Fractions and Decimals Ex-2.2

NCERT solutions for Maths Fractions and Decimals 

NCERT Solutions for Class 7 Maths Fractions and Decimals

Class –VII Mathematics (Ex. 2.2)

Question 1.Which of the drawings $\left( a \right)$ to $\left( d \right)$ show:

(i)$2 \times \frac{1}{5}$

(ii)$2 \times \frac{1}{2}$

(iii)$3 \times \frac{2}{3}$

(iv)$3 \times \frac{1}{4}$

Answer:

(i) – (d) Since $2 \times \frac{1}{5} = \frac{1}{5} + \frac{1}{5}$

(ii) – (b) Since $2 \times \frac{1}{2} = \frac{1}{2} + \frac{1}{2}$

(iii) – (a) Since $3 \times \frac{2}{3} = \frac{2}{3} + \frac{2}{3} + \frac{2}{3}$

(iv) – (c) Since $3 \times \frac{1}{4} = \frac{1}{4} + \frac{1}{4} + \frac{1}{4}$

NCERT Solutions for Class 7 Maths Exercise 2.2

Question 2.Some pictures $\left( a \right)$ to $\left( c \right)$ are given below. Tell which of them show:

(i)$3 \times \frac{1}{5} = \frac{3}{5}$

(ii)$2 \times \frac{1}{3} = \frac{2}{3}$

(iii)$3 \times \frac{3}{4} = 2\frac{1}{4}$

Answer:

(i) – (c) Since $3 \times \frac{1}{5} = \frac{1}{5} + \frac{1}{5} + \frac{1}{5}$

(ii) – (a) Since $2 \times \frac{1}{3} = \frac{1}{3} + \frac{1}{3}$

(iii) – (b) Since $3 \times \frac{3}{4} = \frac{3}{4} + \frac{3}{4} + \frac{3}{4}$

NCERT Solutions for Class 7 Maths Exercise 2.2

Question 3.Multiply and reduce to lowest form and convert into a mixed fraction:

(i) $7 \times \frac{3}{5}$

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

(iii) $2 \times \frac{6}{7}$

(iv) $5 \times \frac{2}{9}$

(v) $\frac{2}{3} \times 4$

(vi) $\frac{5}{2} \times 6$

(vii) $11 \times \frac{4}{7}$

(viii) $20 \times \frac{4}{5}$

(ix) $13 \times \frac{1}{3}$

(x) $15 \times \frac{3}{5}$

Answer:

(i) $7 \times \frac{3}{5}$ = $\frac{{7 \times 3}}{5}$ = $\frac{{21}}{5} = 4\frac{1}{5}$

(ii) $4 \times \frac{1}{3}$ = $\frac{{4 \times 1}}{3}$ = $\frac{4}{3} = 1\frac{1}{3}$

(iii)$2 \times \frac{6}{7}$ = $\frac{{2 \times 6}}{7}$ = $\frac{{12}}{7} = 1\frac{5}{7}$

(iv) $5 \times \frac{2}{9}$ = $\frac{{5 \times 2}}{9}$ = $\frac{{10}}{9} = 1\frac{1}{9}$

(v) $\frac{2}{3} \times 4$ = $\frac{{2 \times 4}}{3}$ = $\frac{8}{3}$ = $2\frac{2}{3}$

(vi) $\frac{5}{2} \times 6$ = $5 \times 3$ = 15

(vii)$11 \times \frac{4}{7}$ = $\frac{{11 \times 4}}{7}$ = $\frac{{44}}{7}$ = $6\frac{2}{7}$

(viii)$20 \times \frac{4}{5}$ = 4 x 4 = 16

(ix)$13 \times \frac{1}{3}$ = $\frac{{13 \times 1}}{3}$ = $\frac{{13}}{3} = 4\frac{1}{3}$

(x)$15 \times \frac{3}{5}$ = 3 x 3 = 9

NCERT Solutions for Class 7 Maths Exercise 2.2

Question 4.Shade:

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

(ii) $\frac{2}{3}$ of the triangles in box

(iii)$\frac{3}{5}$ of the squares inbox

Answer:

(i) $\frac{1}{2}$ of 12 circles = $\frac{1}{2} \times 12$ = 6 circles

(ii) $\frac{2}{3}$ of 9 triangles = $\frac{2}{3} \times 9$ = 2 x 3 = 6 triangles

(iii) $\frac{3}{5}$ of 15 squares = $\frac{3}{5} \times 15$ 3 x 3 = 9 squares

NCERT Solutions for Class 7 Maths Exercise 2.2

Question 5.Find:

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

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

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

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

Answer:

(a)

(i) $\frac{1}{2}$ of 24 = 12

(ii) $\frac{1}{2}$ of 46 = = 23

(b)

(i) $\frac{2}{3}$ of 18 = $\frac{2}{3} \times 18$ = 2 x 6 = 12

(ii) $\frac{2}{3}$ of 27 = $\frac{2}{3} \times 27$ = 2 x 9 = 18

(c)

(i) $\frac{3}{4}$ of 16 = $\frac{3}{4} \times 16$ = 3 x 4 = 12

(ii) $\frac{3}{4}$ of 36 = $\frac{3}{4} \times 36$ = 3 x 9 = 27

(d)

(i) $\frac{4}{5}$ of 20 = $\frac{4}{5} \times 20$ = 4 x 4 = 16

(ii) $\frac{4}{5}$ of 35 = $\frac{4}{5} \times 35$ = 4 x 7 = 28

NCERT Solutions for Class 7 Maths Exercise 2.2

Question 6.Multiply and express as a mixed fraction:

(a) $3 \times 5\frac{1}{5}$

(b) $5 \times 6\frac{3}{4}$

(c) $7 \times 2\frac{1}{4}$

(d) $4 \times 6\frac{1}{3}$

(e) $3\frac{1}{4} \times 6$

(f) $3\frac{2}{5} \times 8$

Answer:

(a) $3 \times 5\frac{1}{5} = 3 \times \frac{{26}}{5} = \frac{{3 \times 26}}{5} = \frac{{78}}{5} = 15\frac{3}{5}$

(b) $5 \times 6\frac{3}{4} = 5 \times \frac{{27}}{4} = \frac{{5 \times 27}}{4} = \frac{{135}}{4} = 33\frac{3}{4}$

(c) $7 \times 2\frac{1}{4} = 7 \times \frac{9}{4} = \frac{{7 \times 9}}{4} = \frac{{63}}{4} = 15\frac{3}{4}$

(d) $4 \times 6\frac{1}{3} = 4 \times \frac{{19}}{3} = \frac{{4 \times 19}}{3} = \frac{{76}}{3} = 25\frac{1}{3}$

(e) $3\frac{1}{4} \times 6 = \frac{{13}}{4} \times 6 = \frac{{13 \times 3}}{2} = \frac{{39}}{2} = 19\frac{1}{2}$

(f) $3\frac{2}{5} \times 8 = \frac{{17}}{5} \times 8 = \frac{{17 \times 8}}{5} = \frac{{136}}{5} = 27\frac{1}{5}$

NCERT Solutions for Class 7 Maths Exercise 2.2

Question 7.Find:

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

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

Answer:

Given: Total quantity of water in bottle = 5 litres

(i) Vidya consumed = $\frac{2}{5}$ of 5 litres = $\frac{2}{5} \times 5$ = 2 litres

Thus, Vidya drank 2 litres water from the bottle.

(ii) Pratap consumed = $\left( {1 – \frac{2}{5}} \right)$ part of bottle

= $\frac{{5 – 2}}{5} = \frac{3}{5}$ part of bottle

Pratap consumed $\frac{3}{5}$ of 5 litres water = $\frac{3}{5} \times 5$ = 3 litres

Thus, Pratap drank $\frac{3}{5}$ part of the total quantity of water.

NCERT Solutions for Class 7 Maths Exercise 2.2

Question 8. Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed $\frac{2}{5}$ 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?

Answer:

Given: Total quantity of water in bottle = 5 litres

(i) Vidya consumed = $\frac{2}{5}$ of 5 litres = $\frac{2}{5} \times 5$ = 2 litres

Thus, Vidya drank 2 litres water from the bottle.

(ii) Pratap consumed = $\left( {1 – \frac{2}{5}} \right)$ part of bottle

= $\frac{{5 – 2}}{5} = \frac{3}{5}$ part of bottle

Pratap consumed $\frac{3}{5}$ of 5 litres water = $\frac{3}{5} \times 5$ = 3 litres

Thus, Pratap drank $\frac{3}{5}$ part of the total quantity of water.