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 }