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

Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.2 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.2

Question 1.
Which of the drawings (a) to (d) show:
(i) 2 x \(\frac { 1 }{ 5 }\)
(ii) 2 x \(\frac { 1 }{ 2 }\)
(iii) 3 x \(\frac { 2 }{ 3 }\)
(iv) 3 x \(\frac { 1 }{ 4 }\)

Solution:
(i) 2 x \(\frac { 1 }{ 5 }\)
= \(\frac { 1 }{ 5 }\) + \(\frac { 1 }{ 5 }\), which is represented by the drawing (d).
Thus (i) → (d).

(ii) 2 x \(\frac { 1 }{ 2 }\)
= \(\frac { 1 }{ 2 }\) + \(\frac { 1 }{ 2 }\), which is represented by the drawing (d).
Thus (ii) → (d).

(iii) 3 x \(\frac { 2 }{ 3 }\)
\(\frac { 2 }{ 3 }\) + \(\frac { 2 }{ 3 }\) + \(\frac { 2 }{ 3 }\), which is represented by the drawing (a).
Thus, (iii) → (a).

(iv) 3 x \(\frac { 1 }{ 4 }\)
\(\frac { 1 }{ 4 }\) + \(\frac { 1 }{ 4 }\) + \(\frac { 1 }{ 4 }\), which is represented by the drawing (c).
Thus, (iv) → (c).

Question 2.
Some pictures (a) to (c) are given below. Tell which of them show:
(i) 3 x \(\frac { 1 }{ 5 }\)
(ii) 2 x \(\frac { 1 }{ 3 }\) = \(\frac { 2 }{ 3 }\)
(iii) 2 x \(\frac { 1 }{ 3 }\) = 2 x \(\frac { 1 }{ 4 }\)

Solution:
(i) ∵ 3 x = \(\frac { 1 }{ 5 }\)
\(\frac { 1 }{ 5 }\) + \(\frac { 1 }{ 5 }\) + \(\frac { 1 }{ 5 }\) = \(\frac { 3 }{ 5 }\), which is shown by the drawing (c).
∴ (i) → (C)

(ii) ∵ 2 x \(\frac { 1 }{ 3 }\) = \(\frac { 1 }{ 3 }\) + \(\frac { 1 }{ 3 }\) = \(\frac { 2 }{ 3 }\), which is shown by the drawing (a).
∴ (ii) → (C)

(iii) ∵ 3 x \(\frac { 3 }{ 4 }\) = \(\frac { 3 }{ 4 }\) + \(\frac { 3 }{ 4 }\) + \(\frac { 3 }{ 4 }\), which is shown by the drawing (a).
∴ (iii) → (C)

Question 3.
Multiply and reduce to lowest form and convert into a mixed fraction:
(i) 7 x \(\frac { 3 }{ 5 }\)
(ii) 4 x \(\frac { 1 }{ 3 }\)
(iii) 2 x \(\frac { 6 }{ 7 }\)
(iv) 5 x \(\frac { 2 }{ 9 }\)
(v) \(\frac { 2 }{ 3 }\) x 4
(vi) \(\frac { 5 }{ 2 }\) x 6
(vii) 11 x \(\frac { 4 }{ 7 }\)
(viii) 20 x \(\frac { 4 }{ 5 }\)
(ix) 13 x \(\frac { 1 }{ 3 }\)
(x) 15 x \(\frac { 3 }{ 5 }\)
Solution:

Question 4.
Shade:
(i) \(\frac { 1 }{ 2 }\) of the circles in box (a)
(ii) \(\frac { 2 }{ 3 }\) of the triangles in box (b)
(ii) \(\frac { 3 }{ 5 }\) of the squares in box (c)

Solution:
(i) \(\frac { 1 }{ 2 }\) of the circles:
∵ \(\frac { 1 }{ 2 }\) of 12 = \(\frac { 1 }{ 2 }\) x 12 = 6
So, we shade 6 circles.

(ii) \(\frac { 2 }{ 3 }\) of the triangles:
∵ \(\frac { 2 }{ 3 }\) of 9 = \(\frac { 2 × 9 }{ 3 }\) = 6
∴ We shade 6 triangles

(ii) \(\frac { 3 }{ 5 }\) of the squares:
∵ \(\frac { 3 }{ 5 }\) or 15 = \(\frac { 3 × 15 }{ 5 }\) = 9
∴ We shade 9 squares.

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
Solution:

Question 6.
Multiply and express as a mixed fraction:
(a) 3 x 5\(\frac { 1 }{ 5 }\)
(b) 5 x 6\(\frac { 3 }{ 4 }\)
(c) 7 x 2\(\frac { 1 }{ 4 }\)
(d) 4 x 6\(\frac { 1 }{ 3 }\)
(e) 3\(\frac { 1 }{ 4 }\) x 6
(f) 3\(\frac { 2 }{ 5 }\) x 8
Solution:

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\(\frac { 2 }{ 3 }\)
Solution:
(a) (i) \(\frac { 1 }{ 2 }\) of 2\(\frac { 3 }{ 4 }\)
= \(\frac { 1 }{ 2 }\) of \(\frac { 11 }{ 4 }\)
= \(\frac { 1×11 }{ 2×4 }\)
= \(\frac { 11 }{ 8 }\)
= 1\(\frac { 3 }{ 8 }\)

(ii) \(\frac { 1 }{ 2 }\) of 4\(\frac { 2 }{ 9 }\)
= \(\frac { 1 }{ 2 }\) of \(\frac { 38 }{ 9 }\)
= \(\frac { 1×38 }{ 2×9 }\)
= \(\frac { 19 }{ 9 }\)
= 2\(\frac { 1 }{ 9 }\)

(b) (i) \(\frac { 5 }{ 8 }\) of 3\(\frac { 5 }{ 6 }\)
= \(\frac { 5 }{ 8 }\) of \(\frac { 23 }{ 6 }\)
= \(\frac { 5×23 }{ 8×6 }\)
= \(\frac { 115 }{ 48 }\)
= 2\(\frac { 19 }{ 48 }\)

(ii) \(\frac { 5 }{ 8 }\) of 9\(\frac { 2 }{ 3 }\)
= \(\frac { 5 }{ 8 }\) of \(\frac { 29 }{ 3 }\)
= \(\frac { 5×29 }{ 8×3 }\)
= \(\frac { 145 }{ 24 }\)
= 6\(\frac { 1 }{ 24 }\)

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 drink7
(ii) What fraction of the total quantity of water did Pratap drink?
Solution:
Total quantity of water = 5 litres
(i) Amount of water consumed by Vidya = \(\frac { 2 }{ 5 }\) of 5 litres = \(\frac { 2 }{ 5 }\) x 5 litres = 2 litres
(ii) Remaining water = water consumed by Pratap
i.e. Amount of water consumed by Pratap = 5 litres – 2 litres = 3 litres
Fraction of water consumed by Pratap = \(\frac { 3 }{ 5 }\)