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#### Question 1:

Write the fraction representing the shaded portion:
(i) Figure
(ii) Figure
(iii) Figure
(iv) Figure
(v) Figure
(vi) Figure

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

#### Question 2:

Shade $\frac{4}{9}$ of the given figure.
Figure

#### Question 3:

In the given figure, if we say that the shaded region is $\frac{1}{4}$, then identify the error in it.
Figure

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:

Write a fraction for each of the following:
(i) three-fourths
(ii) four-sevenths
(iii) two-fifths
(iv) three-tenths
(v) one-eighth
(vi) five-sixths
(vii) eight-ninths
(viii) seven-twelfths

(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:

Write down the numerator and the denominator of each of the fractions given below:
(i) $\frac{4}{9}$
(ii) $\frac{6}{11}$
(iii) $\frac{8}{15}$
(iv) $\frac{12}{17}$
(v) $\frac{5}{1}$

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

#### Question 6:

Write down the fraction in which
(i) numerator = 3, denominator = 8
(ii) numerator = 5, denominator = 12
(iii) numerator = 7, denominator = 16
(iv) numerator = 8, denominator = 15

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

#### Question 7:

Write down the fractional number for each of the following:
(i) $\frac{2}{3}$
(ii) $\frac{4}{9}$
(iii) $\frac{2}{5}$
(iv) $\frac{7}{10}$
(v) $\frac{1}{3}$
(vi) $\frac{3}{4}$
(vii) $\frac{3}{8}$
(viii) $\frac{9}{14}$
(ix) $\frac{5}{11}$
(x) $\frac{6}{15}$

(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:

What fraction of an hour is 24 minutes?

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

#### Question 9:

How many natural numbers are there from 2 to 10? What fraction of them are prime numbers?

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:

Determine:
(i) $\frac{2}{3}$ of 15 pens
(ii) $\frac{2}{3}$ of 27 balls
(iii) $\frac{2}{3}$ of 36 balloons

(i) $\frac{2}{3}$ of 15 pens =
(ii) $\frac{2}{3}$ of 27 balls =
(iii) $\frac{2}{3}$ of 36 balloons = ​

#### Question 11:

Determine:
(i) $\frac{3}{4}$ of 16 cups
(ii) $\frac{3}{4}$ of 28 rackets
(iii) $\frac{3}{4}$ of 32 books

(i) $\frac{3}{4}$ of 16 cups =
(ii) $\frac{3}{4}$ of 28 rackets =
(iii) $\frac{3}{4}$ of 32 books =

#### Question 12:

Neelam has 25 pencils. She gives $\frac{4}{5}$ of them to Meena. How many pencils does Meena get? How many pencils are left with Neelam?

Neelam gives $\frac{4}{5}$ of 25 pencils to Meena.

Thus, Meena gets 20 pencils.
∴ Number of pencils left with Neelam = 25 $-$ 20 = 5 pencils
Thus, 5 pencils are left with Neelam.

#### Question 13:

Represent each of the following fractions on the number line:
(i) $\frac{3}{8}$
(ii) $\frac{5}{9}$
(iii) $\frac{4}{7}$
(iv) $\frac{2}{5}$
(v) $\frac{1}{4}$

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:

Which of the following are proper fractions?

#### Question 2:

Which of the following are improper fractions?

A fraction whose numerator is greater than or equal to its denominator is called an improper fraction. Hence,  are improper fractions.

#### Question 3:

Write six improper fractions with denominator 5.

Clearly,  are improper fractions, each with 5 as the denominator.

#### Question 4:

Write six improper fractions with numerator 13.

Clearly, are improper fractions, each with 13 as the numerator.

#### Question 5:

Convert each of the following into an improper fraction:
(i) $5\frac{5}{7}$
(ii) $9\frac{3}{8}$
(iii) $6\frac{3}{10}$
(iv) $3\frac{5}{11}$
(v) $10\frac{9}{14}$
(vi) $12\frac{7}{15}$
(vii) $8\frac{8}{13}$
(viii) $51\frac{2}{3}$

We have:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

#### Question 6:

Convert each of the following into a mixed fraction:
(i) $\frac{17}{5}$
(ii) $\frac{62}{7}$
(iii) $\frac{101}{8}$
(iv) $\frac{95}{13}$
(v) $\frac{81}{11}$
(vi) $\frac{87}{16}$
(vii) $\frac{103}{12}$
(viii) $\frac{117}{20}$

(i) On dividing 17 by 5, we get:
Quotient = 3
Remainder = 2
∴

(ii) On dividing 62 by 7, we get:
Quotient = 8
Remainder = 6
∴

(iii) On dividing 101 by 8, we get:
Quotient = 12
Remainder = 5
∴

(iv) On dividing 95 by 13, we get:
Quotient = 7
Remainder = 4
∴

(v) On dividing 81 by 11, we get:
Quotient = 7
Remainder = 4
∴

(vi) On dividing 87 by 16, we get:
Quotient = 5
Remainder = 7
∴

(vii) On dividing 103 by 12, we get:
Quotient = 8
Remainder = 7
∴

(viii) On dividing 117 by 20, we get:
Quotient = 5
Remainder = 17
∴

#### Question 7:

Fill up the blanks with '>', '<' or '=':
(i)
(ii)
(iii)
(iv)
(v)
(vi)

An improper fraction is greater than 1. Hence, it is always greater than a proper fraction, which is less than 1.
(i)

(ii)

(iii)

(iv)

(v)

(vi)

#### Question 8:

Draw number lines and locate the following points:
(i)
(ii)
(iii)

(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:

Write five fractions equivalent to each of the following:
(i) $\frac{2}{3}$
(ii) $\frac{4}{5}$
(iii) $\frac{5}{8}$
(iv) $\frac{7}{10}$
(v) $\frac{3}{7}$
(vi) $\frac{6}{11}$
(vii) $\frac{7}{9}$
(viii) $\frac{5}{12}$

(i)

∴

Hence, the five fractions equivalent to $\frac{2}{3}$ are .

(ii) ​

∴

Hence, the five fractions equivalent to $\frac{4}{5}$ are .

(iii) ​

∴

Hence, the five fractions equivalent to $\frac{5}{8}$ are .

(iv) ​

∴

Hence, the five fractions equivalent to $\frac{7}{10}$ are .

(v) ​​

∴

Hence, the five fractions equivalent to $\frac{3}{7}$ are .

(vi)  ​

∴

Hence, the five fractions equivalent to $\frac{6}{11}$ are .

(vii)

∴

Hence, the five fractions equivalent to $\frac{7}{9}$ are .

(viii)

∴

Hence, the five fractions equivalent to $\frac{5}{12}$ are .

#### Question 2:

Which of the following are the pairs of equivalent fractions?
(i)
(ii)
(iii)
(iv)
(v)
(vi)

The pairs of equivalent fractions are as follows:
(i)
(ii)
(iv)

#### Question 3:

Find the equivalent fraction of $\frac{3}{5}$ having
(i) denominator 30
(ii) numerator 24

(i) Let
Clearly, 30 = 5 $×$ 6
So, we multiply the numerator by 6.

∴ ​
Hence, the required fraction is $\frac{18}{30}$.
(ii)  ​Let
Clearly, 24 = 3 $×$ 8
So, we multiply the denominator by 8.

∴ ​
Hence, the required fraction is $\frac{24}{40}$.

#### Question 4:

Find the equivalent fraction of $\frac{5}{9}$ having
(i) denominator 54
(ii) numerator 35

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

#### Question 5:

Find the equivalent fraction of $\frac{6}{11}$ having
(i) denominator 77
(ii) numerator 60

(i) Let
Clearly, 77 = 11 $×$ 7
So, we multiply the numerator by 7.

∴ ​
Hence, the required fraction is $\frac{42}{77}$.
(ii)  ​Let
Clearly, 60 = 6 $×$ 10
So, we multiply the denominator by 10.

∴ ​
Hence, the required fraction is $\frac{60}{110}$.

#### Question 6:

Find the equivalent fraction of $\frac{24}{30}$ having numerator 4.

Let
Clearly, 4 = 24 $÷$ 6
So, we divide the denominator by 6.
∴ ​
Hence, the required fraction is $\frac{4}{5}$.

#### Question 7:

Find the equivalent fraction of $\frac{36}{48}$ with
(i) numerator 9
(ii) denominator 4

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

#### Question 8:

Find the equivalent fraction of $\frac{56}{70}$ with
(i) numerator 4
(ii) denominator 10

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

#### Question 9:

Reduce each of the following fractions into its simplest form:
(i) $\frac{9}{15}$
(ii) $\frac{48}{60}$
(iii) $\frac{84}{98}$
(iv) $\frac{150}{60}$
(v) $\frac{72}{90}$

(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.
∴
Hence, the simplest form of .

(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.
∴
Hence, the simplest form of .

(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.
∴
Hence, the simplest form of .

(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.
∴
Hence, the simplest form of .

(v) ​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.
∴
Hence, the simplest form of .

#### Question 10:

Show that each of the following fractions is in the simplest form:
(i) $\frac{8}{11}$
(ii) $\frac{9}{14}$
(iii) $\frac{25}{36}$
(iv) $\frac{8}{15}$
(v) $\frac{21}{10}$

(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:

Replace by the correct number in each of the following:
(i)
(ii)
(iii)
(iv)
(v)
(vi)

(i) 28
(ii) 21
(iii) 32
(iv) 12
(v) 5
(vi) 9

#### Question 1:

Define like and unlike fractions and give five examples of each.

Like fractions:
Fractions having the same denominator are called like fractions.
Examples:

Unlike fractions:
Fractions having different denominators are called unlike fractions.
Examples:

#### Question 2:

Convert into like fractions.

The given fractions are

L.C.M. of 5, 10, 15 and 30 = (5 $×$ 2 $×$ 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:

Hence, the required like fractions are

#### Question 3:

Convert into like fractions.

The given fractions are
L.C.M. of 4, 8, 12 and 24 = (4 $×$ 2 $×$ 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:

Hence, the required like fractions are

#### Question 4:

Fill in the place holders with the correct symbol > or <:
(i)
(ii)
(iii)
(iv)
(v)
(vi)

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:

Fill in the place holders with the correct symbol > or <:
(i)
(ii)
(iii)
(iv)
(v)
(vi)

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:

Compare the fractions given below:

By cross multiplying:
5 $×$ 5 = 25 and 4 $×$ 7 = 28
Clearly, 28 > 25
$\therefore$

#### Question 7:

Compare the fractions given below:

By cross multiplying:
3 $×$ 6 = 18 and 5 $×$ 8 = 40
Clearly, 18 < 40
$\therefore$

#### Question 8:

Compare the fractions given below:

By cross multiplying:
7 $×$ 7 = 49 and 11 $×$ 6 = 66
Clearly, 49 < 66
$\therefore$

#### Question 9:

Compare the fractions given below:

By cross multiplying:
5 $×$ 11 = 55 and 9 $×$ 6 = 54
Clearly, 55 > 54
$\therefore$

#### Question 10:

Compare the fractions given below:

By cross multiplying:
2 $×$ 9 = 18 and 4 $×$ 3 = 12
Clearly, 18 > 12
$\therefore$

#### Question 11:

Compare the fractions given below:

By cross multiplying:
6 $×$ 4 = 24 and 13 $×$ 3 = 39
Clearly, 24 < 39
$\therefore$

#### Question 12:

Compare the fractions given below:

By cross multiplying:
3 $×$ 6 = 18 and 4 $×$ 5 = 20
Clearly, 18 < 20
$\therefore$

#### Question 13:

Compare the fractions given below:

By cross multiplying:
5 $×$ 12 = 60 and 8 $×$ 7 = 56
Clearly, 60 > 56
$\therefore$

#### Question 14:

Compare the fractions given below:

L.C.M. of 9 and 6 = (3 $×$ 3 $×$ 2) = 18
Now, we convert  into equivalent fractions having 18 as the denominator.
∴​ 4949

Clearly,
$\therefore$

#### Question 15:

Compare the fractions given below:

L.C.M. of 5 and 10 = (5 $×$ 2) = 10
Now, we convert  into an equivalent fraction having 10 as the denominator as the other fraction has already 10 as its denominator.
∴​ 4949

Clearly,
$\therefore$

#### Question 16:

Compare the fractions given below:

L.C.M. of 8 and 10 = (2 $×$ 5 $×$ 2 $×$ 2) = 40
Now, we convert  into equivalent fractions having 40 as the denominator.
∴​ 4949

Clearly,
$\therefore$

#### Question 17:

Compare the fractions given below:

L.C.M. of 12 and 15 = (2 $×$ 2 $×$ 3 $×$ 5) = 60
Now, we convert  into equivalent fractions having 60 as the denominator.
∴​ 4949

Clearly,
$\therefore$

#### Question 18:

Arrange the following fractions in ascending order:

The given fractions are .
L.C.M. of 2, 4, 6 and 8 = (2 $×$ 2 $×$ 2 $×$ 3) = 24
We convert each of the given fractions into an equivalent fraction with denominator 24.
Now, we have:

Clearly,

∴ ​
Hence, the given fractions can be arranged in the ascending order as follows:

#### Question 19:

Arrange the following fractions in ascending order:

The given fractions are

L.C.M. of 3, 6, 9 and 18 = (3 $×$ 2  $×$ 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:

Clearly,
∴ ​

Hence, the given fractions can be arranged in the ascending order as follows:

#### Question 20:

Arrange the following fractions in ascending order:

The given fractions are
L.C.M. of 5, 10, 15 and 30 = (2 $×$ 5 $×$ 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:

Clearly,
∴ ​

Hence, the given fractions can be arranged in the ascending order as follows:

#### Question 21:

Arrange the following fractions in ascending order:

The given fractions are
L.C.M. of 4, 8, 16 and 32 = (2 ⨯ 2 ⨯ 2 ⨯ 2 ⨯ 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:

Clearly,
∴ ​

Hence, the given fractions can be arranged in the ascending order as follows:

#### Question 22:

Arrange the following fractions in descending order:

The given fractions are
L.C.M. of 4, 8, 12 and 24 = (2 ⨯ 2 ⨯ 2 ⨯ 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;

Clearly,

∴ ​

Hence, the given fractions can be arranged in the descending order as follows:

#### Question 23:

Arrange the following fractions in descending order:

The given fractions are
L.C.M. of 9, 12, 18 and 36 = (3 ⨯ 3 ⨯ 2 ⨯ 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:

Clearly,

∴ ​

Hence, the given fractions can be arranged in the descending order as follows:

#### Question 24:

Arrange the following fractions in descending order:

The given fractions are
L.C.M. of 3, 5,10 and 15 = (2 ⨯ 3 ⨯ 5) = 30

So, we convert each of the fractions into an equivalent fraction with denominator 30.
Thus, we have:

Clearly,
∴ ​

Hence, the given fractions can be arranged in the descending order as follows:

#### Question 25:

Arrange the following fractions in descending order:

The given fractions are
L.C.M. of 7, 14, 21 and 42 = (2 ⨯ 3 ⨯ 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:

Clearly,
∴ ​
Hence, the given fractions can be arranged in the descending order as follows:

#### Question 26:

Arrange the following fractions in descending order:

The given fractions are
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,
Hence, the given fractions can be arranged in the descending order as follows:

#### Question 27:

Arrange the following fractions in descending order:

The given fractions are
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,
Hence, the given fractions can be arranged in the descending order as follows:

#### Question 28:

Lalita read 30 pages of a book containing 100 pages while Sarita read $\frac{2}{5}$ of the book. Who read more?

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 = ​
Hence, Sarita read more pages than Lalita as 40 is greater than 30.

#### Question 29:

Rafiq exercised for $\frac{2}{3}$ hour, while Rohit exercise for $\frac{3}{4}$ hour. Who exercised for a longer time?

To know who exercised for a longer time, we have to compare .
On cross multiplying:
4 $×$ 2 = 8 and 3 $×$ 3 = 9
Clearly, 8 < 9
$\therefore$
Hence, Rohit exercised for a longer time.

#### Question 30:

In a school 20 students out of 25 passed in VI A, while 24 out of 30 passed in VI B. Which section gave better result?

Fraction of students who passed in VI A =

Fraction of students who passed in VI B =
In both the sections, the fraction of students who passed is the same, so both the sections have the same result.

#### Question 1:

Find the sum:
$\frac{5}{8}+\frac{1}{8}$

The given fractions are like fractions.
We know:
Sum of like fractions  =
Thus, we have:

#### Question 2:

Find the sum:
$\frac{4}{9}+\frac{8}{9}$

The given fractions are like fractions.
We know:
Sum of like fractions  =
Thus, we have:

#### Question 3:

Find the sum:
$1\frac{3}{5}+2\frac{4}{5}$

The given fractions are like fractions.
We know:
Sum of like fractions  =
Thus, we have:

#### Question 4:

Find the sum:
$\frac{2}{9}+\frac{5}{6}$

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

Now, we have:

#### Question 5:

Find the sum:
$\frac{7}{12}+\frac{9}{16}$

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

Now, we have:

#### Question 6:

Find the sum:
$\frac{4}{15}+\frac{17}{20}$

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

#### Question 7:

Find the sum:
$2\frac{3}{4}+5\frac{5}{6}$

We have:

234+556

#### Question 8:

Find the sum:
$3\frac{1}{8}+1\frac{5}{12}$

We have:

234+556

#### Question 9:

Find the sum:
$2\frac{7}{10}+3\frac{8}{15}$

We have:

234+556

#### Question 10:

Find the sum:
$3\frac{2}{3}+1\frac{5}{6}+2$

We have:

234+556

#### Question 11:

Find the sum:
$3+1\frac{4}{15}+1\frac{3}{20}$

We have:

234+556

#### Question 12:

Find the sum:
$3\frac{1}{3}+4\frac{1}{4}+6\frac{1}{6}$

We have:

234+556

#### Question 13:

Find the sum:
$\frac{2}{3}+3\frac{1}{6}+4\frac{2}{9}+2\frac{5}{18}$

We have:

234+556

#### Question 14:

Find the sum:
$2\frac{1}{3}+1\frac{1}{4}+2\frac{5}{6}+3\frac{7}{12}$

We have:

234+556

#### Question 15:

Find the sum:
$2+\frac{3}{4}+1\frac{5}{8}+3\frac{7}{16}$

We have:

234+556

#### Question 16:

Rohit bought a pencil for Rs $3\frac{2}{5}$ and an eraser for Rs $2\frac{7}{10}$. What is the total cost of both the articles?

Total cost of both articles = Cost of pencil + Cost of eraser
Thus, we have:

Hence, the total cost of both the articles is .

#### Question 17:

Sohini bought $4\frac{1}{2}\mathrm{m}$ of cloth for her kurta and $2\frac{2}{3}\mathrm{m}$ of cloth for her pyjamas. Ho much cloth did she purchase in all?

Total cloth purchased by Sohini = Cloth for kurta + Cloth for pyjamas
Thus, we have:

$\therefore$ Total length of cloth purchased =

#### Question 18:

While coming back home from his school, Kishan covered $4\frac{3}{4}$ km by rickshaw and $1\frac{1}{2}$ km on foot. What is the distance of his house from the school?

Distance from Kishan's house to school = Distance covered by him by rickshaw + Distance covered by him on foot
Thus, we have:

Hence, the distance from Kishan's house to school is .

#### Question 19:

The weight of an empty gas cylinder is $16\frac{4}{5}$ kg and it contains $14\frac{2}{3}$ kg of gas. What is the weight of the cylinder filled with gas?

Weight of the cylinder filled with gas = Weight of the empty cylinder + Weight of the gas inside the cylinder
Thus, we have:

Hence, the weight of the cylinder filled with gas is .

#### Question 1:

Find the difference:
$\frac{5}{8}-\frac{1}{8}$

Difference of like fractions = Difference of numerator $÷$ Common denominator

#### Question 2:

Find the difference:
$\frac{7}{12}-\frac{5}{12}$

Difference of like fractions = Difference of numerator $÷$ Common denominator

#### Question 3:

Find the difference:
$4\frac{3}{7}-2\frac{4}{7}$

Difference of like fractions = Difference of numerator $÷$ Common denominator

#### Question 4:

Find the difference:
$\frac{5}{6}-\frac{4}{9}$

L.C.M. of 6 and 9 = (3 $×$ 2 $×$ 3) = 18
Now, we have:

#### Question 5:

Find the difference:
$\frac{1}{2}-\frac{3}{8}$

L.C.M. of 2 and 8 = (2 $×$ 2 $×$ 2) = 8
Now, we have:

#### Question 6:

Find the difference:
$\frac{5}{8}-\frac{7}{12}$

L.C.M. of 8 and 12 = (2 $×$ 2$×$ 2$×$3) = 24
Now, we have:

#### Question 7:

Find the difference:
$2\frac{7}{9}-1\frac{8}{15}$

#### Question 8:

Find the difference:
$3\frac{5}{8}-2\frac{5}{12}$

#### Question 9:

Find the difference:
$2\frac{3}{10}-1\frac{7}{15}$

#### Question 10:

Find the difference:
$6\frac{2}{3}-3\frac{3}{4}$

#### Question 11:

Find the difference:

#### Question 12:

Find the difference:

#### Question 13:

Simplify:
$\frac{5}{6}-\frac{4}{9}+\frac{2}{3}$

We have:

#### Question 14:

Simplify:
$\frac{5}{8}+\frac{3}{4}-\frac{7}{12}$

We have:

234+556

#### Question 15:

Simplify:
$2+\frac{11}{15}-\frac{5}{9}$

We have:
234+556

#### Question 16:

Simplify:
$5\frac{3}{4}-4\frac{5}{12}+3\frac{1}{6}$

We have:

234+556

#### Question 17:

Simplify:
$2+5\frac{7}{10}-3\frac{14}{15}$

We have:

#### Question 18:

Simplify:
$8-3\frac{1}{2}-2\frac{1}{4}$

We have:

#### Question 19:

Simplify:
$8\frac{5}{6}-3\frac{3}{8}+2\frac{7}{12}$

We have:

#### Question 20:

Simplify:
$6\frac{1}{6}-5\frac{1}{5}+3\frac{1}{3}$

We have:

#### Question 21:

Simplify:
$3+1\frac{1}{5}+\frac{2}{3}-\frac{7}{15}$

We have:

#### Question 22:

What should be added to $9\frac{2}{3}$ to get 19?

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

923

#### Question 23:

What should be added to $6\frac{7}{15}$ to get $8\frac{1}{5}$?

Let x be added to $6\frac{7}{15}$ to get $8\frac{1}{5}$.

#### Question 24:

Subtract the sum of $3\frac{5}{9}$ and $3\frac{1}{3}$ from the sum of $5\frac{5}{6}$ and $4\frac{1}{9}$.

#### Question 25:

Of $\frac{3}{4}$ and $\frac{5}{7}$, which is greater and by how much?

Let us compare .
3 $×$ 7 = 21 and 4 $×$ 5 = 20
Clearly, 21 > 20

Required difference:

Hence, .

#### Question 26:

Mrs Soni bought $7\frac{1}{2}$ litres of milk. Out of this milk, $5\frac{3}{4}$ litres was consumed. How much milk is left with her?

Amount of milk left with Mrs. Soni = Total amount of milk bought by her $-$ Amount of milk consumed
$\therefore$ Amount of milk left with Mrs. Soni

$\therefore$ Milk left with Mrs. Soni =

#### Question 27:

A film show lasted for $3\frac{1}{3}$ hours. Out of his time, $1\frac{3}{4}$ hours was spent on advertisements. What was the actual duration of the film?

Actual duration of the film = Total duration of the show $-$ Time spent on advertisements

Thus, the actual duration of the film was .

#### Question 28:

In one day, a rickshaw puller earned Rs $137\frac{1}{2}$. Out of this money, he spent Rs $56\frac{3}{4}$ on food. How much money is left with him?

Money left with the rickshaw puller = Money earned by him in a day $-$ Money spent by him on food

Hence, Rs $80\frac{3}{4}$ is left with the rickshaw puller.

#### Question 29:

A piece of wire, $2\frac{3}{4}$ metres long, broke into two pieces. One piece is $\frac{5}{8}$ metre long. How long is the other piece?

The length of the other piece = (Length of the wire $-$ Length of one piece)

Hence, the other piece is  long.

#### Question 1:

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)

#### Question 2:

A fraction equivalent to $\frac{8}{12}$ is
(a) $\frac{8+4}{12+4}$
(b) $\frac{8-4}{12-4}$
(c) $\frac{8÷4}{12÷4}$
(d) none of these

(c)

#### Question 3:

A fraction equivalent to $\frac{24}{36}$ is
(a) $\frac{3}{4}$
(b) $\frac{2}{3}$
(c) $\frac{8}{9}$
(d) none of these

#### Question 4:

If $\frac{3}{4}$ is equivalent to $\frac{x}{20}$ then the value of x is
(a) 15
(b) 18
(c)12
(d) none of these

(a) 15

Explanation:

#### Question 5:

If $\frac{45}{60}$ is equivalent to $\frac{3}{x}$ then the value of x is
(a) 4
(b) 5
(c) 6
(d) none of these

(a) 4

Explanation:

#### Question 6:

Which of the following are like fractions?
(a)
(b)
(c)
(d) none of these

(c)

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

#### Question 7:

Which of the following is a proper fraction?
(a) $\frac{5}{3}$
(b) 5
(c) $1\frac{2}{5}$
(d) none of these

(d) none of these

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

#### Question 8:

Which of the following is a proper fractions?
(a) $\frac{7}{8}$
(b) $1\frac{7}{8}$
(c) $\frac{8}{7}$
(d) none of these

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

#### Question 9:

Which of the following statements is correct?
(a) $\frac{3}{4}<\frac{3}{5}$
(b) $\frac{3}{4}>\frac{3}{5}$
(c) $\frac{3}{4}$ and $\frac{3}{5}$ cannot be compared

(b)
Between the two fractions with the same numerator, the one with the smaller denominator is the greater.

#### Question 10:

The smallest of the fractions is
(a) $\frac{2}{3}$
(b) $\frac{7}{10}$
(c) $\frac{3}{5}$
(d) $\frac{5}{6}$

(c) $\frac{3}{5}$

L.C.M. of 5, 3, 6 and 10 = (2 $×$ 3 $×$ 5) = 30
Thus, we have:

#### Question 11:

The largest of the fractions is
(a) $\frac{4}{11}$
(b) $\frac{4}{5}$
(c) $\frac{4}{7}$
(d) $\frac{4}{9}$

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

#### Question 12:

The smallest of the fractions is
(a) $\frac{6}{11}$
(b) $\frac{7}{11}$
(c) $\frac{8}{11}$
(d) $\frac{9}{11}$

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

#### Question 13:

The smallest of the fractions is
(a) $\frac{2}{3}$
(b) $\frac{3}{4}$
(c) $\frac{5}{6}$
(d) $\frac{7}{12}$

(d) $\frac{7}{12}$

Explanation:

​​L.C.M. of 4, 6, 12 and 3 = (2 $×$ 2 $×$ 3) = 12
Thus, we have:

#### Question 14:

$4\frac{3}{5}=?$
(a) $\frac{17}{5}$
(b) $\frac{23}{5}$
(c) $\frac{17}{3}$
(d) none of these

(b) $\frac{23}{5}$

#### Question 15:

$\frac{34}{7}=?$
(a) $3\frac{4}{7}$
(b) $7\frac{3}{4}$
(c) $4\frac{6}{7}$
(d) none of these

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

#### Question 16:

$\frac{5}{8}+\frac{1}{8}=?$
(a) $\frac{3}{8}$
(b) $\frac{3}{4}$
(c) 6
(d) none of these

(b) $\frac{3}{4}$

Explanation:

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

#### Question 17:

$\frac{5}{8}-\frac{1}{8}=?$
(a) $\frac{1}{4}$
(b) $\frac{1}{2}$
(c) $\frac{1}{16}$
(d) none of these

(b) $\frac{1}{2}$
Explanation:

#### Question 18:

$3\frac{3}{4}-2\frac{1}{4}=?$
(a) $1\frac{1}{2}$
(b) $1\frac{1}{4}$
(c) $\frac{1}{4}$
(d) none of these

#### Question 19:

$\frac{5}{6}+\frac{2}{3}-\frac{4}{9}=?$
(a) $1\frac{1}{3}$
(b) $1\frac{1}{6}$
(c) $1\frac{1}{9}$
(d) $1\frac{1}{18}$

(d) $1\frac{1}{18}$

Explanation:

#### Question 20:

Which is greater: ?
(a) $3\frac{1}{3}$
(b) $\frac{33}{10}$
(c) both are equal

(a) $3\frac{1}{3}$

Explanation:
Let us compare  .
10 ⨯ 10 = 100 and 3 ​⨯ 33 = 99
Clearly, 100 > 99
∴

#### Question 1:

Define a fraction. Give five examples of fractions.

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:

#### Question 2:

What fraction of an hour is 35 minutes?

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

#### Question 3:

Find the equivalent fraction of 5/8 with denominator 56.

56 = 8 ⨯ 7
So, we need to multiply the numerator by 7.

$\therefore$
Hence, the required fraction is $\frac{35}{56}$.

#### Question 4:

Represent $2\frac{3}{5}$ on the number line.

Let OA = AB = BC = 1 unit
$\therefore$ 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:

Find the sum $2\frac{4}{5}+1\frac{3}{10}+3\frac{1}{15}$.

We have:

#### Question 6:

The cost of a pen is Rs $16\frac{2}{3}$ and that of a pencil is Rs $4\frac{1}{6}$.
Which costs more and by how much?

Cost of a pen =

Cost of a pencil =

So, the cost of a pen is more than the cost of a pencil.
Difference between their costs:

Hence, the cost of a pen is Rs $12\frac{1}{2}$ more than the cost of a pencil.

#### Question 7:

Of $\frac{3}{4}$ and $\frac{5}{7}$, which is greater and by how much?

Let us compare .
By cross multiplying:
3 ⨯ 7 = 21 and ​4 ⨯ 5 = 20
Clearly, 21 > 20
∴​$\frac{3}{4}>\frac{5}{7}$
Their difference:

Hence,

#### Question 8:

Convert the fractions and $\frac{5}{6}$ into like fractions.

L.C.M. of 2, 3, 9 and 6 = (2 ⨯ 3 ​⨯ 3) = 18
Now, we have:

#### Question 9:

Find the equivalent fraction of $\frac{3}{5}$ having denominator 30.

30 = 5 ​⨯ 6
So, we have to multiply the numerator by 6 to get the equivalent fraction having denominator 30.

Thus,

#### Question 10:

Reduce $\frac{84}{98}$ to the simplest form.

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.:

#### Question 11:

$\frac{24}{11}$ is an example of
(a) a proper fraction
(b) an improper fraction
(c) a mixed fraction
(d) none of these

(b) an improper fraction

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

#### Question 12:

$\frac{3}{8}$ is an example of
(a) a proper fraction
(b) an improper fraction
(c) a mixed fraction
(d) none of these

(a) proper fraction

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

#### Question 13:

$\frac{3}{8}$ and $\frac{5}{12}$ on comparison give
(a) $\frac{3}{8}>\frac{5}{12}$
(b) $\frac{3}{8}<\frac{5}{12}$
(c) $\frac{3}{8}=\frac{5}{12}$
(d) none of these

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

Considering :

#### Question 14:

The largest of the fractions and $\frac{7}{12}$ is
(a) $\frac{2}{3}$
(b) $\frac{5}{9}$
(c) $\frac{7}{12}$
(d) $\frac{1}{2}$

(a) $\frac{2}{3}$

Explanation:
L.C.M. of 3, 9, 2 and 12 = ( 2 ⨯ 2 ⨯ 3 ​⨯ 3) = 36
Now, we have:

#### Question 15:

$3\frac{3}{4}-1\frac{1}{2}=?$
(a) $2\frac{1}{2}$
(b) $2\frac{1}{4}$
(c) $1\frac{1}{2}$
(d) $1\frac{1}{4}$

(b) $2\frac{1}{4}$
Explanation:

#### Question 16:

Which of the following are like fractions?
(a)
(b)
(c)
(d) none of these

(c)
Like fractions have same the denominator.

#### Question 17:

$?-\frac{8}{21}=\frac{8}{21}$
(a) 0
(b) 1
(c) $\frac{21}{8}$
(d) $\frac{16}{21}$

(d) $\frac{16}{21}$

#### Question 18:

Fill in the blanks:
(i) $9\frac{2}{3}+......=19$
(ii) $6\frac{1}{6}-?=\frac{29}{30}$
(iii)
(iv) $\frac{72}{90}$ reduced to simples form is ......
(v)

(ii)

(iii)

(iv)

(v)

#### Question 19:

Write 'T' for true and 'F' for false for each of the statements given below:
(a) $3\frac{1}{3}>\frac{33}{10}$.
(b) $8-1\frac{5}{6}=7\frac{1}{6}$.
(c) and $\frac{1}{4}$ are like fractions.
(d) $\frac{3}{5}$ lies between 3 and 5.
(e) Among the largest fractions is $\frac{4}{3}$.