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#### Question 1:

Convert each of the following into a mixed fraction:

(i) $\frac{28}{9}$
(ii) $\frac{226}{15}$
(iii) $\frac{145}{9}$
(iv) $\frac{128}{5}$

#### Question 2:

Convert each of the following into an improper fraction:

(i) $7\frac{1}{4}$
(ii) $8\frac{5}{7}$
(iii) $5\frac{3}{10}$
(iv) $12\frac{5}{7}$

#### Question 1:

Write the fractions and check whether they are equivalent or no (i) Yes, they are equivalent.

(ii) Yes, they are equivalent.

#### Question 2:

Write the fractions and match fractions in Column I with the equivalent fractions in Column II.  #### Question 3:

Replace  in each of the following by the correct number:

(i)
(ii)
(iii)
(iv)
(v)

(i)

(ii)

(iii)

(iv)

(v)

#### Question 4:

Find the equivalent fraction of $\frac{3}{5}$, having:
(i) numerator 9
(ii) denominator 30
(iii) numerator 21
(iv) denominator 40

(i)

(ii)

(iii)

(iv)

#### Question 5:

Find fraction equivalent of $\frac{45}{60}$, having:

(i) numerator 15
(ii) denominator 4
(iii) denominator 240
(iv) numerator 135

(i)

(ii)

(iii)

(iv)

#### Question 6:

Find the fraction equivalent of $\frac{35}{42}$, having:

(i) numerator 15
(ii) denominator 18
(iii) denominator 30
(iv) numerator 30

#### Question 7:

Check whether the given fraction are equivalent:

(i) $\frac{5}{9},\frac{30}{54}$
(ii) $\frac{2}{7},\frac{16}{42}$
(iii) $\frac{7}{13},\frac{5}{11}$
(iv) $\frac{4}{11},\frac{32}{88}$
(v) $\frac{3}{10},\frac{12}{50}$
(vi) $\frac{9}{27},\frac{25}{75}$.

(i)
$\frac{5}{9}×\frac{6}{6}=\frac{30}{54}\phantom{\rule{0ex}{0ex}}$
So, the given fractions are equivalent.

(ii)
$\frac{2}{7}×\frac{8}{8}=\frac{16}{56}$

(iii)

(iv)

(v)

(vi)

#### Question 8:

Match the equivalent fractions and write another 2 form each:

(i) $\frac{250}{400}$          (a) $\frac{2}{3}$
(ii) $\frac{180}{200}$          (b) $\frac{2}{5}$
(iii) $\frac{660}{990}$          (c) $\frac{1}{2}$
(iv) $\frac{180}{360}$           (d) $\frac{5}{8}$
(v) $\frac{220}{550}$          (e) $\frac{9}{10}$

(i) - (d)
(ii) - (e)
(iii) - (a)
(iv) -(c)
(v)- (b)

#### Question 9:

Write some equivalent fractions which contain all digits from 1 to 9 once only.

$\frac{2}{4}=\frac{3}{6}=\frac{79}{158}\phantom{\rule{0ex}{0ex}}\frac{3}{9}=\frac{2}{6}=\frac{58}{174}$

#### Question 10:

Ravish had 20 pencils, Sikha had 50 pencils and Priya had 80 pencils. After 4 months, Ravish used up 10 pencils. Shikha used up 25 pencils and Priya used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of their pencils?

Total pencils Ravish had = 20
Pencils used by Ravish = 10
Fraction of pencils used by ravish =

Total pencils Shikha had = 50
Pencils used by Shikha = 25
Fraction of pencils used by Shikha =

Total pencils Priya had = 80
Pencils used by Priya = 40
Fraction of pencils used by Priya = $\frac{40÷40}{80÷40}$=

Yes, each of them has utilised an equal fraction of pencils.

#### Question 1:

Reduce each of the following fractions to its lowest term (simplest form):

(i) $\frac{40}{75}$
(ii) $\frac{42}{28}$
(iii) $\frac{12}{52}$
(iv) $\frac{40}{72}$
(v) $\frac{80}{24}$
(vi) $\frac{84}{56}$

#### Question 2:

Simplify each of the following to his lowest term:

(i) $\frac{75}{80}$
(ii) $\frac{52}{76}$
(iii) $\frac{84}{98}$
(iv) $\frac{68}{17}$
(v) $\frac{150}{50}$
(vi) $\frac{162}{108}$

#### Question 1:

Write each fraction. Arrange them in ascending and descending order using correct sign '<',
'=', '>' between the fractions: (i) Ascending order Descending order (ii) Ascending order Descending order (iii) Ascending order Descending order #### Question 2:

Mark $\frac{2}{6},\frac{4}{6},\frac{8}{6}$ and $\frac{6}{6}$ on the number line and put appropriate signs between fractions given below:

(i) $\frac{5}{6}......\frac{2}{6}$
(ii) $\frac{3}{6}......\frac{0}{6}$
(iii) $\frac{1}{6}......\frac{6}{6}$
(iv) $\frac{8}{6}......\frac{5}{6}$ (i) $\frac{5}{6}>\frac{2}{6}$ because 5 > 2 and the denominator is the same.
(ii) $\frac{3}{6}>\frac{0}{6}$ because 3 > 0 and the denominator is the same.
(iii) $\frac{1}{6}<\frac{6}{6}$ because 6 > 1 and the denominator is the same.
(iv) $\frac{8}{6}>\frac{5}{6}$ because 8 > 5 and the denominator is the same.

#### Question 3:

Compare the following fractions and put an appropriate sign:

(i) $\frac{3}{6}......\frac{5}{6}$
(ii) $\frac{4}{5}......\frac{0}{5}$
(iii) $\frac{3}{20}......\frac{4}{20}$
(iv) $\frac{1}{7}......\frac{1}{4}$

(i) $\frac{3}{6}<\frac{5}{6}$ because 3 < 5 and the denominator is the same.
(ii) $\frac{4}{5}>\frac{0}{5}$ because 4 > 0 and the denominator is the same.
(iii) $\frac{3}{20}<\frac{4}{20}$ because 3 < 4 and the denominator is the same.
(iv) $\frac{1}{7}<\frac{1}{4}$ because 7 > 4; if the numerator is the same, then the fraction that has smaller denominator is greater.

#### Question 4:

Compare the following fractions using the symbol > ro <:

(i)  $\frac{6}{7}$and $\frac{6}{11}$
(ii) $\frac{3}{7}$and $\frac{5}{7}$
(iii) $\frac{2}{3}$and $\frac{8}{12}$
(iv) $\frac{1}{5}$and $\frac{4}{15}$
(v) $\frac{8}{3}$and $\frac{8}{13}$
(vi) $\frac{4}{9}$and $\frac{15}{8}$

(i) $\frac{6}{7}>\frac{6}{11}$ because if the numerator is the same, then the fraction with smaller denominator is greater.
(ii) $\frac{3}{7}<\frac{5}{7}$ because 3 < 5 and the denominator is the same.

(iii)

(iv)
(Because 3 < 4 and the denominator is the same. Therefore, $\frac{1}{5}<\frac{4}{15}$.)

(v)
$\frac{8}{3}>\frac{8}{13}$  because if the numerator is the same, then the fraction with smaller denominator is greater.

(vi)
(Because 135 > 32 and the denominator is the same)

$\frac{4}{9}<\frac{15}{8}$

#### Question 5:

The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form:

(i) $\frac{2}{12}$
(ii) $\frac{3}{15}$
(iii) $\frac{8}{50}$
(iv) $\frac{16}{100}$
(v) $\frac{10}{60}$
(vi) $\frac{15}{75}$
(vii) $\frac{12}{60}$
(viii) $\frac{16}{96}$
(ix) $\frac{12}{75}$
(x) $\frac{12}{72}$
(xi) $\frac{3}{18}$
(xii) $\frac{4}{25}$

#### Question 6:

Isha read 25 pages of a book containing 100 pages. Nagma read $\frac{1}{2}$ of the same book. Who read less?

Total pages in the book = 100
Fraction of the book read by Isha =
Fraction of the book read by Nagma = $\frac{1}{2}$
Now, compare .
LCM of 4 & 2 is 4.

Convert each fraction into equivalent fraction with 4 as its denominator.

#### Question 7:

Arrange the following fractions in the ascending order:

(i) $\frac{2}{9},\frac{7}{9},\frac{3}{9},\frac{4}{9},\frac{1}{9},\frac{6}{9},\frac{5}{9}$
(ii) $\frac{7}{8},\frac{7}{25},\frac{7}{11},\frac{7}{18},\frac{7}{10}$
(iii) $\frac{37}{47},\frac{37}{50},\frac{37}{100},\frac{37}{1000},\frac{37}{85},\frac{37}{41}$
(iv) $\frac{3}{5},\frac{1}{5},\frac{4}{5},\frac{2}{5}$
(v) $\frac{2}{5},\frac{3}{4},\frac{1}{2},\frac{3}{5}$
(vi) $\frac{3}{8},\frac{3}{12},\frac{3}{6},\frac{3}{4}$
(vii) $\frac{4}{6},\frac{3}{8},\frac{6}{12},\frac{5}{16}$

(v)

$\frac{2}{5}<\frac{1}{2}<\frac{3}{5}<\frac{3}{4}$
(vi)
(vii)

When denominators are the same & numerators are different, then the fraction with greater numerator has a greater value.

$\frac{5}{16}<\frac{3}{8}<\frac{6}{12}<\frac{4}{6}$

#### Question 8:

Arrange in descending order in each of the following using the symbol >:

(i) $\frac{8}{17},\frac{8}{9},\frac{8}{5},\frac{8}{13}$
(ii) $\frac{5}{9},\frac{3}{12},\frac{1}{3},\frac{4}{15}$
(iii) $\frac{2}{7},\frac{11}{35},\frac{9}{14},\frac{13}{28}$

When numerators are the same and denominators are different, then the fraction with greater denominator has a smaller value.

When denominators are the same and numerators are different, then the fraction with greater numerator has a larger value.

(i)$\frac{8}{5}>\frac{8}{9}>\frac{8}{13}>\frac{8}{17}$
(ii)
$\frac{5}{9}×\frac{20}{20}=\frac{100}{180}$
$\frac{3}{12}×\frac{15}{15}=\frac{45}{180}$
$\frac{1}{3}×\frac{60}{60}=\frac{60}{180}$
$\frac{4}{15}×\frac{12}{12}=\frac{48}{180}$
$\frac{5}{9}>\frac{1}{3}>\frac{4}{15}>\frac{3}{12}$
(iii)$\frac{9}{14}>\frac{13}{28}>\frac{11}{35}>\frac{2}{7}$

#### Question 9:

Find answers to the following. Write and indicate how you solved them.

(i) Is $\frac{5}{9}$ equal to $\frac{4}{5}$?
(ii) Is $\frac{9}{16}$ equal to $\frac{5}{9}$?
(iii) Is $\frac{4}{5}$ equal to $\frac{16}{20}$?
(iv) Is $\frac{1}{15}$ equal to $\frac{4}{30}$?

Two fractions are equal when:

Numerator of the first fraction $×$ Denominator of the second fraction = Numerator of the second fraction $×$ Denominator of the first fraction
(i)

(ii)

(iii)

(iv)

#### Question 1:

Write these fractions appropriately as additions of subtractions: (i) The given fractions are

$\frac{1}{5}+\frac{2}{5}=\frac{3}{5}\phantom{\rule{0ex}{0ex}}\frac{1+2}{5}=\frac{3}{5}\phantom{\rule{0ex}{0ex}}\frac{3}{5}=\frac{3}{5}$

(ii) The given fractions are

$\frac{3}{6}+\frac{2}{6}=\frac{5}{6}\phantom{\rule{0ex}{0ex}}\frac{3+2}{6}=\frac{5}{6}\phantom{\rule{0ex}{0ex}}\frac{5}{6}=\frac{5}{6}$

#### Question 2:

Solve:

(i) $\frac{5}{12}+\frac{1}{12}$
(ii) $\frac{3}{15}+\frac{7}{15}$
(iii) $\frac{3}{22}+\frac{7}{22}$
(iv) $\frac{1}{4}+\frac{0}{4}$
(v) $\frac{4}{13}+\frac{2}{13}+\frac{1}{13}$
(vi) $\frac{0}{15}+\frac{2}{15}+\frac{1}{15}$
(vii) $\frac{7}{31}-\frac{4}{31}+\frac{9}{31}$
(viii) $3\frac{2}{7}+\frac{1}{7}-2\frac{3}{7}$
(ix) $2\frac{1}{3}-1\frac{2}{3}+4\frac{1}{3}$
(x) $1-\frac{2}{3}+\frac{7}{3}$
(xi) $\frac{16}{7}-\frac{5}{7}+\frac{9}{7}$

(i)

(ii)

(iii)

(iv)$\frac{1}{4}+\frac{0}{4}=\frac{1+0}{4}=\frac{1}{4}$

(v)$\frac{4}{13}+\frac{2}{13}+\frac{1}{13}=\frac{4+2+1}{13}=\frac{7}{13}$

(vi)

(vii)$\frac{7}{31}-\frac{4}{31}+\frac{9}{31}=\frac{7-4+9}{31}=\frac{12}{31}$

(viii)$3\frac{2}{7}+\frac{1}{7}-2\frac{3}{7}=\frac{23}{7}+\frac{1}{7}-\frac{17}{7}=\frac{23+1-17}{7}=\frac{7}{7}=1$
(ix)

(x)$1-\frac{2}{3}+\frac{7}{3}=\frac{3-2+7}{3}=\frac{8}{3}$

(xi)$\frac{16}{7}-\frac{5}{7}+\frac{9}{7}=\frac{16-5+9}{7}=\frac{20}{7}$

#### Question 3:

Shikha painted $\frac{1}{5}$ of the wall space in her room. Her brother Ravish helped and painted $\frac{3}{5}$ of the wall space. How much did they paint together? How much the room is left unpainted?

Shikha painted $\frac{1}{5}$ of the wall space.
Ravish painted $\frac{3}{5}$ of the wall space.
Wall space painted by both of them together  = $\frac{1}{5}+\frac{3}{5}=\frac{1+3}{5}=\frac{4}{5}$
Unpainted part of the room = $1-\frac{4}{5}=\frac{5-4}{5}=\frac{1}{5}$

#### Question 4:

Ramesh bought $2\frac{1}{2}$ kg sugar whereas Rohit bought $3\frac{1}{2}$ kg or sugar. Find the total amount of sugar bought by both of them.

Quantity of sugar bought by Ramesh = $2\frac{1}{2}\mathrm{kg}=\frac{\left(2×2\right)+1}{2}=\frac{5}{2}\mathrm{kg}$
Quantity of sugar bought by Rohit = $3\frac{1}{2}\mathrm{kg}=\frac{\left(3×2\right)+1}{2}=\frac{7}{2}\mathrm{kg}$
Total amount of sugar bought by them =

#### Question 5:

The teacher taught $\frac{3}{5}$ of the book, Vivek revised $\frac{1}{5}$ more on his own. How much does he still have to revise?

Fraction of the book taught by the teacher = $\frac{3}{5}$
Fraction of the book revised by Vivek = $\frac{1}{5}$
Fraction of the book still left for revision by Vivek =

#### Question 6:

Amit was given $\frac{5}{7}$ of a bucket of organes. What fraction of oranges was left in the basket?

Fraction of oranges given to Amit = $\frac{5}{7}$
Fraction of oranges left in the basket = $1-\frac{5}{7}=\frac{7×1-5}{7}=\frac{2}{7}$

#### Question 7:

Fill in the missing fractions:

(i)
(ii)
(iii)
(iv)

(i)
$\frac{7}{10}-\square =\frac{3}{10}\phantom{\rule{0ex}{0ex}}\square =\frac{7}{10}-\frac{3}{10}=\frac{7-3}{10}=\frac{4}{10}\phantom{\rule{0ex}{0ex}}\square =\frac{4}{10}$

(ii)
$\square -\frac{3}{21}=\frac{5}{21}\phantom{\rule{0ex}{0ex}}\square =\frac{3}{21}+\frac{5}{21}=\frac{3+5}{21}=\frac{8}{21}$

(iii)
$\square -\frac{3}{6}=\frac{3}{6}\phantom{\rule{0ex}{0ex}}\square =\frac{3}{6}+\frac{3}{6}=\frac{3+3}{6}=\frac{6}{6}=1$

(iv)
$\square -\frac{5}{27}=\frac{12}{27}\phantom{\rule{0ex}{0ex}}\square =\frac{12}{27}+\frac{5}{27}=\frac{12+5}{27}\phantom{\rule{0ex}{0ex}}\square =\frac{17}{27}$

#### Question 1:

(i) $\frac{3}{4}\mathrm{and}\frac{5}{6}$
(ii) $\frac{7}{10}\mathrm{and}\frac{2}{15}$
(iii) $\frac{8}{13}\mathrm{and}\frac{2}{3}$
(iv) $\frac{4}{5}\mathrm{and}\frac{7}{15}$

(i)

(ii)

(iii)

(iv)

#### Question 2:

Subtract:

(i) $\frac{2}{7}\mathrm{from}\frac{19}{21}$
(ii) $\frac{21}{25}\mathrm{from}\frac{18}{20}$
(iii)
(iv)

(i)

(ii)

(iii)

(iv)

#### Question 3:

Find the difference of:

(i) $\frac{13}{24}\mathrm{and}\frac{7}{16}$
(ii) $\frac{5}{18}\mathrm{and}\frac{4}{15}$
(iii) $\frac{1}{12}\mathrm{and}\frac{3}{4}$
(iv) $\frac{2}{3}\mathrm{and}\frac{6}{7}$

(i)

(ii)

(iii)

(iv)

#### Question 4:

Sbutract as indicated:

(i) $\frac{8}{3}-\frac{5}{9}$
(ii) $4\frac{2}{5}-2\frac{1}{5}$
(iii) $5\frac{6}{7}-2\frac{2}{3}$
(iv) $4\frac{3}{4}-2\frac{1}{6}$

#### Question 5:

Simplify:

(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
(ii) $\frac{5}{8}+\frac{2}{5}+\frac{3}{4}$
(iii) $\frac{3}{10}+\frac{7}{15}+\frac{3}{5}$
(iv) $\frac{3}{4}+\frac{7}{16}+\frac{5}{8}$
(v) $4\frac{2}{3}+3\frac{1}{4}+7\frac{1}{2}$
(vi) $7\frac{1}{3}+3\frac{2}{3}+5\frac{1}{6}$
(vii) $7+\frac{7}{4}+5\frac{1}{6}$
(viii) $\frac{5}{6}+3+\frac{3}{4}$
(ix) $\frac{7}{18}+\frac{5}{6}+1\frac{1}{12}$

#### Question 6:

Replace  by the correct number:
(i)
(ii)
(iii)

#### Question 7:

Savita bought $\frac{2}{5}$ m of ribbon and Kavita $\frac{3}{4}$ m of the ribbon. What was of the total length of the ribbon they bought?

Length of the ribbon bought by Savita =
Length of the ribbon bought by Kavita =
Total length of the ribbon bought by them:

#### Question 8:

Ravish takes $2\frac{1}{5}$ minutes to walk across the school ground. Rahul takes $\frac{7}{4}$ minutes to do the same. Who takes less time and by what fraction?

Time taken by Ravish = $2\frac{1}{5}=\frac{\left(5×2\right)+1}{5}=\frac{11}{5}$ minutes
Time taken by Rahul =
Comparing $\frac{11}{5}&\frac{7}{4}$, we get:

Rahul takes less time, i.e., $\frac{44}{20}-\frac{35}{20}=\frac{44-35}{20}=\frac{9}{20}$ minutes.

#### Question 9:

A piece of a wire $\frac{7}{8}$ metres long broke into two pieces. One piece was $\frac{1}{4}$ meter long. How long is the other piece?

Length of the wire = $\frac{7}{8}\mathrm{m}$
Length of one piece of wire =
Let the length of the second piece of wire be x m.

∴ Length of the wire = Length of one piece + Length of the second piece

Therefore, the length of the second piece is $\frac{5}{8}\mathrm{m}$.

#### Question 10:

Shikha and priya have bookshelves of the same size Shikha's shelf is $\frac{5}{6}$ full of book and Priya's shelf is $\frac{2}{5}$ full. Whose bookshelf is more full? By what fraction?

Fraction of Shikha's filled bookshelf = $\frac{5}{6}$

Fraction of Priya's filled bookshelf = $\frac{2}{5}$
Comparing , we get:
LCM of 5 & 6 is 30, so we will convert each fraction into an equivalent fraction with denominator 30.

$=\frac{5×5}{6×5},\frac{2×6}{5×6}\phantom{\rule{0ex}{0ex}}\frac{25}{30}>\frac{12}{30}$

Shikha's shelf is more full.

∴​ $\frac{25}{30}-\frac{12}{30}=\frac{25-12}{30}=\frac{13}{30}$

#### Question 11:

Ravish's house is $\frac{9}{10}$ Km from his school. He walked some distance and then took a bus for $\frac{1}{2}$ Km up to the school. How far did he walk?

Total distance between the house and the school =
Distance covered in the bus =
Distance covered by walking + Distance covered in the bus = Total distance between the house and the school
Distance covered by walking = Total distance between the house and the school - Distance covered in the bus
Distance covered by walking:

#### Question 1:

Which of the following is a proper fraction?

(a) $\frac{4}{3}$
(b) $\frac{3}{4}$
(c) $1\frac{3}{4}$
(d) $2\frac{1}{5}$

(b) $\frac{3}{4}$, because in a proper fraction, the numerator is less than the denominator.

#### Question 2:

Which of the following is an improper fraction ?

(a) $\frac{1}{2}$
(b) $\frac{3}{7}$
(c) $\frac{7}{3}$
(d) $\frac{3}{15}$

(c) $\frac{7}{3}$, because in an improper fraction, the numerator is more than the denominator.

#### Question 3:

Which of the following is a fraction equivalent of $\frac{2}{3}$?
(a) $\frac{4}{5}$
(b) $\frac{8}{6}$
(c) $\frac{10}{25}$
(d) $\frac{10}{15}$

#### Question 4:

A fraction equivalent to $\frac{3}{5}$is
(a) $\frac{3+2}{5+2}$
(b) $\frac{3-2}{5-2}$
(c) $\frac{3×2}{5×2}$
(d) None of these

(c) $\frac{3×2}{5×2}$
On dividing the numerator & denominator by 2, we get $\frac{3}{5}$.

#### Question 5:

If $\frac{5}{12}$ is equivalent of $\frac{x}{3}$, then x =

(a) $\frac{5}{4}$
(b) $\frac{4}{5}$
(c) $\frac{5}{3}$
(d) $\frac{3}{5}$

(a) $\frac{5}{4}$

On cross-multiplying, we get:

#### Question 6:

Which of the following are like fractions?

(a) $\frac{3}{5},\frac{3}{7},\frac{3}{11},\frac{3}{16}$
(b) $\frac{5}{11},\frac{7}{11},\frac{15}{11},\frac{2}{11}$
(c) $\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{6}{7}$
(d) None of these

(b), because like fractions are the fractions with the same denominator.

#### Question 7:

If $\frac{11}{4}=\frac{77}{x}$, then x =

(a) 28

(b) $\frac{77}{28}$
(c) 44

(d) 308

(a) 28

$\frac{11}{4}=\frac{77}{x}\phantom{\rule{0ex}{0ex}}$
On cross-multiplying, we get:

#### Question 8:

$\frac{1}{2\frac{1}{3}}+\frac{1}{1\frac{3}{4}}$ is equal to

(a) $\frac{7}{14}$
(b) $\frac{12}{49}$
(c) $4\frac{1}{12}$
(d) None of these

(d) None of these

$\frac{1}{2\frac{1}{3}}+\frac{1}{1\frac{3}{4}}=\frac{1}{\frac{\left(3×2\right)+1}{3}}+\frac{1}{\frac{\left(4×1\right)+3}{4}}\phantom{\rule{0ex}{0ex}}=\frac{1}{\frac{7}{3}}+\frac{1}{\frac{7}{4}}=\frac{3}{7}+\frac{4}{7}=\frac{3+4}{7}=\frac{7}{7}=1$

#### Question 9:

If $\frac{1}{3}+\frac{1}{2}+\frac{1}{x}=4$, then x = ?

(a) $\frac{5}{18}$
(b) $\frac{6}{19}$
(c) $\frac{18}{5}$
(d) $\frac{24}{11}$

(b) $\frac{6}{19}$

$\frac{1}{3}+\frac{1}{2}+\frac{1}{x}=4\phantom{\rule{0ex}{0ex}}\frac{1}{x}=4-\frac{1}{3}-\frac{1}{2}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{4×6}{1×6}-\frac{1×2}{3×2}-\frac{1×3}{2×3}=\frac{24}{6}-\frac{2}{6}-\frac{3}{6}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{24-2-3}{6}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{19}{6}\phantom{\rule{0ex}{0ex}}x=\frac{6}{19}$

#### Question 10:

If $\frac{1}{2}+\frac{1}{x}=2$, then x =

(a) $\frac{2}{5}$
(b) $\frac{5}{2}$
(c) $\frac{3}{2}$
(d) $\frac{2}{3}$

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

#### Question 11:

Which of the following fractions is the smallest?
$\frac{1}{2},\frac{3}{7},\frac{3}{5},\frac{4}{9}$

(a) $\frac{4}{9}$
(b) $\frac{3}{5}$
(c) $\frac{3}{7}$
(d) $\frac{1}{2}$

(c) $\frac{3}{7}$
The LCM of numerators is 12, so we can convert each fraction into an equivalent fraction with numerator 12.
$\frac{1}{2}=\frac{1}{2}×\frac{12}{12}=\frac{12}{24}\phantom{\rule{0ex}{0ex}}\frac{3}{7}=\frac{3}{7}×\frac{4}{4}=\frac{12}{28}\phantom{\rule{0ex}{0ex}}\frac{3}{5}=\frac{3}{5}×\frac{4}{4}=\frac{12}{20}\phantom{\rule{0ex}{0ex}}\frac{4}{9}=\frac{4}{9}×\frac{3}{3}=\frac{12}{27}$
When numerator is the same, the fraction with greater denominator is the smallest.
Thus, $\frac{3}{7}$ is the smallest fraction.

#### Question 12:

Which of the following fractions is the greatest of all?
$\frac{7}{8},\frac{6}{7},\frac{4}{5},\frac{5}{6}$

(a) $\frac{6}{7}$
(b) $\frac{4}{5}$
(c) $\frac{5}{6}$
(d) $\frac{7}{8}$

(d) $\frac{7}{8}$
The LCM of 8, 7, 6 and 5 is 840, so we can convert each fraction into an equivalent fraction with denominator 840.
$\frac{7}{8}=\frac{7}{8}×\frac{105}{105}=\frac{735}{840}\phantom{\rule{0ex}{0ex}}\frac{6}{7}=\frac{6}{7}×\frac{120}{120}=\frac{720}{840}\phantom{\rule{0ex}{0ex}}\frac{4}{5}=\frac{4}{5}×\frac{168}{168}=\frac{672}{840}\phantom{\rule{0ex}{0ex}}\frac{5}{6}=\frac{5}{6}×\frac{140}{140}=\frac{700}{840}$

When denominator is the same, the fraction with the largest numerator is the greatest.

Thus, $\frac{7}{8}$ is the greatest fraction among all.

#### Question 13:

What is the value of ?

(a) $\frac{3}{5}$
(b) $\frac{5}{3}$
(c) $\frac{4}{5}$
(d) $\frac{5}{4}$

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

#### Question 14:

If $\frac{a}{b}=\frac{4}{3},$ then the value of $\frac{6a+4b}{6a-5b}$ is

(a) −1
(b) 3
(c) 4
(d) 5

(c) 4

#### Question 15:

If $\frac{1}{5}-\frac{1}{6}=\frac{4}{x}$, then x =

(a) −120
(b) −100
(c) 100
(d) 120

(d) 120

$\frac{1}{5}-\frac{1}{6}=\frac{4}{x}\phantom{\rule{0ex}{0ex}}\frac{1×6}{5×6}-\frac{1×5}{6×5}=\frac{4}{x}\phantom{\rule{0ex}{0ex}}\frac{6}{30}-\frac{5}{30}=\frac{4}{x}\phantom{\rule{0ex}{0ex}}\frac{6-5}{30}=\frac{4}{x}\phantom{\rule{0ex}{0ex}}\frac{1}{30}=\frac{4}{x}\phantom{\rule{0ex}{0ex}}x=4×30=120$

#### Question 16:

The fraction to be added to $6\frac{7}{15}$ to get $8\frac{1}{5}$ is equal to

(a) $\frac{11}{15}$
(b) $1\frac{1}{15}$
(c) $\frac{44}{3}$
(d) $\frac{3}{44}$

(b) $1\frac{1}{15}$

Let the fraction to be added is x.

#### Question 17:

If $\frac{45}{60}$ is equivalent to $\frac{3}{x}$, then x =

(a) 5
(b) 4
(c) 6
(d) 20

(b) 4

#### Question 18:

A fraction equivalent to $\frac{45}{105}$ is

(a) $\frac{6}{14}$
(b) $\frac{4}{7}$
(c) $\frac{5}{7}$
(d) $\frac{7}{5}$

(a) $\frac{6}{14}$

$\frac{3}{7}=\frac{3}{7}×\frac{2}{2}=\frac{6}{14}$

#### Question 19:

$\frac{5}{8}+\frac{3}{4}-\frac{7}{12}$ is equal to

(a) $\frac{15}{24}$
(b) $\frac{17}{24}$
(c) $\frac{19}{24}$
(d) $\frac{21}{24}$

(c) $\frac{19}{24}$

#### Question 20:

The correct fraction in the box $\square$ is $\square$ $-\frac{5}{8}=\frac{1}{4}$

(a) $\frac{6}{8}$
(b) $\frac{7}{8}$
(c) $\frac{1}{2}$
(d) None of these

(b) $\frac{7}{8}$

#### Question 1:

Write the fraction represention the shaded portion: Fraction of the shaded portion =
(i) Total number of parts = 3
Number of shaded parts = 2
Fraction of the shaded portion = $\frac{2}{3}$
(ii) Total number of parts = 15
Number of shaded parts = 11
Fraction of the shaded portion = $\frac{11}{15}$
(iii) Total number of parts = 9
Number of shaded parts = 8
Fraction of the shaded portion = $\frac{8}{9}$
(iv) Total number of parts = 7
Number of shaded parts = 3
Fraction of the shaded portion = $\frac{3}{7}$
(v) Total number of parts = 9
Number of shaded parts = 4
Fraction of the shaded portion = $\frac{4}{9}$
(vi) Total number of parts = 4
Number of shaded parts = 2
Fraction of the shaded portion = $\frac{2}{4}=\frac{1}{2}$
(vii) Total number of parts = 2
Number of shaded parts = 1
Fraction of the shaded portion = $\frac{1}{2}$
(viii) Total number of parts = 5
Number of shaded parts = 1
Fraction of the shaded portion = $\frac{1}{5}$
(ix) Total number of parts = 4
Number of shaded parts = 1
Fraction of the shaded portion = $\frac{1}{4}$

#### Question 2:

Write the fraction represtion the shaded parts: Fraction of the shaded portion =

(i) Total number of parts = 9
Number of shaded parts = 3
Fraction of the shaded portion = $\frac{3}{9}=\frac{1}{3}$

(ii) Total number of parts = 8
Number of shaded parts = 5
Fraction of the shaded portion = $\frac{4}{8}$

(iii) Total number of parts = 12
Number of shaded parts = 3
Fraction of the shaded portion = $\frac{3}{12}=\frac{1}{4}$

(iv) Total number of parts = 10
Number of shaded parts = 5
Fraction of the shaded portion = $\frac{5}{10}=\frac{1}{2}$

#### Question 3:

Write the fraction representing the shaded portion: (i) Total number of portions = 2
Number of shaded portions = 1
Fraction of the shaded portions =
(ii) Total number of portions = 8
Number of shaded portions = 4
Fraction of the shaded portions =

#### Question 4:

Colour the part according to the fraction given:  #### Question 5:

What fraction of an hour is 20 minutes?

Minutes in an hour = 60
20 minutes of an hour = $\frac{20}{60}$ = $\frac{1}{3}$

#### Question 6:

Write the natural numbers form 2 to 12. What fraction of them are prime numbers?

Natural numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

Prime numbers from 2 to 12 are 2, 3, 5, 7 and 11.

Out of 11 numbers, 5 are prime.

Fraction of the prime numbers = $\frac{5}{11}$

#### Question 7:

Write the natural numbers from 102 to 113. What fraction of them are prime numbers.

Natural numbers from 102 to 113 are 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112 and 113.

Prime numbers from 102 to 113 are 103, 107, 109 and 113.

Out of 12 natural numbers, 4 are prime.

Fraction of the prime numbers = $\frac{4}{12}=\frac{1}{3}$

#### Question 8:

Mukesh has a box of 24 pencils. He gives half of them of Sunita. How many does sunita get?
How many does Mukesh still have?

Mukesh has 24 pencils.

Sunita gets half of Mukesh's pencils.

Sunita gets $\frac{24}{2}$ pencils, that is, 12 pencils.
Number of pencils Mukesh still has = 24 − 12 = 12

#### Question 9:

Kavita has 44 cassettes. She gives $\frac{3}{4}$ of them to Sonia. How many does Sonia get? How many does Kavita keep?

Kavita has 44 cassettes.

She gives $\frac{3}{4}$ of the cassettes to Sonia.
For this, Kavita divides 44 cassettes in 4 equal parts and takes 3 parts.

∴ 44 $÷$ 4 = 11
It means that Kavita gives 33 cassettes to Sonia.

Number of cassettes Kavita has = 44 - 33 = 11

#### Question 10:

Shikhas has three frocks that she wears when playing. The material is good, but the colours are faded. Her mother buys some blue dye and uses it on two of the frocks. What fraction of all of the Shikha play frocks did her mother dye?

Total frocks Shikha has = 3

Number of frocks dyed by Shikha's mother = 2

Fraction of the dyed frocks = $\frac{2}{3}$
Therefore, Shikha's mother dyed $\frac{2}{3}$ of Shikha's frocks.

#### Question 1:

Represent $\frac{2}{5}$ on a number line. #### Question 2:

Represent and $\frac{10}{10}$ on a number line. #### Question 3:

Represent and $\frac{6}{7}$ on a number line. #### Question 4:

How many fractions lie between 0 and 1.

Infinite. We can check this by taking numerator less than denominator in a fraction.

#### Question 5:

Represent $\frac{0}{8}$ and $\frac{8}{8}$ on a number line. #### Question 1:

Write each of the following division as fraction:

(i) 6 ÷ 3
(ii) 25 ÷ 5
(iii) 125 ÷ 50
(iv) 55 ÷ 11

(i) $\frac{6}{3}$
(ii) $\frac{25}{5}$
(iii) $\frac{125}{50}$
(iv) $\frac{55}{11}$

#### Question 2:

Write each of the following fraction as divisions:

(i) $\frac{9}{7}$
(ii) $\frac{3}{11}$
(iii) $\frac{90}{63}$
(iv) $\frac{1}{5}$