NCERT Solutions Class 7th Math Chapter – 2 Fractions and Decimals Exercise – 2.3

1. Find:

(i) 12 ÷ ¾

Solution:

We have,
= 12 × reciprocal of ¾
= 12 × (4/3)
= 4 × 4
= 16

(ii) 14 ÷ 5/6

Solution:

We have,
= 14 × reciprocal of (5/6)
= 14 × (6/5)
= 84/5

(iii) 8 ÷ 7/3

Solution:

We have,
= 8 × reciprocal of (7/3)
= 8 × (3/7)
= (24/7)

(iv) 4 ÷ 8/3

Solution: 

We have,
= 4 × reciprocal of (8/3)
= 4 × (3/8)
= 1 × (3/2)
= 3/2

Solution:

While dividing a whole number by a mixed fraction, first convert the mixed fraction into improper fraction

Then,
= 3 ÷ (7/3)
= 3 × reciprocal of (7/3)
= 3 × (3/7)
= 9/7

Solution:

While dividing a whole number by a mixed fraction, first convert the mixed fraction into improper fraction

Then,
= 5 ÷ (25/7)
= 5 × reciprocal of (25/7)
= 5 × (7/25)
= 1 × (7/5)
= 7/5

2. Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.

(i) 3/7

Solution:

Reciprocal of (3/7) is (7/3) [∵ ((3/7) × (7/3)) = 1]
So, it is an improper fraction.
Improper fraction is that fraction in which numerator is greater than its denominator.

(ii) 5/8

Solution:

Reciprocal of (5/8) is (8/5) [∵ ((5/8) × (8/5)) = 1]
So, it is an improper fraction.
Improper fraction is that fraction in which numerator is greater than its denominator.

(iii) 9/7

Solution:

Reciprocal of (9/7) is (7/9) [∵ ((9/7) × (7/9)) = 1]
So, it is a proper fraction.
A proper fraction is that fraction in which denominator is greater than the numerator of the fraction.

(iv) 6/5

Solution:

Reciprocal of (6/5) is (5/6) [∵ ((6/5) × (5/6)) = 1]
So, it is a proper fraction.
A proper fraction is that fraction in which denominator is greater than the numerator of the fraction.

(v) 12/7

Solution:

Reciprocal of (12/7) is (7/12) [∵ ((12/7) × (7/12)) = 1]
So, it is a proper fraction.
A proper fraction is that fraction in which denominator is greater than the numerator of the fraction.

(vi) 1/8

Solution:

Reciprocal of (1/8) is (8/1) or 8 [∵ ((1/8) × (8/1)) = 1]
So, it is a whole number.
Whole numbers are collection of all positive integers including 0.

(vii) 1/11

Solution: 

Reciprocal of (1/11) is (11/1) or 11 [∵ ((1/11) × (11/1)) = 1]
So, it is a whole number.
Whole numbers are collection of all positive integers including 0.

3. Find:

(i) 7/3 ÷ 2

Solution:

We have,
= (7/3) × reciprocal of 2
= (7/3) × (1/2)
= (7 × 1) / (3 × 2)
= 7/6

(ii) 4/9 ÷ 5

Solution:

We have,
= (4/9) × reciprocal of 5
= (4/9) × (1/5)
= (4 × 1) / (9 × 5)
= 4/45

(iii) 6/13 ÷ 7

Solution:

We have,
= (6/13) × reciprocal of 7
= (6/13) × (1/7)
= (6 × 1) / (13 × 7)
= 6/91

(iv) 4 _{¹/3 ÷ 3}

Solution:

First covert the mixed fraction into improper fraction. , We have

Then,
= (13/3) × reciprocal of 3
= (13/3) × (1/3)
= (13 × 1) / (3 × 3)
= 13/9

(v) 3 ½ ÷ 4

Solution:

First covert the mixed fraction into improper fraction. ,We have
= 3 ½ = 7/2

Then,
= (31/7) × reciprocal of 7
= (31/7) × (1/7)
= (31 × 1) / (7 × 7)
= 31/49

(vi) 4  ³/₇ ÷ 7 = 31/7 ÷ 7 = 31/7 x 1/7 = 31/49

4. Find:

(i) 2/5 ÷ 1/2

Solution:

We have,
= (2/5) × reciprocal of ½
= (2/5) × (2/1)
= (2 × 2) / (5 × 1)
= 4/5

(ii) 4/9 ÷ 2/3

Solution:

We have,
= (4/9) × reciprocal of (2/3)
= (4/9) × (3/2)
= (4 × 3) / (9 × 2)
= (2 × 1) / (3 × 1)
= 2/3

(iii) 3/7 ÷ 8/7

Solution:

We have,
= (3/7) × reciprocal of (8/7)
= (3/7) × (7/8)
= (3 × 7) / (7 × 8)
= (3 × 1) / (1 × 8)
= 3/8

Solution:

First covert the mixed fraction into improper fraction. We have,

Then,
= (7/3) × reciprocal of (3/5)
= (7/3) × (5/3)
= (7 × 5) / (3 × 3)
= 35/9

(v) 3 ½ ÷ 8/3

Solution:

First covert the mixed fraction into improper fraction.
We have,
= 3 ½ = 7/2

Then,
= (7/2) × reciprocal of (8/3)
= (7/2) × (3/8)
= (7 × 3) / (2 × 8)
= 21/16

(vi) 2/5 ÷ 1 ½

Solution:

First covert the mixed fraction into improper fraction.
We have,
= 1 ½ = 3/2

Then,
= (2/5) × reciprocal of (3/2)
= (2/5) × (2/3)
= (2 × 2) / (5 × 3)
= 4/15

Solution:

First covert the mixed fraction into improper fraction. We have,

Then,
= (16/5) × reciprocal of (5/3)
= (16/5) × (3/5)
= (16 × 3) / (5 × 5)
= 48/25

Solution:

First covert the mixed fraction into improper fraction. We have,

Then,
= (11/5) × reciprocal of (6/5)
= (11/5) × (5/6)
= (11 × 5) / (5 × 6)
= (11 × 1) / (1 × 6)
= 11/6