Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.3 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.3

Question 1.
Find (i) (frac { 1 }{ 4 }) of (a) (frac { 1 }{ 4 }) (b) (frac { 3 }{ 4 }) (c) (frac { 4 }{ 3 })
(ii) (frac { 1 }{ 7 }) of (a) (frac { 2 }{ 9 }) (b) (frac { 6 }{ 5 }) (c) (frac { 3 }{ 10 })
Solution:
(i) (a) (frac { 1 }{ 4 }) of (frac { 1 }{ 4 })
= (frac { 1 }{ 4 }) x (frac { 1 }{ 4 })
= (frac { 1 ×1 }{ 4×4 }) = (frac { 1 }{ 16 })

(b) (frac { 1 }{ 4 }) of (frac { 3 }{ 5 })
= (frac { 1 }{ 4 }) x (frac { 3 }{ 5 })
= (frac { 1 ×3 }{ 4×5 }) = (frac { 3 }{ 20 })

(c) (frac { 1 }{ 4 }) of (frac { 4 }{ 3 })
= (frac { 1 }{ 4 }) x (frac { 4 }{ 3 })
= (frac { 1 ×4 }{ 4×3 }) = (frac { 1 }{ 3 })

(ii) (a) (frac { 1 }{ 7 }) of (frac { 2 }{ 9 })
= (frac { 1 }{ 7 }) x (frac { 2 }{ 9 })
= (frac { 1 ×2 }{ 7×9 }) = (frac { 2 }{ 63 })

(b) (frac { 1 }{ 7 }) of (frac { 6 }{ 5 })
= (frac { 1 }{ 7 }) x (frac { 6 }{ 5 })
= (frac { 1 ×6 }{ 7×5 }) = (frac { 6 }{ 35 })

(c) (frac { 1 }{ 7 }) of (frac { 3 }{ 10 })
= (frac { 1 }{ 7 }) x (frac { 3 }{ 10 })
= (frac { 1 ×3 }{ 7×10 }) = (frac { 3 }{ 70 })

Question 2.
Multiply and reduce to lowest form (if possible):
(i) (frac { 2 }{ 3 }) x 2(frac { 2 }{ 3 })
(ii) (frac { 2 }{ 7 }) x (frac { 7 }{ 9 })
(iii) (frac { 3 }{ 8 }) x (frac { 6 }{ 4 })
(iv) (frac { 9 }{ 5 }) x (frac { 3 }{ 5 })
(v) (frac { 1 }{ 3 }) x (frac { 15 }{ 8 })
(vi) (frac { 11 }{ 2 }) x (frac { 3 }{ 10 })
(vii) (frac { 4 }{ 5 }) x (frac { 12 }{ 7 })
Solution:

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

Question 4.
Which is greater:
(i) (frac { 2 }{ 7 }) of (frac { 3 }{ 4 }) or (frac { 3 }{ 5 }) of (frac { 5 }{ 8 })?
(ii) (frac { 1 }{ 2 }) of (frac { 6 }{ 7 }) or (frac { 2 }{ 3 }) of (frac { 3 }{ 7 })?
Solution:
(i) Comparing (frac { 2 }{ 7 }) of (frac { 3 }{ 4 }) and (frac { 3 }{ 5 }) of (frac { 5 }{ 8 })
∵ (frac { 2 }{ 7 }) of (frac { 3 }{ 4 })
= (frac { 2 }{ 7 }) x (frac { 3 }{ 4 })
= (frac { 1×3 }{ 7×2 })
= (frac { 3 }{ 14 })
and (frac { 3 }{ 5 }) of (frac { 5 }{ 8 })
= (frac { 3 }{ 5 }) x (frac { 5 }{ 8 })
= (frac { 3×1 }{ 1×8 })
= (frac { 3 }{ 8 })
Again (frac { 3 }{ 14 }) = (frac { 3×4 }{ 14×4 })
= (frac { 12 }{ 56 }) [∵ LCM of 14 and 8 is 56]
= (frac { 3 }{ 8 }) = (frac { 3×7 }{ 8×7 }) = (frac { 21 }{ 56 })
Now, (frac { 21 }{ 56 }) > (frac { 12 }{ 56 })
∴ (frac { 3 }{ 5 }) of (frac { 5 }{ 8 }) is greater than (frac { 2 }{ 7 }) of (frac { 3 }{ 4 }).

(ii) Comparing (frac { 1 }{ 2 }) of (frac { 6 }{ 7 }) or (frac { 2 }{ 3 }) of (frac { 3 }{ 7 }):
∵ (frac { 1 }{ 2 }) of (frac { 6 }{ 7 }) = (frac { 1 }{ 2 }) x (frac { 6 }{ 7 })
= (frac { 1×3 }{ 1×7 }) = (frac { 3 }{ 7 })
and, (frac { 2 }{ 3 }) of (frac { 3 }{ 7 })
= (frac { 2 }{ 3 }) x (frac { 3 }{ 7 })
= (frac { 2×1 }{ 1×7 }) = (frac { 2 }{ 7 })
Also 3 > 2 ⇒ (frac { 3 }{ 7 }) > (frac { 2 }{ 7 })
∴ (frac { 1 }{ 2 }) of (frac { 6 }{ 7 }) is greater than (frac { 2 }{ 3 }) of (frac { 3 }{ 7 })

Question 5.
Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is (frac { 3 }{ 4 }) m. Find the distance between the first and the last sapling.
Solution:

Number of saplings = 4
Distance between two adjacent saplings = (frac { 3 }{ 4 })m
∴ Distance between 1st and last (4th) sapling , 3
= 3 x (frac { 3 }{ 4 })m
= (frac { 3×3 }{ 4 })m
= (frac { 9 }{ 4 })m
= 2(frac { 1 }{ 4 })m

Question 6.
Lipika reads a book for 1(frac { 3 }{ 4 }) hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
Solution:
Number of days = 6
Reading hours per day (for one day) = 1(frac { 3 }{ 4 }) hours
∴ Total number of reading hours
= 6 x 1(frac { 3 }{ 4 })
= 6 x (frac { 7 }{ 4 }) hours
= (frac { 3×7 }{ 2 }) hours = (frac { 21 }{ 2 }) hours = 10(frac { 1 }{ 2 }) hours

Question 7.
A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2(frac { 3 }{ 4 }) litres of petrol.
Solution:
Distance covered in 1 litre of petrol =16 km
∴ Distance covered in 2(frac { 3 }{ 4 }) litres of petrol
= 16 x 2(frac { 3 }{ 4 }) km
= 16 x (frac { 11 }{ 4 }) km
= (frac { 16×11 }{ 4 }) km
= (frac { 4×11 }{ 1 }) km
= 44 km

Question 8.
(a)
(i) Provide the number in the box , such that (frac { 2 }{ 3 }) x = (frac { 10 }{ 30 }).
(ii) The simplest form of the number obtained in is ______.

(b)
(i) Provide the number in the box , such that (frac { 3 }{ 5 }) x = (frac { 24 }{ 75 }).
(ii) The simplest form of the number obtained in is ______.
Solution:
(a)
(i) We have: (frac { 2 }{ 3 }) x (frac { 5 }{ 10 }) = (frac { 10 }{ 30 }) , i.e. the required number = (frac { 5 }{ 10 })

(ii) Simplest form of

(b)
(i) We have: (frac { 3 }{ 5 }) x (frac { 8 }{ 15 })
= (frac { 24 }{ 75 }), i.e. the required number = (frac { 8 }{ 15 })

(ii) The simplest form of (frac { 8 }{ 15 }) is (frac { 8 }{ 15 }).