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