simplest form of $\frac{48}{60} is \frac{4}{5}$ .

(iii) Here, numerator = 84 and denominator = 98
Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 42 and 84.
Factors of 98 are 1, 2, 7, 14, 49 and 98.
Common factors of 84 and 98 are 1, 2, 7 and 14.
H.C.F. of 84 and 98 is 14.
∴ $\frac{84}{98} = \frac{84 \div 14}{98 \div 14} = \frac{6}{7}$
Hence, the simplest form of $\frac{84}{98} is \frac{6}{7}$ .

(iv) Here, numerator = 150 and denominator = 60
Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75 and 150.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Common factors of 150 and 60 are 1, 2, 3, 5, 6, 10, 15 and 30.
H.C.F. of 150 and 60 is 30.
∴ $\frac{150}{60} = \frac{150 \div 30}{60 \div 30} = \frac{5}{2}$
Hence, the simplest form of $\frac{150}{60} is \frac{5}{2}$ .

(v) â€‹Here, numerator = 72 and denominator = 90
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
Common factors of 72 and 90 are 1, 2, 3, 6, 9 and 18.
H.C.F. of 72 and 90 is 18.
∴ $\frac{72}{90} = \frac{72 \div 18}{90 \div 18} = \frac{4}{5}$
Hence, the simplest form of $\frac{72}{90} is \frac{4}{5}$ .

Answer:

(i) Here, numerator = 8 and denominator = 11
Factors of 8 are 1, 2, 4 and 8.
Factors of 11 are 1 and 11.

Common factor of 8 and 11 is 1.
Thus, H.C.F. of 8 and 11 is 1.
Hence,

\frac{8}{11}

is the simplest form.

(ii) Here, numerator = 9 and denominator = 14
Factors of 9 are 1, 3 and 9.
Factors of 14 are 1, 2, 7 and 14.

Common factor of 9 and 14 is 1.
Thus, H.C.F. of 9 and 14 is 1.
Hence,

\frac{9}{14}

is the simplest form.

(iii) Here, numerator = 25 and denominator = 36
Factors of 25 are 1, 5 and 25.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Common factor of 25 and 36 is 1.
Thus, H.C.F. of 25 and 36 is 1.
Hence,

\frac{25}{36}

is the simplest form.

(iv) Here, numerator = 8 and denominator = 15
Factors of 8 are 1, 2, 4 and 8.
Factors of 15 are 1, 3, 5 and 15.

Common factor of 8 and 15 is 1.
Thus, H.C.F. of 8 and 15 is 1.
Hence,

\frac{8}{15}

is the simplest form.
(v) Here, numerator = 21 and denominator = 10
Factors of 21 are 1, 3, 7 and 21.
Factors of 10 are 1, 2, 5 and 10.

Common factor of 21 and 10 is 1.
Thus, H.C.F. of 21 and 10 is 1.
Hence,

\frac{21}{10}

is the simplest form.

Question 11:

(i) Here, numerator = 8 and denominator = 11
Factors of 8 are 1, 2, 4 and 8.
Factors of 11 are 1 and 11.

Common factor of 8 and 11 is 1.
Thus, H.C.F. of 8 and 11 is 1.
Hence,

\frac{8}{11}

is the simplest form.

(ii) Here, numerator = 9 and denominator = 14
Factors of 9 are 1, 3 and 9.
Factors of 14 are 1, 2, 7 and 14.

Common factor of 9 and 14 is 1.
Thus, H.C.F. of 9 and 14 is 1.
Hence,

\frac{9}{14}

is the simplest form.

(iii) Here, numerator = 25 and denominator = 36
Factors of 25 are 1, 5 and 25.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Common factor of 25 and 36 is 1.
Thus, H.C.F. of 25 and 36 is 1.
Hence,

\frac{25}{36}

is the simplest form.

(iv) Here, numerator = 8 and denominator = 15
Factors of 8 are 1, 2, 4 and 8.
Factors of 15 are 1, 3, 5 and 15.

Common factor of 8 and 15 is 1.
Thus, H.C.F. of 8 and 15 is 1.
Hence,

\frac{8}{15}

is the simplest form.
(v) Here, numerator = 21 and denominator = 10
Factors of 21 are 1, 3, 7 and 21.
Factors of 10 are 1, 2, 5 and 10.

Common factor of 21 and 10 is 1.
Thus, H.C.F. of 21 and 10 is 1.
Hence,

\frac{21}{10}

is the simplest form.

Answer:

(i) 28 $(\frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28})$
(ii) 21 $(\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35})$
(iii) 32 $(\frac{5}{8} = \frac{5 \times 4}{8 \times 4} = \frac{20}{32})$
(iv) 12 $(\frac{45}{60} = \frac{45 \div 5}{60 \div 5} = \frac{9}{12})$
(v) 5 $(\frac{40}{56} = \frac{40 \div 8}{56 \div 8} = \frac{5}{7})$
(vi) 9 $(\frac{42}{54} = \frac{42 \div 6}{54 \div 6} = \frac{7}{9})$

Question 1:

(i) 28 $(\frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28})$
(ii) 21 $(\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35})$
(iii) 32 $(\frac{5}{8} = \frac{5 \times 4}{8 \times 4} = \frac{20}{32})$
(iv) 12 $(\frac{45}{60} = \frac{45 \div 5}{60 \div 5} = \frac{9}{12})$
(v) 5 $(\frac{40}{56} = \frac{40 \div 8}{56 \div 8} = \frac{5}{7})$
(vi) 9 $(\frac{42}{54} = \frac{42 \div 6}{54 \div 6} = \frac{7}{9})$

Answer:

Like fractions:
Fractions having the same denominator are called like fractions.
Examples: $\frac{3}{11}, \frac{5}{11}, \frac{7}{11}, \frac{9}{11}, \frac{10}{11}$

Unlike fractions:
Fractions having different denominators are called unlike fractions.
Examples: $\frac{3}{4}, \frac{4}{5}, \frac{6}{7}, \frac{9}{11}, \frac{2}{13}$

Question 2:

Like fractions:
Fractions having the same denominator are called like fractions.
Examples: $\frac{3}{11}, \frac{5}{11}, \frac{7}{11}, \frac{9}{11}, \frac{10}{11}$

Unlike fractions:
Fractions having different denominators are called unlike fractions.
Examples: $\frac{3}{4}, \frac{4}{5}, \frac{6}{7}, \frac{9}{11}, \frac{2}{13}$

Answer:

The given fractions are $\frac{3}{5}, \frac{7}{10}, \frac{8}{15} and \frac{11}{30} .$

L.C.M. of 5, 10, 15 and 30 = (5 $\times$ 2 $\times$ 3) = 30
So, we convert the given fractions into equivalent fractions with 30 as the denominator.
(But, one of the fractions already has 30 as its denominator. So, there is no need to convert it into an equivalent fraction.)
Thus, we have:
$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}; \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}; \frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30}$

Hence, the required like fractions are $\frac{18}{30}, \frac{21}{30}, \frac{16}{30} and \frac{11}{30} .$

Question 3:

The given fractions are $\frac{3}{5}, \frac{7}{10}, \frac{8}{15} and \frac{11}{30} .$

L.C.M. of 5, 10, 15 and 30 = (5 $\times$ 2 $\times$ 3) = 30
So, we convert the given fractions into equivalent fractions with 30 as the denominator.
(But, one of the fractions already has 30 as its denominator. So, there is no need to convert it into an equivalent fraction.)
Thus, we have:
$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}; \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}; \frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30}$

Hence, the required like fractions are $\frac{18}{30}, \frac{21}{30}, \frac{16}{30} and \frac{11}{30} .$

Answer:

The given fractions are $\frac{1}{4}, \frac{5}{8}, \frac{7}{12} and \frac{13}{24} .$
L.C.M. of 4, 8, 12 and 24 = (4 $\times$ 2 $\times$ 3) = 24
So, we convert the given fractions into equivalent fractions with 24 as the denominator.
(But one of the fractions already has 24 as the denominator. So, there is no need to convert it into an equivalent fraction.)
Thus, we have:
$\frac{1}{4} = \frac{1 \times 6}{4 \times 6} = \frac{6}{24}; \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}; \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}$

Hence, the required like fractions are $\frac{6}{24}, \frac{15}{24}, \frac{14}{24} and \frac{13}{24} .$

Question 4:

The given fractions are $\frac{1}{4}, \frac{5}{8}, \frac{7}{12} and \frac{13}{24} .$
L.C.M. of 4, 8, 12 and 24 = (4 $\times$ 2 $\times$ 3) = 24
So, we convert the given fractions into equivalent fractions with 24 as the denominator.
(But one of the fractions already has 24 as the denominator. So, there is no need to convert it into an equivalent fraction.)
Thus, we have:
$\frac{1}{4} = \frac{1 \times 6}{4 \times 6} = \frac{6}{24}; \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}; \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}$

Hence, the required like fractions are $\frac{6}{24}, \frac{15}{24}, \frac{14}{24} and \frac{13}{24} .$

Answer:

Between two fractions with the same denominator, the one with the greater numerator is the greater of the two.

(i) >
(ii) >
(iii) <
(iv) >
(v) >
(vi) <

Question 5:

Between two fractions with the same denominator, the one with the greater numerator is the greater of the two.

(i) >
(ii) >
(iii) <
(iv) >
(v) >
(vi) <

Answer:

Between two fractions with the same numerator, the one with the smaller denominator is the greater of the two.

(i) >
(ii) >
(iii)<
(iv) >
(v) <
(vi) >

Question 6:

Between two fractions with the same numerator, the one with the smaller denominator is the greater of the two.

(i) >
(ii) >
(iii)<
(iv) >
(v) <
(vi) >

Answer:

$\frac{4}{5}, \frac{5}{7}$
By cross multiplying:
5 $\times$ 5 = 25 and 4 $\times$ 7 = 28
Clearly, 28 > 25
$∴$ $\frac{4}{5} > \frac{5}{7}$

Question 7:

$\frac{4}{5}, \frac{5}{7}$
By cross multiplying:
5 $\times$ 5 = 25 and 4 $\times$ 7 = 28
Clearly, 28 > 25
$∴$ $\frac{4}{5} > \frac{5}{7}$

Answer:

$\frac{3}{8}, \frac{5}{6}$
By cross multiplying:
3 $\times$ 6 = 18 and 5 $\times$ 8 = 40
Clearly, 18 < 40
$∴$ $\frac{3}{8} < \frac{5}{6}$

Question 8:

$\frac{3}{8}, \frac{5}{6}$
By cross multiplying:
3 $\times$ 6 = 18 and 5 $\times$ 8 = 40
Clearly, 18 < 40
$∴$ $\frac{3}{8} < \frac{5}{6}$

Answer:

$\frac{7}{11}, \frac{6}{7}$

By cross multiplying:
7 $\times$ 7 = 49 and 11 $\times$ 6 = 66
Clearly, 49 < 66
$∴$ $\frac{7}{11} < \frac{6}{7}$

Question 9:

$\frac{7}{11}, \frac{6}{7}$

By cross multiplying:
7 $\times$ 7 = 49 and 11 $\times$ 6 = 66
Clearly, 49 < 66
$∴$ $\frac{7}{11} < \frac{6}{7}$

Answer:

$\frac{7}{11}, \frac{6}{7}$
By cross multiplying:
5 $\times$ 11 = 55 and 9 $\times$ 6 = 54
Clearly, 55 > 54
$∴$ $\frac{5}{6} > \frac{9}{11}$

Question 10:

$\frac{7}{11}, \frac{6}{7}$
By cross multiplying:
5 $\times$ 11 = 55 and 9 $\times$ 6 = 54
Clearly, 55 > 54
$∴$ $\frac{5}{6} > \frac{9}{11}$

Answer:

$\frac{7}{11}, \frac{6}{7}$
By cross multiplying:
2 $\times$ 9 = 18 and 4 $\times$ 3 = 12
Clearly, 18 > 12
$∴$ $\frac{2}{3} > \frac{4}{9}$

Question 11:

$\frac{7}{11}, \frac{6}{7}$
By cross multiplying:
2 $\times$ 9 = 18 and 4 $\times$ 3 = 12
Clearly, 18 > 12
$∴$ $\frac{2}{3} > \frac{4}{9}$

Answer:

$\frac{6}{13}, \frac{3}{4}$
By cross multiplying:
6 $\times$ 4 = 24 and 13 $\times$ 3 = 39
Clearly, 24 < 39
$∴$ $\frac{6}{13} < \frac{3}{4}$

Question 12:

$\frac{6}{13}, \frac{3}{4}$
By cross multiplying:
6 $\times$ 4 = 24 and 13 $\times$ 3 = 39
Clearly, 24 < 39
$∴$ $\frac{6}{13} < \frac{3}{4}$

Answer:

$\frac{6}{13}, \frac{3}{4}$
By cross multiplying:
3 $\times$ 6 = 18 and 4 $\times$ 5 = 20
Clearly, 18 < 20
$∴$ $\frac{3}{4} < \frac{5}{6}$

Question 13:

$\frac{6}{13}, \frac{3}{4}$
By cross multiplying:
3 $\times$ 6 = 18 and 4 $\times$ 5 = 20
Clearly, 18 < 20
$∴$ $\frac{3}{4} < \frac{5}{6}$

Answer:

$\frac{5}{8}, \frac{7}{12}$
By cross multiplying:
5 $\times$ 12 = 60 and 8 $\times$ 7 = 56
Clearly, 60 > 56
$∴$ $\frac{5}{8} > \frac{7}{12}$

Question 14:

$\frac{5}{8}, \frac{7}{12}$
By cross multiplying:
5 $\times$ 12 = 60 and 8 $\times$ 7 = 56
Clearly, 60 > 56
$∴$ $\frac{5}{8} > \frac{7}{12}$

Answer:

L.C.M. of 9 and 6 = (3 $\times$ 3 $\times$ 2) = 18
Now, we convert $\frac{4}{9} and \frac{5}{6}$ into equivalent fractions having 18 as the denominator.
∴â€‹ $\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} and \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}$ 4949

Clearly, $\frac{8}{18} < \frac{15}{18}$
$∴$ $\frac{4}{9} < \frac{5}{6}$

Question 15:

L.C.M. of 9 and 6 = (3 $\times$ 3 $\times$ 2) = 18
Now, we convert $\frac{4}{9} and \frac{5}{6}$ into equivalent fractions having 18 as the denominator.
∴â€‹ $\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} and \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}$ 4949

Clearly, $\frac{8}{18} < \frac{15}{18}$
$∴$ $\frac{4}{9} < \frac{5}{6}$

Answer:

L.C.M. of 5 and 10 = (5 $\times$ 2) = 10
Now, we convert $\frac{4}{5}$ into an equivalent fraction having 10 as the denominator as the other fraction has already 10 as its denominator.
∴â€‹ $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$ 4949

Clearly, $\frac{8}{10} > \frac{7}{10}$
$∴$ $\frac{4}{5} > \frac{7}{10}$

Question 16:

L.C.M. of 5 and 10 = (5 $\times$ 2) = 10
Now, we convert $\frac{4}{5}$ into an equivalent fraction having 10 as the denominator as the other fraction has already 10 as its denominator.
∴â€‹ $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$ 4949

Clearly, $\frac{8}{10} > \frac{7}{10}$
$∴$ $\frac{4}{5} > \frac{7}{10}$

Answer:

L.C.M. of 8 and 10 = (2 $\times$ 5 $\times$ 2 $\times$ 2) = 40
Now, we convert $\frac{7}{8} and \frac{9}{10}$ into equivalent fractions having 40 as the denominator.
∴â€‹ $\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40} and \frac{9}{10} = \frac{9 \times 4}{10 \times 4} = \frac{36}{40}$ 4949

Clearly, $\frac{35}{40} < \frac{36}{40}$
$∴$ $\frac{7}{8} < \frac{9}{10}$

Question 17:

L.C.M. of 8 and 10 = (2 $\times$ 5 $\times$ 2 $\times$ 2) = 40
Now, we convert $\frac{7}{8} and \frac{9}{10}$ into equivalent fractions having 40 as the denominator.
∴â€‹ $\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40} and \frac{9}{10} = \frac{9 \times 4}{10 \times 4} = \frac{36}{40}$ 4949

Clearly, $\frac{35}{40} < \frac{36}{40}$
$∴$ $\frac{7}{8} < \frac{9}{10}$

Answer:

L.C.M. of 12 and 15 = (2 $\times$ 2 $\times$ 3 $\times$ 5) = 60
Now, we convert $\frac{11}{12} and \frac{13}{15}$ into equivalent fractions having 60 as the denominator.
∴â€‹ $\frac{11}{12} = \frac{11 \times 5}{12 \times 5} = \frac{55}{60} and \frac{13}{15} = \frac{13 \times 4}{15 \times 4} = \frac{52}{60}$ 4949

Clearly, $\frac{55}{60} > \frac{52}{60}$
$∴$ $\frac{11}{12} > \frac{13}{15}$

Question 18:

L.C.M. of 12 and 15 = (2 $\times$ 2 $\times$ 3 $\times$ 5) = 60
Now, we convert $\frac{11}{12} and \frac{13}{15}$ into equivalent fractions having 60 as the denominator.
∴â€‹ $\frac{11}{12} = \frac{11 \times 5}{12 \times 5} = \frac{55}{60} and \frac{13}{15} = \frac{13 \times 4}{15 \times 4} = \frac{52}{60}$ 4949

Clearly, $\frac{55}{60} > \frac{52}{60}$
$∴$ $\frac{11}{12} > \frac{13}{15}$

Answer:

The given fractions are $\frac{1}{2}, \frac{3}{4}, \frac{5}{6} and \frac{7}{8}$ .
L.C.M. of 2, 4, 6 and 8 = (2 $\times$ 2 $\times$ 2 $\times$ 3) = 24
We convert each of the given fractions into an equivalent fraction with denominator 24.
Now, we have:
$\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}; \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}; \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}$

Clearly, $\frac{12}{24} < \frac{18}{24} < \frac{20}{24} < \frac{21}{24}$

∴ â€‹ $\frac{1}{2} < \frac{3}{4} < \frac{5}{6} < \frac{7}{8}$
Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{8}$ â€‹

Question 19:

The given fractions are $\frac{1}{2}, \frac{3}{4}, \frac{5}{6} and \frac{7}{8}$ .
L.C.M. of 2, 4, 6 and 8 = (2 $\times$ 2 $\times$ 2 $\times$ 3) = 24
We convert each of the given fractions into an equivalent fraction with denominator 24.
Now, we have:
$\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}; \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}; \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}$

Clearly, $\frac{12}{24} < \frac{18}{24} < \frac{20}{24} < \frac{21}{24}$

∴ â€‹ $\frac{1}{2} < \frac{3}{4} < \frac{5}{6} < \frac{7}{8}$
Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{8}$ â€‹

Answer:

The given fractions are $\frac{2}{3}, \frac{5}{6}, \frac{7}{9} and \frac{11}{18} .$

L.C.M. of 3, 6, 9 and 18 = (3 $\times$ 2 $\times$ 3) = 18
So, we convert each of the fractions whose denominator is not equal to 18 into an equivalent fraction with denominator 18.
Now, we have:
$\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}; \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}; \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}$
Clearly, $\frac{11}{18} < \frac{12}{18} < \frac{14}{18} < \frac{15}{18}$
∴ â€‹ $\frac{11}{18} < \frac{2}{3} < \frac{7}{9} < \frac{5}{6}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{11}{18}, \frac{2}{3}, \frac{7}{9}, \frac{5}{6}$

Question 20:

The given fractions are $\frac{2}{3}, \frac{5}{6}, \frac{7}{9} and \frac{11}{18} .$

L.C.M. of 3, 6, 9 and 18 = (3 $\times$ 2 $\times$ 3) = 18
So, we convert each of the fractions whose denominator is not equal to 18 into an equivalent fraction with denominator 18.
Now, we have:
$\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}; \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}; \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}$
Clearly, $\frac{11}{18} < \frac{12}{18} < \frac{14}{18} < \frac{15}{18}$
∴ â€‹ $\frac{11}{18} < \frac{2}{3} < \frac{7}{9} < \frac{5}{6}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{11}{18}, \frac{2}{3}, \frac{7}{9}, \frac{5}{6}$

Answer:

The given fractions are $\frac{2}{5}, \frac{7}{10}, \frac{11}{15} and \frac{17}{30} .$
L.C.M. of 5, 10, 15 and 30 = (2 $\times$ 5 $\times$ 3) = 30

So, we convert each of the fractions whose denominator is not equal to 30 into an equivalent fraction with denominator 30.
Now, we have:
$\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}; \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}; \frac{11}{15} = \frac{11 \times 2}{15 \times 2} = \frac{22}{30}$
Clearly, $\frac{12}{30} < \frac{17}{30} < \frac{21}{30} < \frac{22}{30}$
∴ â€‹ $\frac{2}{5} < \frac{17}{30} < \frac{7}{10} < \frac{11}{15}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{2}{5}, \frac{17}{30}, \frac{7}{10}, \frac{11}{15}$

Question 21:

The given fractions are $\frac{2}{5}, \frac{7}{10}, \frac{11}{15} and \frac{17}{30} .$
L.C.M. of 5, 10, 15 and 30 = (2 $\times$ 5 $\times$ 3) = 30

So, we convert each of the fractions whose denominator is not equal to 30 into an equivalent fraction with denominator 30.
Now, we have:
$\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}; \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}; \frac{11}{15} = \frac{11 \times 2}{15 \times 2} = \frac{22}{30}$
Clearly, $\frac{12}{30} < \frac{17}{30} < \frac{21}{30} < \frac{22}{30}$
∴ â€‹ $\frac{2}{5} < \frac{17}{30} < \frac{7}{10} < \frac{11}{15}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{2}{5}, \frac{17}{30}, \frac{7}{10}, \frac{11}{15}$

Answer:

The given fractions are $\frac{3}{4}, \frac{7}{8}, \frac{11}{16} and \frac{23}{32} .$
L.C.M. of 4, 8, 16 and 32 = (2 â¨¯ 2 â¨¯ 2 â¨¯ 2 â¨¯ 2) = 32

So, we convert each of the fractions whose denominator is not equal to 32 into an equivalent fraction with denominator 32.
Now, we have:
$\frac{3}{4} = \frac{3 \times 8}{4 \times 8} = \frac{24}{32}; \frac{7}{8} = \frac{7 \times 4}{8 \times 4} = \frac{28}{32}; \frac{11}{16} = \frac{11 \times 2}{16 \times 2} = \frac{22}{32}$
Clearly, $\frac{22}{32} < \frac{23}{32} < \frac{24}{32} < \frac{28}{32}$
∴ â€‹ $\frac{11}{16} < \frac{23}{32} < \frac{3}{4} < \frac{7}{8}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{11}{16}, \frac{23}{32}, \frac{3}{4}, \frac{7}{8}$

Question 22:

The given fractions are $\frac{3}{4}, \frac{7}{8}, \frac{11}{16} and \frac{23}{32} .$
L.C.M. of 4, 8, 16 and 32 = (2 â¨¯ 2 â¨¯ 2 â¨¯ 2 â¨¯ 2) = 32

So, we convert each of the fractions whose denominator is not equal to 32 into an equivalent fraction with denominator 32.
Now, we have:
$\frac{3}{4} = \frac{3 \times 8}{4 \times 8} = \frac{24}{32}; \frac{7}{8} = \frac{7 \times 4}{8 \times 4} = \frac{28}{32}; \frac{11}{16} = \frac{11 \times 2}{16 \times 2} = \frac{22}{32}$
Clearly, $\frac{22}{32} < \frac{23}{32} < \frac{24}{32} < \frac{28}{32}$
∴ â€‹ $\frac{11}{16} < \frac{23}{32} < \frac{3}{4} < \frac{7}{8}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{11}{16}, \frac{23}{32}, \frac{3}{4}, \frac{7}{8}$

Answer:

The given fractions are $\frac{3}{4}, \frac{5}{8}, \frac{11}{12} and \frac{17}{24} .$
L.C.M. of 4, 8, 12 and 24 = (2 â¨¯ 2 â¨¯ 2 â¨¯ 3) = 24

So, we convert each of the fractions whose denominator is not equal to 24 into an equivalent fraction with denominator 24.
Thus, we have;
$\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}; \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}; \frac{11}{12} = \frac{11 \times 2}{12 \times 2} = \frac{22}{24}$
Clearly, $\frac{22}{24} > \frac{18}{24} > \frac{17}{24} > \frac{15}{24}$

∴ â€‹ $\frac{11}{12} > \frac{3}{4} > \frac{17}{24} > \frac{5}{8}$

Hence, the given fractions can be arranged in the descending order as follows:
$\frac{11}{12}, \frac{3}{4}, \frac{17}{24}, \frac{5}{8}$

Question 23:

The given fractions are $\frac{3}{4}, \frac{5}{8}, \frac{11}{12} and \frac{17}{24} .$
L.C.M. of 4, 8, 12 and 24 = (2 â¨¯ 2 â¨¯ 2 â¨¯ 3) = 24

So, we convert each of the fractions whose denominator is not equal to 24 into an equivalent fraction with denominator 24.
Thus, we have;
$\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}; \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}; \frac{11}{12} = \frac{11 \times 2}{12 \times 2} = \frac{22}{24}$
Clearly, $\frac{22}{24} > \frac{18}{24} > \frac{17}{24} > \frac{15}{24}$

∴ â€‹ $\frac{11}{12} > \frac{3}{4} > \frac{17}{24} > \frac{5}{8}$

Hence, the given fractions can be arranged in the descending order as follows:
$\frac{11}{12}, \frac{3}{4}, \frac{17}{24}, \frac{5}{8}$

Answer:

The given fractions are $\frac{7}{9}, \frac{5}{12}, \frac{11}{18} and \frac{17}{36} .$
L.C.M. of 9, 12, 18 and 36 = (3 â¨¯ 3 â¨¯ 2 â¨¯ 2) = 36

We convert each of the fractions whose denominator is not equal to 36 into an equivalent fraction with denominator 36.
Thus, we have:
$\frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36}; \frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}; \frac{11}{18} = \frac{11 \times 2}{18 \times 2} = \frac{22}{36}$
Clearly, $\frac{28}{36} > \frac{22}{36} > \frac{17}{36} > \frac{15}{36}$

∴ â€‹ $\frac{7}{9} > \frac{11}{18} > \frac{17}{36} > \frac{5}{12}$

Hence, the given fractions can be arranged in the descending order as follows:
$\frac{7}{9}, \frac{11}{18}, \frac{17}{36}, \frac{5}{12}$

Question 24:

The given fractions are $\frac{7}{9}, \frac{5}{12}, \frac{11}{18} and \frac{17}{36} .$
L.C.M. of 9, 12, 18 and 36 = (3 â¨¯ 3 â¨¯ 2 â¨¯ 2) = 36

We convert each of the fractions whose denominator is not equal to 36 into an equivalent fraction with denominator 36.
Thus, we have:
$\frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36}; \frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}; \frac{11}{18} = \frac{11 \times 2}{18 \times 2} = \frac{22}{36}$
Clearly, $\frac{28}{36} > \frac{22}{36} > \frac{17}{36} > \frac{15}{36}$

∴ â€‹ $\frac{7}{9} > \frac{11}{18} > \frac{17}{36} > \frac{5}{12}$

Hence, the given fractions can be arranged in the descending order as follows:
$\frac{7}{9}, \frac{11}{18}, \frac{17}{36}, \frac{5}{12}$

Answer:

The given fractions are $\frac{2}{3}, \frac{3}{5}, \frac{7}{10} and \frac{8}{15} .$
L.C.M. of 3, 5,10 and 15 = (2 â¨¯ 3 â¨¯ 5) = 30

So, we convert each of the fractions into an equivalent fraction with denominator 30.
Thus, we have:
$\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}; \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}; \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}; \frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30}$
Clearly, $\frac{21}{30} > \frac{20}{30} > \frac{18}{30} > \frac{16}{30}$
∴ â€‹ $\frac{7}{10} > \frac{2}{3} > \frac{3}{5} > \frac{8}{15}$

Hence, the given fractions can be arranged in the descending order as follows:
$\frac{7}{10}, \frac{2}{3}, \frac{3}{5}, \frac{8}{15}$

Question 25:

The given fractions are $\frac{2}{3}, \frac{3}{5}, \frac{7}{10} and \frac{8}{15} .$
L.C.M. of 3, 5,10 and 15 = (2 â¨¯ 3 â¨¯ 5) = 30

So, we convert each of the fractions into an equivalent fraction with denominator 30.
Thus, we have:
$\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}; \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}; \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}; \frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30}$
Clearly, $\frac{21}{30} > \frac{20}{30} > \frac{18}{30} > \frac{16}{30}$
∴ â€‹ $\frac{7}{10} > \frac{2}{3} > \frac{3}{5} > \frac{8}{15}$

Hence, the given fractions can be arranged in the descending order as follows:
$\frac{7}{10}, \frac{2}{3}, \frac{3}{5}, \frac{8}{15}$

Answer:

The given fractions are $\frac{5}{7}, \frac{9}{14}, \frac{17}{21} and \frac{31}{42} .$
L.C.M. of 7, 14, 21 and 42 = (2 â¨¯ 3 â¨¯ 7) = 42

We convert each one of the fractions whose denominator is not equal to 42 into an equivalent fraction with denominator 42.
Thus, we have:
$\frac{5}{7} = \frac{5 \times 6}{7 \times 6} = \frac{30}{42}; \frac{9}{14} = \frac{9 \times 3}{14 \times 3} = \frac{27}{42}; \frac{17}{21} = \frac{17 \times 2}{21 \times 2} = \frac{34}{42}$
Clearly, $\frac{34}{42} > \frac{31}{42} > \frac{30}{42} > \frac{27}{42}$
∴ â€‹ $\frac{17}{21} > \frac{31}{42} > \frac{5}{7} > \frac{9}{14}$
Hence, the given fractions can be arranged in the descending order as follows:
$\frac{17}{21}, \frac{31}{42}, \frac{5}{7}, \frac{9}{14}$

Question 26:

The given fractions are $\frac{5}{7}, \frac{9}{14}, \frac{17}{21} and \frac{31}{42} .$
L.C.M. of 7, 14, 21 and 42 = (2 â¨¯ 3 â¨¯ 7) = 42

We convert each one of the fractions whose denominator is not equal to 42 into an equivalent fraction with denominator 42.
Thus, we have:
$\frac{5}{7} = \frac{5 \times 6}{7 \times 6} = \frac{30}{42}; \frac{9}{14} = \frac{9 \times 3}{14 \times 3} = \frac{27}{42}; \frac{17}{21} = \frac{17 \times 2}{21 \times 2} = \frac{34}{42}$
Clearly, $\frac{34}{42} > \frac{31}{42} > \frac{30}{42} > \frac{27}{42}$
∴ â€‹ $\frac{17}{21} > \frac{31}{42} > \frac{5}{7} > \frac{9}{14}$
Hence, the given fractions can be arranged in the descending order as follows:
$\frac{17}{21}, \frac{31}{42}, \frac{5}{7}, \frac{9}{14}$

Answer:

The given fractions are $\frac{1}{12}, \frac{1}{23}, \frac{1}{7}, \frac{1}{9}, \frac{1}{17} and \frac{1}{50} .$
As the fractions have the same numerator, we can follow the rule for the comparison of such fractions.
This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.
Clearly, $\frac{1}{7} > \frac{1}{9} > \frac{1}{12} > \frac{1}{17} > \frac{1}{23} > \frac{1}{50}$
Hence, the given fractions can be arranged in the descending order as follows:
$\frac{1}{7}, \frac{1}{9}, \frac{1}{12}, \frac{1}{17}, \frac{1}{23}, \frac{1}{50}$

Question 27:

The given fractions are $\frac{1}{12}, \frac{1}{23}, \frac{1}{7}, \frac{1}{9}, \frac{1}{17} and \frac{1}{50} .$
As the fractions have the same numerator, we can follow the rule for the comparison of such fractions.
This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.
Clearly, $\frac{1}{7} > \frac{1}{9} > \frac{1}{12} > \frac{1}{17} > \frac{1}{23} > \frac{1}{50}$
Hence, the given fractions can be arranged in the descending order as follows:
$\frac{1}{7}, \frac{1}{9}, \frac{1}{12}, \frac{1}{17}, \frac{1}{23}, \frac{1}{50}$

Answer:

The given fractions are $\frac{3}{7}, \frac{3}{11}, \frac{3}{5}, \frac{3}{13}, \frac{3}{4} and \frac{3}{17} .$
As the fractions have the same numerator, so we can follow the rule for the comparison of such fractions.
This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.

Clearly, $\frac{3}{4} > \frac{3}{5} > \frac{3}{7} > \frac{3}{11} > \frac{3}{13} > \frac{3}{17}$
Hence, the given fractions can be arranged in the descending order as follows:
$\frac{3}{4}, \frac{3}{5}, \frac{3}{7}, \frac{3}{11}, \frac{3}{13}, \frac{3}{17}$

Question 28:

The given fractions are $\frac{3}{7}, \frac{3}{11}, \frac{3}{5}, \frac{3}{13}, \frac{3}{4} and \frac{3}{17} .$
As the fractions have the same numerator, so we can follow the rule for the comparison of such fractions.
This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.

Clearly, $\frac{3}{4} > \frac{3}{5} > \frac{3}{7} > \frac{3}{11} > \frac{3}{13} > \frac{3}{17}$
Hence, the given fractions can be arranged in the descending order as follows:
$\frac{3}{4}, \frac{3}{5}, \frac{3}{7}, \frac{3}{11}, \frac{3}{13}, \frac{3}{17}$

Answer:

Lalita read 30 pages of a book having 100 pages.
Sarita read $\frac{2}{5}$ of the same book.
$\frac{2}{5}$ of 100 pages = â€‹ $\frac{2}{5} \times 100 = \frac{200}{5} = 40 pages$
Hence, Sarita read more pages than Lalita as 40 is greater than 30.

Question 29:

Lalita read 30 pages of a book having 100 pages.
Sarita read $\frac{2}{5}$ of the same book.
$\frac{2}{5}$ of 100 pages = â€‹ $\frac{2}{5} \times 100 = \frac{200}{5} = 40 pages$
Hence, Sarita read more pages than Lalita as 40 is greater than 30.

Answer:

To know who exercised for a longer time, we have to compare $\frac{2}{3} hour with \frac{3}{4} hour$ .
On cross multiplying:
4 $\times$ 2 = 8 and 3 $\times$ 3 = 9
Clearly, 8 < 9
$∴$ $\frac{2}{3} hour < \frac{3}{4} hour$
Hence, Rohit exercised for a longer time.

Question 30:

To know who exercised for a longer time, we have to compare $\frac{2}{3} hour with \frac{3}{4} hour$ .
On cross multiplying:
4 $\times$ 2 = 8 and 3 $\times$ 3 = 9
Clearly, 8 < 9
$∴$ $\frac{2}{3} hour < \frac{3}{4} hour$
Hence, Rohit exercised for a longer time.

Answer:

Fraction of students who passed in VI A = $\frac{20}{25} = \frac{20 \div 5}{25 \div 5} = \frac{4}{5}$

Fraction of students who passed in VI B = $\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}$
In both the sections, the fraction of students who passed is the same, so both the sections have the same result.

Question 1:

Fraction of students who passed in VI A = $\frac{20}{25} = \frac{20 \div 5}{25 \div 5} = \frac{4}{5}$

Fraction of students who passed in VI B = $\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}$
In both the sections, the fraction of students who passed is the same, so both the sections have the same result.

Answer:

The given fractions are like fractions.
We know:
Sum of like fractions = $\frac{Sum of the numerators}{C ommon d enominator}$
Thus, we have:
$\frac{5}{8} + \frac{1}{8} = \frac{(5 + 1)}{8} = \frac{6^{3}}{8_{4}} = \frac{3}{4}$

Question 2:

The given fractions are like fractions.
We know:
Sum of like fractions = $\frac{Sum of the numerators}{C ommon d enominator}$
Thus, we have:
$\frac{5}{8} + \frac{1}{8} = \frac{(5 + 1)}{8} = \frac{6^{3}}{8_{4}} = \frac{3}{4}$

Answer:

The given fractions are like fractions.
We know:
Sum of like fractions = $\frac{Sum of the numeratos}{Common d enominator}$
Thus, we have:
$\frac{4}{9} + \frac{8}{9} = \frac{(4 + 8)}{9} = \frac{12^{4}}{9_{3}} = \frac{4}{3} = 1 \frac{1}{3}$

Question 3:

The given fractions are like fractions.
We know:
Sum of like fractions = $\frac{Sum of the numeratos}{Common d enominator}$
Thus, we have:
$\frac{4}{9} + \frac{8}{9} = \frac{(4 + 8)}{9} = \frac{12^{4}}{9_{3}} = \frac{4}{3} = 1 \frac{1}{3}$

Answer:

The given fractions are like fractions.
We know:
Sum of like fractions = $\frac{Sum of the numerators}{Common d enominator}$
Thus, we have:
$1 \frac{3}{5} + 2 \frac{4}{5} = \frac{8}{5} + \frac{14}{5} = \frac{(8 + 14)}{5} = \frac{22}{5} = 4 \frac{2}{5}$

Question 4:

The given fractions are like fractions.
We know:
Sum of like fractions = $\frac{Sum of the numerators}{Common d enominator}$
Thus, we have:
$1 \frac{3}{5} + 2 \frac{4}{5} = \frac{8}{5} + \frac{14}{5} = \frac{(8 + 14)}{5} = \frac{22}{5} = 4 \frac{2}{5}$

Answer:

L.C.M. of 9 and 6 = (2 $\times$ 3 $\times$ 3) = 18

Now, we have:

$\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}; \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} ∴ \frac{2}{9} + \frac{5}{6} = \frac{4}{18} + \frac{15}{18} = \frac{(4 + 15)}{18} = \frac{19}{18} = 1 \frac{1}{18}$

Question 5:

L.C.M. of 9 and 6 = (2 $\times$ 3 $\times$ 3) = 18

Now, we have:

$\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}; \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} ∴ \frac{2}{9} + \frac{5}{6} = \frac{4}{18} + \frac{15}{18} = \frac{(4 + 15)}{18} = \frac{19}{18} = 1 \frac{1}{18}$

Answer:

L.C.M. of 12 and 16 = (2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3) = 48

Now, we have:

$\frac{7}{12} = \frac{7 \times 4}{12 \times 4} = \frac{28}{48}; \frac{9}{16} = \frac{9 \times 3}{16 \times 3} = \frac{27}{48} ∴ \frac{7}{12} + \frac{9}{16} = \frac{28}{48} + \frac{27}{48} = \frac{(28 + 27)}{48} = \frac{55}{48} = 1 \frac{7}{48}$

Question 6:

L.C.M. of 12 and 16 = (2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3) = 48

Now, we have:

$\frac{7}{12} = \frac{7 \times 4}{12 \times 4} = \frac{28}{48}; \frac{9}{16} = \frac{9 \times 3}{16 \times 3} = \frac{27}{48} ∴ \frac{7}{12} + \frac{9}{16} = \frac{28}{48} + \frac{27}{48} = \frac{(28 + 27)}{48} = \frac{55}{48} = 1 \frac{7}{48}$

Answer:

L.C.M. of 15 and 20 = (3 $\times$ 5 $\times$ 2 $\times$ 2) = 60

$∴ \frac{4}{15} + \frac{17}{20} = \frac{(16 + 51)}{60} \{[60 \div 15 = 4, 4 \times 4 = 16] and [60 \div 20 = 3, 17 \times 3 = 51]\} = \frac{67}{60} = 1 \frac{7}{60}$

Question 7:

L.C.M. of 15 and 20 = (3 $\times$ 5 $\times$ 2 $\times$ 2) = 60

$∴ \frac{4}{15} + \frac{17}{20} = \frac{(16 + 51)}{60} \{[60 \div 15 = 4, 4 \times 4 = 16] and [60 \div 20 = 3, 17 \times 3 = 51]\} = \frac{67}{60} = 1 \frac{7}{60}$

Answer:

We have:

$2 \frac{3}{4} + 5 \frac{5}{6} = \frac{11}{4} + \frac{35}{6} L . C . M . of 4 and 6 = (2 \times 2 \times 3) = 12 = \frac{(66 + 140)}{24} \{[24 \div 4 = 6, 6 \times 11 = 66] and [24 \div 6 = 4, 4 \times 35 = 140]\} = \frac{206^{103}}{24_{12}} = \frac{103}{12} = 8 \frac{7}{12}$
234+556

Question 8:

We have:

$2 \frac{3}{4} + 5 \frac{5}{6} = \frac{11}{4} + \frac{35}{6} L . C . M . of 4 and 6 = (2 \times 2 \times 3) = 12 = \frac{(66 + 140)}{24} \{[24 \div 4 = 6, 6 \times 11 = 66] and [24 \div 6 = 4, 4 \times 35 = 140]\} = \frac{206^{103}}{24_{12}} = \frac{103}{12} = 8 \frac{7}{12}$
234+556

Answer:

We have:

$3 \frac{1}{8} + 1 \frac{5}{12} = \frac{25}{8} + \frac{17}{12} L . C . M . of 8 and 12 = (2 \times 2 \times 2 \times 3) = 24 = \frac{(75 + 34)}{24} \{[24 \div 8 = 3, 3 \times 25 = 75] and [24 \div 12 = 2, 2 \times 17 = 34]\} = \frac{109^{}}{24} = 4 \frac{13}{24}$
234+556

Question 9:

We have:

$3 \frac{1}{8} + 1 \frac{5}{12} = \frac{25}{8} + \frac{17}{12} L . C . M . of 8 and 12 = (2 \times 2 \times 2 \times 3) = 24 = \frac{(75 + 34)}{24} \{[24 \div 8 = 3, 3 \times 25 = 75] and [24 \div 12 = 2, 2 \times 17 = 34]\} = \frac{109^{}}{24} = 4 \frac{13}{24}$
234+556

Answer:

We have:

$2 \frac{7}{10} + 3 \frac{8}{15} = \frac{27}{10} + \frac{53}{15} L . C . M . of 10 and 15 = (2 \times 3 \times 5) = 30 = \frac{(81 + 106)}{30} \{[30 \div 10 = 3, 3 \times 27 = 81] and [30 \div 15 = 2, 2 \times 53 = 106]\} = \frac{187^{}}{30} = 6 \frac{7}{30}$
234+556

Question 10:

We have:

$2 \frac{7}{10} + 3 \frac{8}{15} = \frac{27}{10} + \frac{53}{15} L . C . M . of 10 and 15 = (2 \times 3 \times 5) = 30 = \frac{(81 + 106)}{30} \{[30 \div 10 = 3, 3 \times 27 = 81] and [30 \div 15 = 2, 2 \times 53 = 106]\} = \frac{187^{}}{30} = 6 \frac{7}{30}$
234+556

Answer:

We have:

$3 \frac{2}{3} + 1 \frac{5}{6} + 2 = \frac{11}{3} + \frac{11}{6} + \frac{2}{1} L . C . M . of 3 and 6 = (2 \times 3) = 6 = \frac{(22 + 11 + 12)}{6} \{[6 \div 3 = 2, 2 \times 11 = 22], [6 \div 6 = 1, 1 \times 11 = 11] and [6 \div 1 = 6, 6 \times 2 = 12]\} = \frac{45^{15}}{6_{2}} = \frac{15}{2} = 7 \frac{1}{2}$
234+556

Question 11:

We have:

$3 \frac{2}{3} + 1 \frac{5}{6} + 2 = \frac{11}{3} + \frac{11}{6} + \frac{2}{1} L . C . M . of 3 and 6 = (2 \times 3) = 6 = \frac{(22 + 11 + 12)}{6} \{[6 \div 3 = 2, 2 \times 11 = 22], [6 \div 6 = 1, 1 \times 11 = 11] and [6 \div 1 = 6, 6 \times 2 = 12]\} = \frac{45^{15}}{6_{2}} = \frac{15}{2} = 7 \frac{1}{2}$
234+556

Answer:

We have:

$3 + 1 \frac{4}{15} + 1 \frac{3}{20} = \frac{3}{1} + \frac{19}{15} + \frac{23}{20} L . C . M . of 15 and 20 = (2 \times 2 \times 3 \times 5) = 60 = \frac{(180 + 76 + 69)}{60} \{[60 \div 1 = 60, 60 \times 3 = 180], [60 \div 15 = 4, 4 \times 19 = 76] and [60 \div 20 = 3, 3 \times 23 = 69]\} = \frac{325^{65}}{60_{12}} = \frac{65}{12} = 5 \frac{5}{12}$
234+556

Question 12:

We have:

$3 + 1 \frac{4}{15} + 1 \frac{3}{20} = \frac{3}{1} + \frac{19}{15} + \frac{23}{20} L . C . M . of 15 and 20 = (2 \times 2 \times 3 \times 5) = 60 = \frac{(180 + 76 + 69)}{60} \{[60 \div 1 = 60, 60 \times 3 = 180], [60 \div 15 = 4, 4 \times 19 = 76] and [60 \div 20 = 3, 3 \times 23 = 69]\} = \frac{325^{65}}{60_{12}} = \frac{65}{12} = 5 \frac{5}{12}$
234+556

Answer:

We have:

$3 \frac{1}{3} + 4 \frac{1}{4} + 6 \frac{1}{6} = \frac{10}{3} + \frac{17}{4} + \frac{37}{6} L . C . M . of 3, 4 and 6 = (2 \times 2 \times 3) = 12 = \frac{(40 + 51 + 74)}{12} \{[12 \div 3 = 4, 4 \times 10 = 40], [12 \div 4 = 3, 3 \times 17 = 51] and [12 \div 6 = 2, 2 \times 37 = 74]\} = \frac{165^{55}}{12_{4}} = \frac{55}{4} = 13 \frac{3}{4}$
234+556

Question 13:

We have:

$3 \frac{1}{3} + 4 \frac{1}{4} + 6 \frac{1}{6} = \frac{10}{3} + \frac{17}{4} + \frac{37}{6} L . C . M . of 3, 4 and 6 = (2 \times 2 \times 3) = 12 = \frac{(40 + 51 + 74)}{12} \{[12 \div 3 = 4, 4 \times 10 = 40], [12 \div 4 = 3, 3 \times 17 = 51] and [12 \div 6 = 2, 2 \times 37 = 74]\} = \frac{165^{55}}{12_{4}} = \frac{55}{4} = 13 \frac{3}{4}$
234+556

Answer:

We have:

$\frac{2}{3} + 3 \frac{1}{6} + 4 \frac{2}{9} + 2 \frac{5}{18} = \frac{2}{3} + \frac{19}{6} + \frac{38}{9} + \frac{41}{18} L . C . M . of 3, 6 and 9 = (2 \times 3 \times 3) = 18 = \frac{(12 + 57 + 76 + 41)}{18} \{[18 \div 3 = 6, 6 \times 2 = 12], [18 \div 6 = 3, 3 \times 19 = 57], [18 \div 9 = 2, 2 \times 38 = 76] and [18 \div 18 = 1, 1 \times 41 = 41]\} = \frac{186^{31}}{18_{3}} = \frac{31}{3} = 10 \frac{1}{3}$
234+556

Question 14:

We have:

$\frac{2}{3} + 3 \frac{1}{6} + 4 \frac{2}{9} + 2 \frac{5}{18} = \frac{2}{3} + \frac{19}{6} + \frac{38}{9} + \frac{41}{18} L . C . M . of 3, 6 and 9 = (2 \times 3 \times 3) = 18 = \frac{(12 + 57 + 76 + 41)}{18} \{[18 \div 3 = 6, 6 \times 2 = 12], [18 \div 6 = 3, 3 \times 19 = 57], [18 \div 9 = 2, 2 \times 38 = 76] and [18 \div 18 = 1, 1 \times 41 = 41]\} = \frac{186^{31}}{18_{3}} = \frac{31}{3} = 10 \frac{1}{3}$
234+556

Answer:

We have:

$2 \frac{1}{3} + 1 \frac{1}{4} + 2 \frac{5}{6} + 3 \frac{7}{12} = \frac{7}{3} + \frac{5}{4} + \frac{17}{6} + \frac{43}{12} L . C . M . of 3, 4, 6 and 12 = (2 \times 2 \times 3) = 12 = \frac{(28 + 15 + 34 + 43)}{12} \{[12 \div 3 = 4, 4 \times 7 = 28], [12 \div 4 = 3, 3 \times 5 = 15], [12 \div 6 = 2, 2 \times 17 = 34] and [12 \div 12 = 1, 1 \times 43 = 43]\} = \frac{120^{10}}{12_{1}} = 10$
234+556

Question 15:

We have:

$2 \frac{1}{3} + 1 \frac{1}{4} + 2 \frac{5}{6} + 3 \frac{7}{12} = \frac{7}{3} + \frac{5}{4} + \frac{17}{6} + \frac{43}{12} L . C . M . of 3, 4, 6 and 12 = (2 \times 2 \times 3) = 12 = \frac{(28 + 15 + 34 + 43)}{12} \{[12 \div 3 = 4, 4 \times 7 = 28], [12 \div 4 = 3, 3 \times 5 = 15], [12 \div 6 = 2, 2 \times 17 = 34] and [12 \div 12 = 1, 1 \times 43 = 43]\} = \frac{120^{10}}{12_{1}} = 10$
234+556

Answer:

We have:

$2 + \frac{3}{4} + 1 \frac{5}{8} + 3 \frac{7}{16} = \frac{2}{1} + \frac{3}{4} + \frac{13}{8} + \frac{55}{16} L . C . M . of 4, 8, and 16 = (2 \times 2 \times 2 \times 2) = 16 = \frac{(32 + 12 + 26 + 55)}{16} \{[16 \div 1 = 16, 16 \times 2 = 32], [16 \div 4 = 4, 4 \times 3 = 12], [16 \div 8 = 2, 2 \times 13 = 26] and [16 \div 16 = 1, 1 \times 55 = 55]\} = \frac{125}{16} = 7 \frac{13}{16}$
234+556

Question 16:

We have:

$2 + \frac{3}{4} + 1 \frac{5}{8} + 3 \frac{7}{16} = \frac{2}{1} + \frac{3}{4} + \frac{13}{8} + \frac{55}{16} L . C . M . of 4, 8, and 16 = (2 \times 2 \times 2 \times 2) = 16 = \frac{(32 + 12 + 26 + 55)}{16} \{[16 \div 1 = 16, 16 \times 2 = 32], [16 \div 4 = 4, 4 \times 3 = 12], [16 \div 8 = 2, 2 \times 13 = 26] and [16 \div 16 = 1, 1 \times 55 = 55]\} = \frac{125}{16} = 7 \frac{13}{16}$
234+556

Answer:

Total cost of both articles = Cost of pencil + Cost of eraser
Thus, we have:
$Rs 3 \frac{2}{5} + Rs 2 \frac{7}{10} = \frac{17}{5} + \frac{27}{10} = \frac{(34 + 27)}{10} (L . C . M . of 5 and 10 = (5 \times 2) = 10) = \frac{61}{10} = Rs 6 \frac{1}{10}$
Hence, the total cost of both the articles is $Rs 6 \frac{1}{10}$ .

Question 17:

Total cost of both articles = Cost of pencil + Cost of eraser
Thus, we have:
$Rs 3 \frac{2}{5} + Rs 2 \frac{7}{10} = \frac{17}{5} + \frac{27}{10} = \frac{(34 + 27)}{10} (L . C . M . of 5 and 10 = (5 \times 2) = 10) = \frac{61}{10} = Rs 6 \frac{1}{10}$
Hence, the total cost of both the articles is $Rs 6 \frac{1}{10}$ .

Answer:

Total cloth purchased by Sohini = Cloth for kurta + Cloth for pyjamas
Thus, we have:
$(4 \frac{1}{2} + 2 \frac{2}{3}) m = (\frac{9}{2} + \frac{8}{3}) m (L . C . M . of 2 and 3 = (2 \times 3) = 6) = (\frac{(27 + 16)}{6}) m \{[6 \div 2 = 3, 3 \times 9 = 27] and [6 \div 3 = 2, 2 \times 8 = 16]\} = (\frac{43}{6}) m = 7 \frac{1}{6} m$
$∴$ Total length of cloth purchased = $7 \frac{1}{6} m$

Question 18:

Total cloth purchased by Sohini = Cloth for kurta + Cloth for pyjamas
Thus, we have:
$(4 \frac{1}{2} + 2 \frac{2}{3}) m = (\frac{9}{2} + \frac{8}{3}) m (L . C . M . of 2 and 3 = (2 \times 3) = 6) = (\frac{(27 + 16)}{6}) m \{[6 \div 2 = 3, 3 \times 9 = 27] and [6 \div 3 = 2, 2 \times 8 = 16]\} = (\frac{43}{6}) m = 7 \frac{1}{6} m$
$∴$ Total length of cloth purchased = $7 \frac{1}{6} m$

Answer:

Distance from Kishan's house to school = Distance covered by him by rickshaw + Distance covered by him on foot
Thus, we have:
$(4 \frac{3}{4} + 1 \frac{1}{2}) km = (\frac{19}{4} + \frac{3}{2}) km = (\frac{(19 + 6)}{4}) km (L . C . M . of 2 and 4 = (2 \times 2) = 4) = (\frac{25}{4}) km = 6 \frac{1}{4} km$

Hence, the distance from Kishan's house to school is $6 \frac{1}{4} km$ .

Question 19:

Distance from Kishan's house to school = Distance covered by him by rickshaw + Distance covered by him on foot
Thus, we have:
$(4 \frac{3}{4} + 1 \frac{1}{2}) km = (\frac{19}{4} + \frac{3}{2}) km = (\frac{(19 + 6)}{4}) km (L . C . M . of 2 and 4 = (2 \times 2) = 4) = (\frac{25}{4}) km = 6 \frac{1}{4} km$

Hence, the distance from Kishan's house to school is $6 \frac{1}{4} km$ .

Answer:

Weight of the cylinder filled with gas = Weight of the empty cylinder + Weight of the gas inside the cylinder
Thus, we have:
$(16 \frac{4}{5} + 14 \frac{2}{3}) kg = (\frac{84}{5} + \frac{44}{3}) kg (L . C . M . of 5 and 3 = (3 \times 5) = 15) = (\frac{(252 + 220)}{15}) kg = (\frac{472}{15}) kg = 31 \frac{7}{15} kg$
Hence, the weight of the cylinder filled with gas is $31 \frac{7}{15} kg$ .

Question 1:

Weight of the cylinder filled with gas = Weight of the empty cylinder + Weight of the gas inside the cylinder
Thus, we have:
$(16 \frac{4}{5} + 14 \frac{2}{3}) kg = (\frac{84}{5} + \frac{44}{3}) kg (L . C . M . of 5 and 3 = (3 \times 5) = 15) = (\frac{(252 + 220)}{15}) kg = (\frac{472}{15}) kg = 31 \frac{7}{15} kg$
Hence, the weight of the cylinder filled with gas is $31 \frac{7}{15} kg$ .

Answer:

Difference of like fractions = Difference of numerator $\div$ Common denominator
$\frac{5}{8} - \frac{1}{8} = \frac{(5 - 1)}{8} = \frac{4^{1}}{8_{2}} = \frac{1}{2}$

Question 2:

Difference of like fractions = Difference of numerator $\div$ Common denominator
$\frac{5}{8} - \frac{1}{8} = \frac{(5 - 1)}{8} = \frac{4^{1}}{8_{2}} = \frac{1}{2}$

Answer:

Difference of like fractions = Difference of numerator $\div$ Common denominator
$\frac{7}{12} - \frac{5}{12} = \frac{(7 - 5)}{12} = \frac{2^{1}}{12_{6}} = \frac{1}{6}$

Question 3:

Difference of like fractions = Difference of numerator $\div$ Common denominator
$\frac{7}{12} - \frac{5}{12} = \frac{(7 - 5)}{12} = \frac{2^{1}}{12_{6}} = \frac{1}{6}$

Answer:

Difference of like fractions = Difference of numerator $\div$ Common denominator
$4 \frac{3}{7} - 2 \frac{4}{7} = \frac{31}{7} - \frac{18}{7} = \frac{(31 - 18)}{7} = \frac{13^{}}{7}$

Question 4:

Difference of like fractions = Difference of numerator $\div$ Common denominator
$4 \frac{3}{7} - 2 \frac{4}{7} = \frac{31}{7} - \frac{18}{7} = \frac{(31 - 18)}{7} = \frac{13^{}}{7}$

Answer:

$\frac{5}{6} - \frac{4}{9}$

$3 6, 9 2 2, 3 3 1, 3 1, 1$
L.C.M. of 6 and 9 = (3 $\times$ 2 $\times$ 3) = 18
Now, we have:
$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}; \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} ∴ \frac{5}{6} - \frac{4}{9} = \frac{15}{18} - \frac{8}{18} = \frac{(15 - 8)}{18} = \frac{7}{18}$

Question 5:

$\frac{5}{6} - \frac{4}{9}$

$3 6, 9 2 2, 3 3 1, 3 1, 1$
L.C.M. of 6 and 9 = (3 $\times$ 2 $\times$ 3) = 18
Now, we have:
$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}; \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} ∴ \frac{5}{6} - \frac{4}{9} = \frac{15}{18} - \frac{8}{18} = \frac{(15 - 8)}{18} = \frac{7}{18}$

Answer:

$\frac{1}{2} - \frac{3}{8}$

L.C.M. of 2 and 8 = (2 $\times$ 2 $\times$ 2) = 8
Now, we have:
$\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} ∴ \frac{1}{2} - \frac{3}{8} = \frac{4}{8} - \frac{3}{8} = \frac{(4 - 3)}{8} = \frac{1}{8}$

Question 6:

$\frac{1}{2} - \frac{3}{8}$

L.C.M. of 2 and 8 = (2 $\times$ 2 $\times$ 2) = 8
Now, we have:
$\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} ∴ \frac{1}{2} - \frac{3}{8} = \frac{4}{8} - \frac{3}{8} = \frac{(4 - 3)}{8} = \frac{1}{8}$

Answer:

$\frac{5}{8} - \frac{7}{12}$

$2 8, 12 2 4, 6 2 2, 3 3 1, 3 1, 1$
L.C.M. of 8 and 12 = (2 $\times$ 2 $\times$ 2 $\times$ 3) = 24
Now, we have:
$\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}; \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24} ∴ \frac{5}{8} - \frac{7}{12} = \frac{15}{24} - \frac{14}{24} = \frac{(15 - 14)}{24} = \frac{1}{24}$

Question 7:

$\frac{5}{8} - \frac{7}{12}$

$2 8, 12 2 4, 6 2 2, 3 3 1, 3 1, 1$
L.C.M. of 8 and 12 = (2 $\times$ 2 $\times$ 2 $\times$ 3) = 24
Now, we have:
$\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}; \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24} ∴ \frac{5}{8} - \frac{7}{12} = \frac{15}{24} - \frac{14}{24} = \frac{(15 - 14)}{24} = \frac{1}{24}$

Answer:

$2 \frac{7}{9} - 1 \frac{8}{15} = \frac{25}{9} - \frac{23}{15} 3 9, 15 3 3, 5 5 1, 5 1, 1 L . C . M . of 9 and 15 = (3 \times 3 \times 5) = 45 ∴ \frac{25}{9} - \frac{23}{15} = \frac{(125 - 69)}{45} = \frac{56}{45} = 1 \frac{11}{45} \{[45 \div 9 = 5, 5 \times 25 = 125] and [45 \div 15 = 3, 3 \times 23 = 69]\}$

Question 8:

$2 \frac{7}{9} - 1 \frac{8}{15} = \frac{25}{9} - \frac{23}{15} 3 9, 15 3 3, 5 5 1, 5 1, 1 L . C . M . of 9 and 15 = (3 \times 3 \times 5) = 45 ∴ \frac{25}{9} - \frac{23}{15} = \frac{(125 - 69)}{45} = \frac{56}{45} = 1 \frac{11}{45} \{[45 \div 9 = 5, 5 \times 25 = 125] and [45 \div 15 = 3, 3 \times 23 = 69]\}$

Answer:

$3 \frac{5}{8} - 2 \frac{5}{12} = \frac{29}{8} - \frac{29}{12} 2 8, 12 24, 6 2 2, 3 3 1, 3 1, 1 L . C . M . of 8 and 12 = (2 \times 2 \times 2 \times 3) = 24 ∴ \frac{29}{8} - \frac{29}{12} = \frac{(87 - 58)}{24} = \frac{29}{24} = 1 \frac{5}{24} \{[24 \div 8 = 3, 3 \times 29 = 87] and [24 \div 12 = 2, 2 \times 29 = 58]\}$

Question 9:

$3 \frac{5}{8} - 2 \frac{5}{12} = \frac{29}{8} - \frac{29}{12} 2 8, 12 24, 6 2 2, 3 3 1, 3 1, 1 L . C . M . of 8 and 12 = (2 \times 2 \times 2 \times 3) = 24 ∴ \frac{29}{8} - \frac{29}{12} = \frac{(87 - 58)}{24} = \frac{29}{24} = 1 \frac{5}{24} \{[24 \div 8 = 3, 3 \times 29 = 87] and [24 \div 12 = 2, 2 \times 29 = 58]\}$

Answer:

$2 \frac{3}{10} - 1 \frac{7}{15} = \frac{23}{10} - \frac{22}{15} 5 10, 15 2 2, 3 3 1, 3 1, 1 L . C . M . of 10 and 15 = (2 \times 3 \times 5) = 30 = \frac{(69 - 44)}{30} \{[30 \div 10 = 3, 3 \times 23 = 69] and [30 \div 15 = 2, 2 \times 22 = 44]\} = \frac{25^{5}}{30_{6}} = \frac{5}{6}$

Question 10:

$2 \frac{3}{10} - 1 \frac{7}{15} = \frac{23}{10} - \frac{22}{15} 5 10, 15 2 2, 3 3 1, 3 1, 1 L . C . M . of 10 and 15 = (2 \times 3 \times 5) = 30 = \frac{(69 - 44)}{30} \{[30 \div 10 = 3, 3 \times 23 = 69] and [30 \div 15 = 2, 2 \times 22 = 44]\} = \frac{25^{5}}{30_{6}} = \frac{5}{6}$

Answer:

$6 \frac{2}{3} - 3 \frac{3}{4} = \frac{20}{3} - \frac{15}{4} L . C . M . of 3 and 4 = (2 \times 2 \times 3) = 12 = \frac{(80 - 45)}{12} \{[12 \div 3 = 4, 4 \times 20 = 80] and [12 \div 4 = 3, 3 \times 15 = 45]\} = \frac{35}{12} = 2 \frac{11}{12}$

Question 11:

$6 \frac{2}{3} - 3 \frac{3}{4} = \frac{20}{3} - \frac{15}{4} L . C . M . of 3 and 4 = (2 \times 2 \times 3) = 12 = \frac{(80 - 45)}{12} \{[12 \div 3 = 4, 4 \times 20 = 80] and [12 \div 4 = 3, 3 \times 15 = 45]\} = \frac{35}{12} = 2 \frac{11}{12}$

Answer:

$7 - 5 \frac{2}{3} = \frac{7}{1} - \frac{17}{3} L . C . M . of 1 and 3 = 3 = \frac{(21 - 17)}{3} \{[3 \div 1 = 3, 3 \times 7 = 21] and [3 \div 3 = 1, 1 \times 17 = 17]\} = \frac{4}{3} = 1 \frac{1}{3}$

Question 12:

$7 - 5 \frac{2}{3} = \frac{7}{1} - \frac{17}{3} L . C . M . of 1 and 3 = 3 = \frac{(21 - 17)}{3} \{[3 \div 1 = 3, 3 \times 7 = 21] and [3 \div 3 = 1, 1 \times 17 = 17]\} = \frac{4}{3} = 1 \frac{1}{3}$

Answer:

$10 - 6 \frac{3}{8} = \frac{10}{1} - \frac{51}{8} L . C . M . of 1 and 8 = 8 = \frac{(80 - 51)}{8} \{[8 \div 1 = 8, 8 \times 10 = 80] and [8 \div 8 = 1, 1 \times 51 = 51]\} = \frac{29}{8} = 3 \frac{5}{8}$

Question 13:

$10 - 6 \frac{3}{8} = \frac{10}{1} - \frac{51}{8} L . C . M . of 1 and 8 = 8 = \frac{(80 - 51)}{8} \{[8 \div 1 = 8, 8 \times 10 = 80] and [8 \div 8 = 1, 1 \times 51 = 51]\} = \frac{29}{8} = 3 \frac{5}{8}$

Answer:

We have:

$\frac{5}{6} - \frac{4}{9} + \frac{2}{3} L . C . M . of 3, 6 and 9 = (2 \times 3 \times 3) = 18 = \frac{(15 - 8 + 12)}{18} \{[18 \div 6 = 3, 3 \times 5 = 15], [18 \div 9 = 2, 2 \times 4 = 8] and [18 \div 3 = 6, 6 \times 2 = 12]\} = \frac{(27 - 8)}{18} = \frac{19}{18} = 1 \frac{1}{18}$
$3 3, 6, 9 3 1, 2, 3 2 1, 2, 1 1, 1, 1$

Question 14:

We have:

$\frac{5}{6} - \frac{4}{9} + \frac{2}{3} L . C . M . of 3, 6 and 9 = (2 \times 3 \times 3) = 18 = \frac{(15 - 8 + 12)}{18} \{[18 \div 6 = 3, 3 \times 5 = 15], [18 \div 9 = 2, 2 \times 4 = 8] and [18 \div 3 = 6, 6 \times 2 = 12]\} = \frac{(27 - 8)}{18} = \frac{19}{18} = 1 \frac{1}{18}$
$3 3, 6, 9 3 1, 2, 3 2 1, 2, 1 1, 1, 1$

Answer:

We have:
$\frac{5}{8} + \frac{3}{4} - \frac{7}{12} 2 4, 8, 12 2 2, 4, 6 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L . C . M . of 4, 8 and 12 = (2 \times 2 \times 2 \times 3) = 24 = \frac{(15 + 18 - 14)}{24} \{[24 \div 8 = 3, 3 \times 5 = 15], [24 \div 4 = 6, 6 \times 3 = 18] and [24 \div 12 = 2, 2 \times 7 = 14]\} = \frac{(33 - 14)}{24} = \frac{19}{24}$
234+556

Question 15:

We have:
$\frac{5}{8} + \frac{3}{4} - \frac{7}{12} 2 4, 8, 12 2 2, 4, 6 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L . C . M . of 4, 8 and 12 = (2 \times 2 \times 2 \times 3) = 24 = \frac{(15 + 18 - 14)}{24} \{[24 \div 8 = 3, 3 \times 5 = 15], [24 \div 4 = 6, 6 \times 3 = 18] and [24 \div 12 = 2, 2 \times 7 = 14]\} = \frac{(33 - 14)}{24} = \frac{19}{24}$
234+556

Answer:

We have: $\frac{2}{1} + \frac{11}{15} - \frac{5}{9} 3 1, 15, 9 3 1, 5, 3 5 1, 5, 1 1, 1, 1 L . C . M . of 15 and 9 = (3 \times 3 \times 5) = 45 = \frac{(90 + 33 - 25)}{45} \{[45 \div 1 = 45, 45 \times 2 = 90], [45 \div 15 = 3, 3 \times 11 = 33] and [45 \div 9 = 5, 5 \times 5 = 25]\} = \frac{(90 + 8)}{45} = \frac{98}{45} = 2 \frac{8}{45}$
234+556

Question 16:

We have: $\frac{2}{1} + \frac{11}{15} - \frac{5}{9} 3 1, 15, 9 3 1, 5, 3 5 1, 5, 1 1, 1, 1 L . C . M . of 15 and 9 = (3 \times 3 \times 5) = 45 = \frac{(90 + 33 - 25)}{45} \{[45 \div 1 = 45, 45 \times 2 = 90], [45 \div 15 = 3, 3 \times 11 = 33] and [45 \div 9 = 5, 5 \times 5 = 25]\} = \frac{(90 + 8)}{45} = \frac{98}{45} = 2 \frac{8}{45}$
234+556

Answer:

We have:
$5 \frac{3}{4} - 4 \frac{5}{12} + 3 \frac{1}{6} = \frac{23}{4} - \frac{53}{12} + \frac{19}{6} L . C . M . of 4, 12 and 6 = (2 \times 2 \times 3) = 12 2 4, 12, 6 2 2, 6, 3 3 1, 2, 3 2 1, 2, 1 1, 1, 1 = \frac{(69 - 53 + 38)}{12} \{[12 \div 4 = 3, 3 \times 23 = 69], [12 \div 12 = 1, 1 \times 53 = 53] and [12 \div 6 = 2, 2 \times 19 = 38]\} = \frac{(107 - 53)}{12} = \frac{54}{12} = \frac{9}{2} = 4 \frac{1}{2}$
234+556

Question 17:

We have:
$5 \frac{3}{4} - 4 \frac{5}{12} + 3 \frac{1}{6} = \frac{23}{4} - \frac{53}{12} + \frac{19}{6} L . C . M . of 4, 12 and 6 = (2 \times 2 \times 3) = 12 2 4, 12, 6 2 2, 6, 3 3 1, 2, 3 2 1, 2, 1 1, 1, 1 = \frac{(69 - 53 + 38)}{12} \{[12 \div 4 = 3, 3 \times 23 = 69], [12 \div 12 = 1, 1 \times 53 = 53] and [12 \div 6 = 2, 2 \times 19 = 38]\} = \frac{(107 - 53)}{12} = \frac{54}{12} = \frac{9}{2} = 4 \frac{1}{2}$
234+556

Answer:

We have: $2 + 5 \frac{7}{10} - 3 \frac{14}{15} = \frac{2}{1} + \frac{57}{10} - \frac{59}{15} 5 1, 10, 15 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L . C . M . of 10 and 15 = (2 \times 5 \times 3) = 30 = \frac{(60 + 171 - 118)}{30} \{[30 \div 1 = 30, 30 \times 2 = 60], [30 \div 10 = 3, 3 \times 57 = 171] and [30 \div 15 = 2, 2 \times 59 = 118]\} = \frac{(231 - 118)}{30} = \frac{113}{30} = 3 \frac{23}{30}$

Question 18:

We have: $2 + 5 \frac{7}{10} - 3 \frac{14}{15} = \frac{2}{1} + \frac{57}{10} - \frac{59}{15} 5 1, 10, 15 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L . C . M . of 10 and 15 = (2 \times 5 \times 3) = 30 = \frac{(60 + 171 - 118)}{30} \{[30 \div 1 = 30, 30 \times 2 = 60], [30 \div 10 = 3, 3 \times 57 = 171] and [30 \div 15 = 2, 2 \times 59 = 118]\} = \frac{(231 - 118)}{30} = \frac{113}{30} = 3 \frac{23}{30}$

Answer:

We have:
$8 - 3 \frac{1}{2} - 2 \frac{1}{4} = \frac{8}{1} - \frac{7}{2} - \frac{9}{4} 2 1, 2, 4 2 1, 1, 2 1, 1, 1 L . C . M . of 1, 2 and 4 = (2 \times 2) = 4 = \frac{(32 - 14 - 9)}{4} \{[4 \div 1 = 4, 4 \times 8 = 32], [4 \div 2 = 2, 2 \times 7 = 14] and [4 \div 4 = 1, 1 \times 9 = 9]\} = \frac{(32 - 23)}{4} = \frac{9}{4} = 2 \frac{1}{4}$

Question 19:

We have:
$8 - 3 \frac{1}{2} - 2 \frac{1}{4} = \frac{8}{1} - \frac{7}{2} - \frac{9}{4} 2 1, 2, 4 2 1, 1, 2 1, 1, 1 L . C . M . of 1, 2 and 4 = (2 \times 2) = 4 = \frac{(32 - 14 - 9)}{4} \{[4 \div 1 = 4, 4 \times 8 = 32], [4 \div 2 = 2, 2 \times 7 = 14] and [4 \div 4 = 1, 1 \times 9 = 9]\} = \frac{(32 - 23)}{4} = \frac{9}{4} = 2 \frac{1}{4}$

Answer:

We have:
$8 \frac{5}{6} - 3 \frac{3}{8} + 2 \frac{7}{12} = \frac{53}{6} - \frac{27}{8} + \frac{31}{12} 2 6, 8, 12 2 3, 4, 6 3 3, 2, 3 2 1, 2, 1 1, 1, 1 L . C . M . of 6, 8 and 12 = (2 \times 2 \times 2 \times 3) = 24 = \frac{(212 - 81 + 62)}{24} \{[24 \div 6 = 4, 4 \times 53 = 212], [24 \div 8 = 3, 3 \times 27 = 81] and [24 \div 12 = 2, 2 \times 31 = 62]\} = \frac{(274 - 81)}{24} = \frac{193}{24} = 8 \frac{1}{24}$

Question 20:

We have:
$8 \frac{5}{6} - 3 \frac{3}{8} + 2 \frac{7}{12} = \frac{53}{6} - \frac{27}{8} + \frac{31}{12} 2 6, 8, 12 2 3, 4, 6 3 3, 2, 3 2 1, 2, 1 1, 1, 1 L . C . M . of 6, 8 and 12 = (2 \times 2 \times 2 \times 3) = 24 = \frac{(212 - 81 + 62)}{24} \{[24 \div 6 = 4, 4 \times 53 = 212], [24 \div 8 = 3, 3 \times 27 = 81] and [24 \div 12 = 2, 2 \times 31 = 62]\} = \frac{(274 - 81)}{24} = \frac{193}{24} = 8 \frac{1}{24}$

Answer:

We have:
$6 \frac{1}{6} - 5 \frac{1}{5} + 3 \frac{1}{3} = \frac{37}{6} - \frac{26}{5} + \frac{10}{3} 2 6, 5, 3 3 3, 5, 3 5 1, 5, 1 1, 1, 1 L . C . M . of 6, 5 and 3 = (2 \times 5 \times 3) = 30 = \frac{(185 - 156 + 100)}{30} \{[30 \div 6 = 5, 5 \times 37 = 185], [30 \div 5 = 6, 6 \times 26 = 156], and [30 \div 3 = 10, 10 \times 10 = 100]\} = \frac{(285 - 156)}{30} = \frac{129^{43}}{30_{10}} = 4 \frac{3}{10}$

Question 21:

We have:
$6 \frac{1}{6} - 5 \frac{1}{5} + 3 \frac{1}{3} = \frac{37}{6} - \frac{26}{5} + \frac{10}{3} 2 6, 5, 3 3 3, 5, 3 5 1, 5, 1 1, 1, 1 L . C . M . of 6, 5 and 3 = (2 \times 5 \times 3) = 30 = \frac{(185 - 156 + 100)}{30} \{[30 \div 6 = 5, 5 \times 37 = 185], [30 \div 5 = 6, 6 \times 26 = 156], and [30 \div 3 = 10, 10 \times 10 = 100]\} = \frac{(285 - 156)}{30} = \frac{129^{43}}{30_{10}} = 4 \frac{3}{10}$

Answer:

We have:
$3 + 1 \frac{1}{5} + \frac{2}{3} - \frac{7}{15} = \frac{3}{1} + \frac{6}{5} + \frac{2}{3} - \frac{7}{15} 5 5, 3, 15 3 1, 3, 3 1, 1, 1 L . C . M . of 1, 5, 3 and 15 = (5 \times 3) = 15 = \frac{(45 + 18 + 10 - 7)}{15} \{[15 \div 1 = 15, 15 \times 3 = 45], [15 \div 5 = 3, 3 \times 6 = 18], [15 \div 3 = 5, 5 \times 2 = 10] and [15 \div 15 = 1, 1 \times 7 = 7]\} = \frac{(73 - 7)}{15} = \frac{66^{22}}{15_{5}} = \frac{22}{5} = 4 \frac{2}{5}$

Question 22:

We have:
$3 + 1 \frac{1}{5} + \frac{2}{3} - \frac{7}{15} = \frac{3}{1} + \frac{6}{5} + \frac{2}{3} - \frac{7}{15} 5 5, 3, 15 3 1, 3, 3 1, 1, 1 L . C . M . of 1, 5, 3 and 15 = (5 \times 3) = 15 = \frac{(45 + 18 + 10 - 7)}{15} \{[15 \div 1 = 15, 15 \times 3 = 45], [15 \div 5 = 3, 3 \times 6 = 18], [15 \div 3 = 5, 5 \times 2 = 10] and [15 \div 15 = 1, 1 \times 7 = 7]\} = \frac{(73 - 7)}{15} = \frac{66^{22}}{15_{5}} = \frac{22}{5} = 4 \frac{2}{5}$

Answer:

Let x be added to $9 \frac{2}{3}$ to get 19.

$∴ 9 \frac{2}{3} + x = 19 Thus, we have : x = 19 - 9 \frac{2}{3} = \frac{19}{1} - \frac{29}{3} L . C . M . of 1 and 3 is 3 . = \frac{(57 - 29)}{3} \{[3 \div 1 = 3, 3 \times 19 = 57] and [3 \div 3 = 1, 1 \times 29 = 29]\} = \frac{28}{3} = 9 \frac{1}{3}$ 923

Question 23:

Let x be added to $9 \frac{2}{3}$ to get 19.

$∴ 9 \frac{2}{3} + x = 19 Thus, we have : x = 19 - 9 \frac{2}{3} = \frac{19}{1} - \frac{29}{3} L . C . M . of 1 and 3 is 3 . = \frac{(57 - 29)}{3} \{[3 \div 1 = 3, 3 \times 19 = 57] and [3 \div 3 = 1, 1 \times 29 = 29]\} = \frac{28}{3} = 9 \frac{1}{3}$ 923

Answer:

Let x be added to $6 \frac{7}{15}$ to get $8 \frac{1}{5}$ .
$∴ 6 \frac{7}{15} + x = 8 \frac{1}{5} Therefore, we have : x = 8 \frac{1}{5} - 6 \frac{7}{15} = \frac{41}{5} - \frac{97}{15} L . C . M . of 5 and 15 = (5 \times 3) = 15 = \frac{(123 - 97)}{15} \{[15 \div 5 = 3, 3 \times 41 = 123] and [15 \div 15 = 1, 1 \times 97 = 97]\} = \frac{26}{15} = 1 \frac{11}{15}$

Question 24:

Let x be added to $6 \frac{7}{15}$ to get $8 \frac{1}{5}$ .
$∴ 6 \frac{7}{15} + x = 8 \frac{1}{5} Therefore, we have : x = 8 \frac{1}{5} - 6 \frac{7}{15} = \frac{41}{5} - \frac{97}{15} L . C . M . of 5 and 15 = (5 \times 3) = 15 = \frac{(123 - 97)}{15} \{[15 \div 5 = 3, 3 \times 41 = 123] and [15 \div 15 = 1, 1 \times 97 = 97]\} = \frac{26}{15} = 1 \frac{11}{15}$

Answer:

$(5 \frac{5}{6} + 4 \frac{1}{9}) - (3 \frac{5}{9} + 3 \frac{1}{3}) = (\frac{35}{6} + \frac{37}{9}) - (\frac{32}{9} + \frac{10}{3}) 2 6, 9, 3 3 3, 9, 3 3 1, 3, 1 1, 1, 1 L . C . M . of 3, 6, 9 = (2 \times 3 \times 3) = 18 = \frac{[105 + 74] - [64 + 60]}{18} \{[18 \div 6 = 3, 3 \times 35 = 105] and [18 \div 9 = 2, 2 \times 37 = 74]\} \{[18 \div 9 = 2, 2 \times 32 = 64] and [18 \div 3 = 6, 6 \times 10 = 60]\} = \frac{[179] - [124]}{18} = \frac{55}{18} = 3 \frac{1}{18}$

Question 25:

$(5 \frac{5}{6} + 4 \frac{1}{9}) - (3 \frac{5}{9} + 3 \frac{1}{3}) = (\frac{35}{6} + \frac{37}{9}) - (\frac{32}{9} + \frac{10}{3}) 2 6, 9, 3 3 3, 9, 3 3 1, 3, 1 1, 1, 1 L . C . M . of 3, 6, 9 = (2 \times 3 \times 3) = 18 = \frac{[105 + 74] - [64 + 60]}{18} \{[18 \div 6 = 3, 3 \times 35 = 105] and [18 \div 9 = 2, 2 \times 37 = 74]\} \{[18 \div 9 = 2, 2 \times 32 = 64] and [18 \div 3 = 6, 6 \times 10 = 60]\} = \frac{[179] - [124]}{18} = \frac{55}{18} = 3 \frac{1}{18}$

Answer:

Let us compare $\frac{3}{4} and \frac{5}{7}$ .
3 $\times$ 7 = 21 and 4 $\times$ 5 = 20
Clearly, 21 > 20
∴ $\frac{3}{4} > \frac{5}{7}$
Required difference:
$= \frac{3}{4} - \frac{5}{7} L . C . M . of 4 and 7 = (2 \times 2 \times 7) = 28 = \frac{21 - 20}{28} \{[28 \div 4 = 7, 7 \times 3 = 21] and [28 \div 7 = 4, 4 \times 5 = 20]\} = \frac{1}{28}$
Hence, $\frac{3}{4} is greater than \frac{5}{7} by \frac{1}{28}$ .

Question 26:

Let us compare $\frac{3}{4} and \frac{5}{7}$ .
3 $\times$ 7 = 21 and 4 $\times$ 5 = 20
Clearly, 21 > 20
∴ $\frac{3}{4} > \frac{5}{7}$
Required difference:
$= \frac{3}{4} - \frac{5}{7} L . C . M . of 4 and 7 = (2 \times 2 \times 7) = 28 = \frac{21 - 20}{28} \{[28 \div 4 = 7, 7 \times 3 = 21] and [28 \div 7 = 4, 4 \times 5 = 20]\} = \frac{1}{28}$
Hence, $\frac{3}{4} is greater than \frac{5}{7} by \frac{1}{28}$ .

Answer:

Amount of milk left with Mrs. Soni = Total amount of milk bought by her $-$ Amount of milk consumed
$∴$ Amount of milk left with Mrs. Soni $= 7 \frac{1}{2} - 5 \frac{3}{4} = \frac{15}{2} - \frac{23}{4} L . C . M . of 2 and 4 = (2 \times 2) = 4 = \frac{(30 - 23)}{4} \{[4 \div 2 = 2, 2 \times 15 = 30] and [4 \div 4 = 1, 1 \times 23 = 23]\} = \frac{7}{4} = 1 \frac{3}{4} litres$

$∴$ Milk left with Mrs. Soni = $1 \frac{3}{4} litres$

Question 27:

Amount of milk left with Mrs. Soni = Total amount of milk bought by her $-$ Amount of milk consumed
$∴$ Amount of milk left with Mrs. Soni $= 7 \frac{1}{2} - 5 \frac{3}{4} = \frac{15}{2} - \frac{23}{4} L . C . M . of 2 and 4 = (2 \times 2) = 4 = \frac{(30 - 23)}{4} \{[4 \div 2 = 2, 2 \times 15 = 30] and [4 \div 4 = 1, 1 \times 23 = 23]\} = \frac{7}{4} = 1 \frac{3}{4} litres$

$∴$ Milk left with Mrs. Soni = $1 \frac{3}{4} litres$

Answer:

Actual duration of the film = Total duration of the show $-$ Time spent on advertisements
$= (3 \frac{1}{3} - 1 \frac{3}{4}) hours = (\frac{10}{3} - \frac{7}{4}) hours L . C . M . of 3 and 4 = (2 \times 2 \times 3) = 12 = (\frac{40 - 21}{12}) hours \{[12 \div 3 = 4, 4 \times 10 = 40] and [12 \div 4 = 3, 3 \times 7 = 21]\} = (\frac{19}{12}) hours = 1 \frac{7}{12} hours$
Thus, the actual duration of the film was $1 \frac{7}{12} hours$ .

Question 28:

Actual duration of the film = Total duration of the show $-$ Time spent on advertisements
$= (3 \frac{1}{3} - 1 \frac{3}{4}) hours = (\frac{10}{3} - \frac{7}{4}) hours L . C . M . of 3 and 4 = (2 \times 2 \times 3) = 12 = (\frac{40 - 21}{12}) hours \{[12 \div 3 = 4, 4 \times 10 = 40] and [12 \div 4 = 3, 3 \times 7 = 21]\} = (\frac{19}{12}) hours = 1 \frac{7}{12} hours$
Thus, the actual duration of the film was $1 \frac{7}{12} hours$ .

Answer:

Money left with the rickshaw puller = Money earned by him in a day $-$ Money spent by him on food
$= Rs (137 \frac{1}{2} - 56 \frac{3}{4}) L . C . M . of 2 and 4 = (2 \times 2) = 4 = Rs (\frac{275}{2} - \frac{227}{4}) \{[4 \div 2 = 2, 2 \times 275 = 550] and [4 \div 4 = 1, 1 \times 227 = 227]\} = Rs (\frac{550 - 227}{4}) = Rs (\frac{323}{4}) = Rs 80 \frac{3}{4}$
Hence, Rs $80 \frac{3}{4}$ is left with the rickshaw puller.

Question 29:

Money left with the rickshaw puller = Money earned by him in a day $-$ Money spent by him on food
$= Rs (137 \frac{1}{2} - 56 \frac{3}{4}) L . C . M . of 2 and 4 = (2 \times 2) = 4 = Rs (\frac{275}{2} - \frac{227}{4}) \{[4 \div 2 = 2, 2 \times 275 = 550] and [4 \div 4 = 1, 1 \times 227 = 227]\} = Rs (\frac{550 - 227}{4}) = Rs (\frac{323}{4}) = Rs 80 \frac{3}{4}$
Hence, Rs $80 \frac{3}{4}$ is left with the rickshaw puller.

Answer:

The length of the other piece = (Length of the wire $-$ Length of one piece)
$= (2 \frac{3}{4} - \frac{5}{8}) m = (\frac{11}{4} - \frac{5}{8}) m L . C . M . of 4 and 8 = (2 \times 2 \times 2) = 8 = (\frac{22 - 5}{8}) m \{[8 \div 4 = 2, 2 \times 11 = 22] and [8 \div 8 = 1, 1 \times 5 = 5]\} = (\frac{17}{8}) m = 2 \frac{1}{8} m$
Hence, the other piece is $2 \frac{1}{8} m$ long.

Question 1:

The length of the other piece = (Length of the wire $-$ Length of one piece)
$= (2 \frac{3}{4} - \frac{5}{8}) m = (\frac{11}{4} - \frac{5}{8}) m L . C . M . of 4 and 8 = (2 \times 2 \times 2) = 8 = (\frac{22 - 5}{8}) m \{[8 \div 4 = 2, 2 \times 11 = 22] and [8 \div 8 = 1, 1 \times 5 = 5]\} = (\frac{17}{8}) m = 2 \frac{1}{8} m$
Hence, the other piece is $2 \frac{1}{8} m$ long.

Answer:

(c) $\frac{3 \times 2}{5 \times 2}$

Question 2:

(c) $\frac{3 \times 2}{5 \times 2}$

Answer:

(c) $\frac{8 \div 4}{12 \div 4}$

Question 3:

(c) $\frac{8 \div 4}{12 \div 4}$

Answer:

$(b) \frac{2}{3} Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 . Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 . Common factors of 24 and 36 are 1, 2, 3, 4, 6, 12 . H . C . F . = 12 Dividing both the numerator and the denominator by 12 : \frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}$

Question 4:

$(b) \frac{2}{3} Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 . Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 . Common factors of 24 and 36 are 1, 2, 3, 4, 6, 12 . H . C . F . = 12 Dividing both the numerator and the denominator by 12 : \frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}$

Answer:

(a) 15

Explanation:
$(\frac{3}{4} = \frac{x}{20}) We have : 20 = 4 \times 5 So, we have to multiply the numerator by 5 . ∴ x = 3 \times 5 = 15$

Question 5:

(a) 15

Explanation:
$(\frac{3}{4} = \frac{x}{20}) We have : 20 = 4 \times 5 So, we have to multiply the numerator by 5 . ∴ x = 3 \times 5 = 15$

Answer:

(a) 4

Explanation:
$(\frac{45}{60} = \frac{3}{x}) Now, 3 = 45 \div 15 So, we have to divide the denominator by 15 . ∴ x = 60 \div 15 = 4$

Question 6:

(a) 4

Explanation:
$(\frac{45}{60} = \frac{3}{x}) Now, 3 = 45 \div 15 So, we have to divide the denominator by 15 . ∴ x = 60 \div 15 = 4$

Answer:

(c) $\frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}$

(Fractions having the same denominator are called like fractions.)

Question 7:

(c) $\frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}$

(Fractions having the same denominator are called like fractions.)

Answer:

(d) none of these

In a proper fraction, the numerator is less than the denominator.

Question 8:

(d) none of these

In a proper fraction, the numerator is less than the denominator.

Answer:

(a) $\frac{7}{8}$
In a proper fraction, the numerator is less than the denominator.

Question 9:

(a) $\frac{7}{8}$
In a proper fraction, the numerator is less than the denominator.

Answer:

(b) $\frac{3}{4} > \frac{3}{5}$
Between the two fractions with the same numerator, the one with the smaller denominator is the greater.

Question 10:

(b) $\frac{3}{4} > \frac{3}{5}$
Between the two fractions with the same numerator, the one with the smaller denominator is the greater.

Answer:

(c) $\frac{3}{5}$

$2 5, 3, 6, 10 5 5, 3, 3, 5 3 1, 3, 3, 1 1, 1, 1, 1$

L.C.M. of 5, 3, 6 and 10 = (2 $\times$ 3 $\times$ 5) = 30
Thus, we have:
$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30} \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30} ∴ The smallest fraction = \frac{18}{30} = \frac{3}{5}$

Question 11:

(c) $\frac{3}{5}$

$2 5, 3, 6, 10 5 5, 3, 3, 5 3 1, 3, 3, 1 1, 1, 1, 1$

L.C.M. of 5, 3, 6 and 10 = (2 $\times$ 3 $\times$ 5) = 30
Thus, we have:
$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30} \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30} ∴ The smallest fraction = \frac{18}{30} = \frac{3}{5}$

Answer:

( b ) $\frac{4}{5}$
Among the given fractions with the same numerator, the one with the smallest denominator is the greatest.

Question 12:

( b ) $\frac{4}{5}$
Among the given fractions with the same numerator, the one with the smallest denominator is the greatest.

Answer:

(a) $\frac{6}{11}$
Among like fractions, the fraction with the smallest numerator is the smallest.

Question 13:

(a) $\frac{6}{11}$
Among like fractions, the fraction with the smallest numerator is the smallest.

Answer:

(d) $\frac{7}{12}$

Explanation:
$2 4, 6, 12, 3 2 2, 3, 6, 3 3 1, 3, 3, 3 1, 1, 1, 1$

â€‹â€‹L.C.M. of 4, 6, 12 and 3 = (2 $\times$ 2 $\times$ 3) = 12
Thus, we have:
$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \frac{7}{12} Clearly, \frac{7}{12} is the smallest fraction .$

Question 14:

(d) $\frac{7}{12}$

Explanation:
$2 4, 6, 12, 3 2 2, 3, 6, 3 3 1, 3, 3, 3 1, 1, 1, 1$

â€‹â€‹L.C.M. of 4, 6, 12 and 3 = (2 $\times$ 2 $\times$ 3) = 12
Thus, we have:
$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \frac{7}{12} Clearly, \frac{7}{12} is the smallest fraction .$

Answer:

(b) $\frac{23}{5}$

Question 15:

(b) $\frac{23}{5}$

Answer:

(c) $4 \frac{6}{7}$
On dividing 34 by 7:
Quotient = 4
Remainder = 6
$\frac{34}{7} = 4 + \frac{6}{7} = 4 \frac{6}{7}$

Question 16:

(c) $4 \frac{6}{7}$
On dividing 34 by 7:
Quotient = 4
Remainder = 6
$\frac{34}{7} = 4 + \frac{6}{7} = 4 \frac{6}{7}$

Answer:

(b) $\frac{3}{4}$

Explanation:

Addition of like fractions = Sum of the numerators / Common denominator
=

\frac{5}{8} + \frac{1}{8} = \frac{(5 + 1)}{8} = \frac{6^{3}}{8_{4}} = \frac{3}{4}

Question 17:

(b) $\frac{3}{4}$

Explanation:

Addition of like fractions = Sum of the numerators / Common denominator
=

\frac{5}{8} + \frac{1}{8} = \frac{(5 + 1)}{8} = \frac{6^{3}}{8_{4}} = \frac{3}{4}

Answer:

(b) $\frac{1}{2}$
Explanation:
$\frac{5}{8} - \frac{1}{8} = \frac{(5 - 1)}{8} = \frac{4^{1}}{8_{2}} = \frac{1}{2}$

Question 18:

(b) $\frac{1}{2}$
Explanation:
$\frac{5}{8} - \frac{1}{8} = \frac{(5 - 1)}{8} = \frac{4^{1}}{8_{2}} = \frac{1}{2}$

Answer:

$(a) 1 \frac{1}{2} Explanation : 3 \frac{3}{4} - 2 \frac{1}{4} \Rightarrow \frac{15}{4} - \frac{9}{4} \Rightarrow \frac{(15 - 9)}{4} \Rightarrow \frac{6}{4} = \frac{3}{2} = 1 \frac{1}{2}$

Question 19:

$(a) 1 \frac{1}{2} Explanation : 3 \frac{3}{4} - 2 \frac{1}{4} \Rightarrow \frac{15}{4} - \frac{9}{4} \Rightarrow \frac{(15 - 9)}{4} \Rightarrow \frac{6}{4} = \frac{3}{2} = 1 \frac{1}{2}$

Answer:

(d) $1 \frac{1}{18}$

Explanation:
$3 3, 6, 9 2 1, 2, 3 3 1, 1, 3 1, 1, 1$

$\frac{5}{6} + \frac{2}{3} - \frac{4}{9} (L . C . M . of 3, 6 and 9 = (2 \times 3 \times 3) = 18) = \frac{(15 + 12 - 8)}{18} \{[18 \div 6 = 3, 3 \times 5 = 15], [18 \div 3 = 6, 6 \times 2 = 12] and [18 \div 9 = 2, 2 \times 4 = 8]\} = \frac{(27 - 8)}{18} = \frac{19}{18} = 1 \frac{1}{18}$

Question 20:

(d) $1 \frac{1}{18}$

Explanation:
$3 3, 6, 9 2 1, 2, 3 3 1, 1, 3 1, 1, 1$

$\frac{5}{6} + \frac{2}{3} - \frac{4}{9} (L . C . M . of 3, 6 and 9 = (2 \times 3 \times 3) = 18) = \frac{(15 + 12 - 8)}{18} \{[18 \div 6 = 3, 3 \times 5 = 15], [18 \div 3 = 6, 6 \times 2 = 12] and [18 \div 9 = 2, 2 \times 4 = 8]\} = \frac{(27 - 8)}{18} = \frac{19}{18} = 1 \frac{1}{18}$

Answer:

(a) $3 \frac{1}{3}$

Explanation:
Let us compare $3 \frac{1}{3} and \frac{33}{10} or \frac{10}{3} and \frac{33}{10}$ .
10 â¨¯ 10 = 100 and 3 â€‹â¨¯ 33 = 99
Clearly, 100 > 99
∴ $\frac{10}{3} > \frac{33}{10} or 3 \frac{1}{3} > \frac{33}{10}$

Question 1:

(a) $3 \frac{1}{3}$

Explanation:
Let us compare $3 \frac{1}{3} and \frac{33}{10} or \frac{10}{3} and \frac{33}{10}$ .
10 â¨¯ 10 = 100 and 3 â€‹â¨¯ 33 = 99
Clearly, 100 > 99
∴ $\frac{10}{3} > \frac{33}{10} or 3 \frac{1}{3} > \frac{33}{10}$

Answer:

A fraction is defined as a number representing a part of a whole, where the whole may be a single object or a group of objects.

Examples: $\frac{5}{7}, \frac{8}{5}, \frac{2}{3}, \frac{4}{3}, \frac{4}{9}$

Question 2:

A fraction is defined as a number representing a part of a whole, where the whole may be a single object or a group of objects.

Examples: $\frac{5}{7}, \frac{8}{5}, \frac{2}{3}, \frac{4}{3}, \frac{4}{9}$

Answer:

An hour has 60 minutes.
$∴$ Fraction for 35 minutes = $\frac{35^{7}}{60_{12}} = \frac{7}{12}$
Hence, $\frac{7}{12}$ part of an hour is equal to 35 minutes.

Question 3:

An hour has 60 minutes.
$∴$ Fraction for 35 minutes = $\frac{35^{7}}{60_{12}} = \frac{7}{12}$
Hence, $\frac{7}{12}$ part of an hour is equal to 35 minutes.

Answer:

56 = 8 â¨¯ 7
So, we need to multiply the numerator by 7.

∴

\frac{5}{8} = \frac{5 \times 7}{8 \times 7} = \frac{35}{56}

Hence, the required fraction is

\frac{35}{56}

.

Question 4:

56 = 8 â¨¯ 7
So, we need to multiply the numerator by 7.

∴

\frac{5}{8} = \frac{5 \times 7}{8 \times 7} = \frac{35}{56}

Hence, the required fraction is

\frac{35}{56}

.

Answer:

Let OA = AB = BC = 1 unit
$∴$ OB = 2 units and OC = 3 units
Divide BC into 5 equal parts and take 3 parts out to reach point P.
Clearly, point P represents the number $2 \frac{3}{5}$ .

Question 5:

Let OA = AB = BC = 1 unit
$∴$ OB = 2 units and OC = 3 units
Divide BC into 5 equal parts and take 3 parts out to reach point P.
Clearly, point P represents the number $2 \frac{3}{5}$ .

Answer:

We have:
$2 \frac{4}{5} + 1 \frac{3}{10} + 3 \frac{1}{15} = \frac{14}{5} + \frac{13}{10} + \frac{46}{15} 5 5, 10, 15 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L . C . M . of 5, 10 and 15 = (5 \times 2 \times 3) = 30 = \frac{84 + 39 + 92}{30} \{[30 \div 5 = 6, 6 \times 14 = 84], [30 \div 10 = 3, 3 \times 13 = 39] and [30 \div 15 = 2, 2 \times 46 = 92]\} = \frac{215^{43}}{30_{6}} = \frac{43}{6} = 7 \frac{1}{6}$

Question 6:

We have:
$2 \frac{4}{5} + 1 \frac{3}{10} + 3 \frac{1}{15} = \frac{14}{5} + \frac{13}{10} + \frac{46}{15} 5 5, 10, 15 2 1, 2, 3 3 1, 1, 3 1, 1, 1 L . C . M . of 5, 10 and 15 = (5 \times 2 \times 3) = 30 = \frac{84 + 39 + 92}{30} \{[30 \div 5 = 6, 6 \times 14 = 84], [30 \div 10 = 3, 3 \times 13 = 39] and [30 \div 15 = 2, 2 \times 46 = 92]\} = \frac{215^{43}}{30_{6}} = \frac{43}{6} = 7 \frac{1}{6}$

Answer:

Cost of a pen = $Rs 16 \frac{2}{3} = Rs \frac{50}{3} = Rs \frac{50 \times 2}{3 \times 2} = Rs \frac{100}{6}$

Cost of a pencil = $Rs 4 \frac{1}{6} = Rs \frac{25}{6}$
$\frac{100}{6} > \frac{25}{6} ∴ Rs 16 \frac{2}{3} > Rs 4 \frac{1}{6}$
So, the cost of a pen is more than the cost of a pencil.
Difference between their costs:
$= Rs (\frac{50}{3} - \frac{25}{6}) = Rs (\frac{100 - 25}{6}) = Rs (\frac{75^{25}}{6_{2}}) = Rs (\frac{25}{2}) = Rs 12 \frac{1}{2}$
Hence, the cost of a pen is Rs $12 \frac{1}{2}$ more than the cost of a pencil.

Question 7:

Cost of a pen = $Rs 16 \frac{2}{3} = Rs \frac{50}{3} = Rs \frac{50 \times 2}{3 \times 2} = Rs \frac{100}{6}$

Cost of a pencil = $Rs 4 \frac{1}{6} = Rs \frac{25}{6}$
$\frac{100}{6} > \frac{25}{6} ∴ Rs 16 \frac{2}{3} > Rs 4 \frac{1}{6}$
So, the cost of a pen is more than the cost of a pencil.
Difference between their costs:
$= Rs (\frac{50}{3} - \frac{25}{6}) = Rs (\frac{100 - 25}{6}) = Rs (\frac{75^{25}}{6_{2}}) = Rs (\frac{25}{2}) = Rs 12 \frac{1}{2}$
Hence, the cost of a pen is Rs $12 \frac{1}{2}$ more than the cost of a pencil.

Answer:

Let us compare $\frac{3}{4} and \frac{5}{7}$ .
By cross multiplying:
3 â¨¯ 7 = 21 and â€‹4 â¨¯ 5 = 20
Clearly, 21 > 20
∴â€‹ $\frac{3}{4} > \frac{5}{7}$
Their difference:
$\frac{3}{4} - \frac{5}{7} L . C . M . of 4 and 7 = (2 \times 2 \times 7) = 28 = \frac{21 - 20}{28} \{[28 \div 4 = 7, 7 \times 3 = 21] and [28 \div 7 = 4, 4 \times 5 = 20]\} = \frac{1}{28}$
Hence, $\frac{3}{4} is greater than \frac{5}{7} by \frac{1}{28} .$

Question 8:

Let us compare $\frac{3}{4} and \frac{5}{7}$ .
By cross multiplying:
3 â¨¯ 7 = 21 and â€‹4 â¨¯ 5 = 20
Clearly, 21 > 20
∴â€‹ $\frac{3}{4} > \frac{5}{7}$
Their difference:
$\frac{3}{4} - \frac{5}{7} L . C . M . of 4 and 7 = (2 \times 2 \times 7) = 28 = \frac{21 - 20}{28} \{[28 \div 4 = 7, 7 \times 3 = 21] and [28 \div 7 = 4, 4 \times 5 = 20]\} = \frac{1}{28}$
Hence, $\frac{3}{4} is greater than \frac{5}{7} by \frac{1}{28} .$

Answer:

$The given fractions are \frac{1}{2}, \frac{2}{3}, \frac{4}{9}, \frac{5}{6} .$
L.C.M. of 2, 3, 9 and 6 = (2 â¨¯ 3 â€‹â¨¯ 3) = 18
Now, we have:
$\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} Hence, \frac{9}{18}, \frac{12}{18}, \frac{8}{18} and \frac{15}{18} are like fractions .$

Question 9:

$The given fractions are \frac{1}{2}, \frac{2}{3}, \frac{4}{9}, \frac{5}{6} .$
L.C.M. of 2, 3, 9 and 6 = (2 â¨¯ 3 â€‹â¨¯ 3) = 18
Now, we have:
$\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} Hence, \frac{9}{18}, \frac{12}{18}, \frac{8}{18} and \frac{15}{18} are like fractions .$

Answer:

$Let \frac{3}{5} = \frac{}{30}$

30 = 5 â€‹â¨¯ 6
So, we have to multiply the numerator by 6 to get the equivalent fraction having denominator 30.

∴ $\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$

Thus, $\frac{18}{30} is the equivalent fraction of \frac{3}{5} .$

Question 10:

$Let \frac{3}{5} = \frac{}{30}$

30 = 5 â€‹â¨¯ 6
So, we have to multiply the numerator by 6 to get the equivalent fraction having denominator 30.

∴ $\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$

Thus, $\frac{18}{30} is the equivalent fraction of \frac{3}{5} .$

Answer:

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
The factors of 98 are 1, 2, 7, 14, 49, 98.
The common factors of 84 and 98 are 1, 2, 7, 14.
The H.C.F. of 84 and 98 is 14.
Dividing both the numerator and the denominator by the H.C.F.:
$\frac{84}{98} = \frac{84 \div 14}{98 \div 14} = \frac{6}{7}$

Question 11:

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
The factors of 98 are 1, 2, 7, 14, 49, 98.
The common factors of 84 and 98 are 1, 2, 7, 14.
The H.C.F. of 84 and 98 is 14.
Dividing both the numerator and the denominator by the H.C.F.:
$\frac{84}{98} = \frac{84 \div 14}{98 \div 14} = \frac{6}{7}$

Answer:

(b) an improper fraction

In an improper fraction, the numerator is greater than the denominator.

Question 12:

(b) an improper fraction

In an improper fraction, the numerator is greater than the denominator.

Answer:

(a) proper fraction

In a proper fraction, the numerator is less than the denominator.

Question 13:

(a) proper fraction

In a proper fraction, the numerator is less than the denominator.

Answer:

(b) $\frac{3}{8} < \frac{5}{12}$

Considering $\frac{3}{8} and \frac{5}{12}$ :

$On cross multiplying, we get : 3 \times 12 = 36 and 8 \times 5 = 40 Clearly, 36 < 40 ∴ \frac{3}{8} < \frac{5}{12}$

Question 14:

(b) $\frac{3}{8} < \frac{5}{12}$

Considering $\frac{3}{8} and \frac{5}{12}$ :

$On cross multiplying, we get : 3 \times 12 = 36 and 8 \times 5 = 40 Clearly, 36 < 40 ∴ \frac{3}{8} < \frac{5}{12}$

Answer:

(a) $\frac{2}{3}$

Explanation:
L.C.M. of 3, 9, 2 and 12 = ( 2 â¨¯ 2 â¨¯ 3 â€‹â¨¯ 3) = 36
Now, we have:
$\frac{2}{3} = \frac{2 \times 12}{3 \times 12} = \frac{24}{36} \frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36} \frac{1}{2} = \frac{1 \times 18}{2 \times 18} = \frac{18}{36} \frac{7}{12} = \frac{7 \times 3}{12 \times 3} = \frac{21}{36} Hence, \frac{24}{36} = \frac{2}{3} is the largest fraction .$

Question 15:

(a) $\frac{2}{3}$

Explanation:
L.C.M. of 3, 9, 2 and 12 = ( 2 â¨¯ 2 â¨¯ 3 â€‹â¨¯ 3) = 36
Now, we have:
$\frac{2}{3} = \frac{2 \times 12}{3 \times 12} = \frac{24}{36} \frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36} \frac{1}{2} = \frac{1 \times 18}{2 \times 18} = \frac{18}{36} \frac{7}{12} = \frac{7 \times 3}{12 \times 3} = \frac{21}{36} Hence, \frac{24}{36} = \frac{2}{3} is the largest fraction .$

Answer:

(b) $2 \frac{1}{4}$
Explanation:

$3 \frac{3}{4} - 1 \frac{1}{2} = \frac{15}{4} - \frac{3}{2} (L . C . M . of 2 and 4 = (2 \times 2) = 4) = \frac{15 - 6}{4} = \frac{9}{4} = 2 \frac{1}{4}$

Question 16:

(b) $2 \frac{1}{4}$
Explanation:

$3 \frac{3}{4} - 1 \frac{1}{2} = \frac{15}{4} - \frac{3}{2} (L . C . M . of 2 and 4 = (2 \times 2) = 4) = \frac{15 - 6}{4} = \frac{9}{4} = 2 \frac{1}{4}$

Answer:

(c) $\frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}$
Like fractions have same the denominator.

Question 17:

(c) $\frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}$
Like fractions have same the denominator.

Answer:

(d) $\frac{16}{21}$

$? - \frac{8}{21} = \frac{8}{21} ? = \frac{8}{21} + \frac{8}{21} = \frac{16}{21}$

Question 18:

(d) $\frac{16}{21}$

$? - \frac{8}{21} = \frac{8}{21} ? = \frac{8}{21} + \frac{8}{21} = \frac{16}{21}$

Answer:

$(i) 9 \frac{2}{3} + . . . . . . = 19 . . . . . . = 19 - 9 \frac{2}{3} . . . . . . = \frac{19}{1} - \frac{29}{3} . . . . . . = \frac{57 - 29}{3} . . . . . . = \frac{28}{3} . . . . . = 9 \frac{1}{3}$

(ii)
$6 \frac{1}{6} - ? = \frac{29}{30} ? = 6 \frac{1}{6} - \frac{29}{30} ? = \frac{37}{6} - \frac{29}{30} ? = \frac{185 - 29}{30} ? = \frac{156^{26}}{30_{5}} ? = 5 \frac{1}{5}$

(iii)
$7 - 5 \frac{2}{3} = \frac{7}{1} - \frac{17}{3} = \frac{21 - 17}{3} = \frac{4}{3} = 1 \frac{1}{3}$

(iv)

$The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 . The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 . The common factors of 72 and 90 are 1, 2, 3, 6, 9, 18 . H . C . F . of 72 and 90 is 18 . \frac{72 \div 18}{90 \div 18} = \frac{4}{5}$

(v)

$\frac{42}{54} = \frac{7}{9} \Rightarrow \frac{42 \div 6}{54 \div 6} = \frac{7}{9}$

Question 19:

$(i) 9 \frac{2}{3} + . . . . . . = 19 . . . . . . = 19 - 9 \frac{2}{3} . . . . . . = \frac{19}{1} - \frac{29}{3} . . . . . . = \frac{57 - 29}{3} . . . . . . = \frac{28}{3} . . . . . = 9 \frac{1}{3}$

(ii)
$6 \frac{1}{6} - ? = \frac{29}{30} ? = 6 \frac{1}{6} - \frac{29}{30} ? = \frac{37}{6} - \frac{29}{30} ? = \frac{185 - 29}{30} ? = \frac{156^{26}}{30_{5}} ? = 5 \frac{1}{5}$

(iii)
$7 - 5 \frac{2}{3} = \frac{7}{1} - \frac{17}{3} = \frac{21 - 17}{3} = \frac{4}{3} = 1 \frac{1}{3}$

(iv)

$The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 . The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 . The common factors of 72 and 90 are 1, 2, 3, 6, 9, 18 . H . C . F . of 72 and 90 is 18 . \frac{72 \div 18}{90 \div 18} = \frac{4}{5}$

(v)

$\frac{42}{54} = \frac{7}{9} \Rightarrow \frac{42 \div 6}{54 \div 6} = \frac{7}{9}$

Answer:

(a) T
(b) F    $(\frac{8}{1} - \frac{11}{6} = \frac{48 - 11}{6} = \frac{37}{6} = 6 \frac{1}{6})$
(c) F (Because like fractions have the same denominator.)
â€‹(d) F    (It lies between 0 and 1 as all proper fractions are less than 1.)
(e) T    (Because it is an improper fraction, while the others are proper fractions.)

RS Aggrawal 2020 2021 Solutions for Class 6 Maths Chapter 5 - Fractions

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