## MP Board Class 7th Maths Solutions Chapter 2 Fractions and Decimals Ex 2.2

Without a calculator who wants to convert 11/16 to decimal then 7/16 to decimal to do the math, you just learn to do it.

Question 1.

Which of the drawings (a) to (d) show:

Solution:

(i) 2 × \(\frac{1}{5}\) represents addition of 2 figures, each representing 1 shaded part out of 5 equal parts. Hence, 2 × \(\frac{1}{5}\) is represented by (d)

(ii) 2 × \(\frac{1}{2}\) represents addition of 2 figures, each representing 1 shaded part out of 2 equal parts. Hence, 2 × \(\frac{1}{2}\) is represented by

(b) .

(iii) 3 × \(\frac{2}{3}\) represents addition of 3 figures, each representing 2 shaded parts out of 3 equal parts. Hence, 3 × \(\frac{2}{3}\) is represented by (a).

(iv) 3 × \(\frac{1}{4}\) represents addition of 3 figures, each representing 1 shaded part out of 4 equal parts. Hence, 3 × \(\frac{1}{4}\) is represented by (c).

Question 2.

Some pictures (a) to (c) are given below. Tell which of them show:

Solution:

(i) 3 × \(\frac{1}{5}\) represents the addition of 3 figures, each representing 1 shaded part out of 5 equal parts and \(\frac{3}{5}\) represents 3 shaded parts out of 5 equal parts.

Hence, \(3 \times \frac{1}{5}=\frac{3}{5}\) is represented by (c).

(ii) \(2 \times \frac{1}{3}\) represents the addition of 3 figures, each representing 1 shaded part out of 3 equal parts and \(\frac{2}{3}\) represents 2 shaded parts out of 3 equal parts.

Hence, \(2 \times \frac{1}{3}=\frac{2}{3}\) is represented by (a).

(iii) \(3 \times \frac{3}{4}\) represents the addition of 3 figures, each representing 3 shaded parts out of 4 equal parts and \(2 \frac{1}{4}\) represents 2 fully shaded figures and one figure having 1 shaded part out of 4 equal parts.

Hence, \(3 \times \frac{3}{4}=2 \frac{1}{4}\) is represented by (b).

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Question 3.

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

Solution:

Question 4.

Solution:

(i) There are 12 circles in the given box.

(a)

(iii) There are 15 squares in the given box (c). To shade \(\frac{3}{5}\) of the squares in it i.e., \(\frac{3}{5} \times 15=9\), we will shade any 9 squares of it.

Question 5.

Solution:

Question 6.

Multiply and express as a mixed fraction:

Solution:

Question 7.

Find:

Solution:

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?

Solution:

(i) Water consumed by Vidya

(ii) Fraction of remaining water

Thus, Pratap consumed \(\frac{3}{5}\) of the total quantity of water.