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 })