NCERT Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.2

NCERT Solutions Class 7 Maths
Chapter – 2 (Fractions and Decimals)

The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 2 Fractions and Decimals Exercise 2.2 has been provided here to help the students in solving the questions from this exercise.

Chapter : 2 Fractions and Decimals

Exercise – 2.2

1. Which of the drawings (a) to (d) show:
(i) 2 × \mathbf{\frac{1}{5}}

(ii) 2 × \mathbf{\frac{1}{2}}

(iii) 3 × \mathbf{\frac{2}{3}}

(iv) 3 × \mathbf{\frac{1}{4}}

NCERT Class 7 Maths Solution

Solution –

(i) 2 × \frac{1}{5} represents drawing (d)

(ii) 2 × \frac{1}{2} represents drawing (b)

(iii) 3 × \frac{2}{3} represents drawing (a)

(iv) 3 × \frac{1}{4} represents drawing (c)

2. Some pictures (a) to (c) are given below. Tell which of them show:
(i) 3 × \mathbf{\frac{1}{5}} = \mathbf{\frac{3}{5}}

(ii) 2 × \mathbf{\frac{1}{3}} = \mathbf{\frac{2}{3}}

(iii) 3 × \mathbf{\frac{3}{4}} = \mathbf{2\frac{1}{4}}

NCERT Class 7 Maths Solution

Solution –

(i) 3 × \mathbf{\frac{1}{5}} = \mathbf{\frac{3}{5}} represents figure (c)

(ii) 2 × \mathbf{\frac{1}{3}} = \mathbf{\frac{2}{3}} represents figure (a)

(iii) 3 × \mathbf{\frac{3}{4}} = \mathbf{2\frac{1}{4}} represents figure (b)

3. Multiply and reduce to lowest form and convert into a mixed fraction:
(i) 7 × \mathbf{\frac{3}{5}}

(ii) 4 × \mathbf{\frac{1}{3}}

(iii) 2 × \mathbf{\frac{6}{7}}

(iv) 5 × \mathbf{\frac{2}{9}}

(v) \mathbf{\frac{2}{3}} × 4

(vi) \mathbf{\frac{5}{2}} × 6

(vii) 11 × \mathbf{\frac{4}{7}}

(viii) 20 × \mathbf{\frac{4}{5}}

(ix) 13 × \mathbf{\frac{1}{3}}

(x) 15 × \mathbf{\frac{3}{5}}

Solution –

(i) 7 × \mathbf{\frac{3}{5}} = \frac{21}{5} = 4\frac{1}{5}

(ii) 4 × \mathbf{\frac{1}{3}} = \frac{4}{3} = 1\frac{1}{3}

(iii) 2 × \mathbf{\frac{6}{7}} = \frac{12}{7} = 1\frac{5}{7}

(iv) 5 × \mathbf{\frac{2}{9}} = \frac{10}{9} = 1\frac{1}{9}

(v) \mathbf{\frac{2}{3}} × 4 = \frac{8}{3} = 2\frac{2}{3}

(vi) \mathbf{\frac{5}{2}} × 6 = \frac{30}{2} = 15

(vii) 11 × \mathbf{\frac{4}{7}} = \frac{44}{7} = 6\frac{2}{7}

(viii) 20 × \mathbf{\frac{4}{5}} = \frac{80}{5} = 16

(ix) 13 × \mathbf{\frac{1}{3}} = \frac{13}{3} = 4\frac{1}{3}

(x) 15 × \mathbf{\frac{3}{5}} = \frac{45}{5} = 9

4. Shade:

(i) \mathbf{\frac{1}{2}} of the circles in box (a)

(b) \mathbf{\frac{2}{3}} of the triangles in box (b)

(iii) \mathbf{\frac{3}{5}} of the squares in the box (c)

NCERT Class 7 Maths Solution

Solution –

(i) \mathbf{\frac{1}{2}} of the circles in box (a)

∴ 12 × \frac{1}{2} = \frac{12}{2} = 6

NCERT Class 7 Maths Solution

(b) \mathbf{\frac{2}{3}} of the triangles in box (b)

∴ 9 × \frac{2}{3} = \frac{18}{3} = 6

NCERT Class 7 Maths Solution

(iii) \mathbf{\frac{3}{5}} of the squares in the box (c)

∴ 15 × \frac{3}{5} = \frac{45}{5} = 9

NCERT Class 7 Maths Solution

5. Find:
(a) \mathbf{\frac{1}{2}} of (i) 24 (ii) 46

(b) \mathbf{\frac{2}{3}} of (i) 18 (ii) 27

(c) \mathbf{\frac{3}{4}} of (i) 16 (ii) 36

(d) \mathbf{\frac{4}{5}} of (i) 20 (ii) 35

Solution –

(a) \mathbf{\frac{1}{2}} of (i) 24 (ii) 46

(i) 24
We have,
= \frac{1}{2} × 24 = \frac{24}{2} = 12

(ii) 46
We have,

= \frac{1}{2} × 46 = \frac{46}{2} = 23

(b) \mathbf{\frac{2}{3}} of (i) 18 (ii) 27

(i) 18
We have,
= \frac{2}{3} × 18 = \frac{36}{3} = 12

(ii) 27
We have,
= \frac{2}{3} × 27 = 2 × 9 = 18

(c) \mathbf{\frac{3}{4}} of (i) 16 (ii) 36

(i) 16
We have,
= ¾ × 16 = 3 × 4 = 12

(ii) 36
We have
= ¾ × 36 = 3 × 9 = 27

(d) \mathbf{\frac{4}{5}} of (i) 20 (ii) 35

(i) 20
We have,
= \frac{4}{5} × 20 = 4 × 4 = 16

(ii) 35
We have,
= \frac{4}{5} × 35 = 4 × 7 = 28

6. Multiply and express as a mixed fraction:

(a) 3 × \mathbf{5\frac{1}{5}} 

(b) 5 × 6 \mathbf{\frac{3}{4}}

(c) 7 × 2 \mathbf{\frac{1}{4}}

(d) 4 × 6 \mathbf{\frac{1}{3}}

(e) 3 \mathbf{\frac{1}{4}} × 6

(f) 3 \mathbf{\frac{2}{5}} × 8

Solution –

(a) 3 × \mathbf{5\frac{1}{5}} 

= 3 × \frac{26}{5} = \frac{78}{5} = 15\frac{3}{5}

(b) 5 × 6 \mathbf{\frac{3}{4}}

= 5 × \frac{27}{4} = \frac{135}{4} = 33\frac{3}{4}

(c) 7 × 2 \mathbf{\frac{1}{4}}

= 7 × \frac{9}{4} = \frac{63}{4} = 15\frac{3}{4}

(d) 4 × 6 \mathbf{\frac{1}{3}}

= 4 × \frac{19}{3} = \frac{76}{3} = 25\frac{1}{3}

(e) 3 \mathbf{\frac{1}{4}} × 6

= \frac{13}{4} × 6 = \frac{13}{2} × 3 = \frac{39}{2} = 19 \frac{1}{2}

(f) 3 \mathbf{\frac{2}{5}} × 8

= \frac{17}{5} × 8 = \frac{136}{5} = 27 \frac{1}{5}

7. Find:
(a) \mathbf{\frac{1}{2}} of (i) 2 \mathbf{\frac{3}{4}} (ii) \mathbf{4\frac{2}{9}}

(b) \mathbf{\frac{5}{8}} of (i) \mathbf{3\frac{5}{6}} (ii) \mathbf{9\frac{2}{3}}

Solution –

(a) \mathbf{\frac{1}{2}} of (i) 2 \mathbf{\frac{3}{4}} (ii) \mathbf{4\frac{2}{9}}

(i) \mathbf{\frac{1}{2}} of 2 \mathbf{\frac{3}{4}}

= \frac{1}{2} \times \frac{11}{4} = \frac{11}{8} = 1\frac{3}{8}

(ii) \mathbf{\frac{1}{2}} of  \mathbf{4\frac{2}{9}}

= \frac{1}{2} \times \frac{38}{9} = \frac{19}{9} = 2\frac{1}{9}

(b) \mathbf{\frac{5}{8}} of (i) \mathbf{3\frac{5}{6}} (ii) \mathbf{9\frac{2}{3}}

(i) \mathbf{\frac{5}{8}} of \mathbf{3\frac{5}{6}}

= \frac{5}{8} × \frac{23}{6} = \frac{115}{48} = 2\frac{19}{48}

(ii) \mathbf{\frac{5}{8}} of \mathbf{9\frac{2}{3}}

= \frac{5}{8} × \frac{29}{3} = \frac{145}{24} = 6\frac{1}{24}

8. Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 liters water. Vidya consumed \mathbf{\frac{2}{5}}of the water. Pratap consumed the remaining water.
(i) How much water did Vidya drink?
(ii) What fraction of the total quantity of water did Pratap drink?

Solution –
(i) Amount of water in the water bottle = 5 liters
Amount of water consumed by Vidya = \frac{2}{5} of 5 liters
= \frac{2}{5} × 5 = 2 liters

So, the total amount of water drank by Vidya is 2 liters

(ii) Amount of water in the water bottle = 5 liters
Amount of water consumed by Pratap = (1 – water consumed by Vidya)
= (1 – \frac{2}{5})

= \frac{5-2}{5} = \frac{3}{5}

∴ Total amount of water consumed by Pratap = \frac{3}{5} of 5 liters
= \frac{3}{5} × 5 = 3 liters
So, the total amount of water drank by Pratap is 3 liters

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