In Chapter 2, exercise 2.2, we will explore multiplying one fraction by another. For example, if we have half of a cake and only want to use three-quarters of that half, we multiply 1/2 (the half cake) by 3/4 (the half of the half we want to use). The calculation would be (1/2) × (3/4) = 3/8. This result means that we will use 3/8 of the whole cake.
Let’s take another example where we want to use a recipe requiring 2/3 of a cup of sugar. Here, we want to make just half the recipe. We multiply 2/3 (the original amount of sugar) by 1/2. The multiplication (2/3) × (1/2) = 2/6 or 1/3. This shows we only require one-third of a cup of sugar.
This chapter deals with various exercises that will help you understand how to apply the multiplication of fractions in different contexts.
Let’s look at various questions in exercise 2.2 and try to solve this easily.
Class 8 Maths for Chapter 2 Exercise 2.2 Fractions and Decimals – NCERT Book Solutions
Question 1. Find:
(i) ¼ of (a) ¼ (b) 3/5 (c) 4/3
(ii) 1/7 of (a) 2/9 (b) 6/5 (c) 3/10
(i) ¼ of
(a) ¼
Multiply ¼ by ¼
(1/4) × (1/4) = 1/16
(b) 3/5
Multiply ¼ by 3/5
(1/4) × (3/5) = 3/20
(c) 4/3
Multiply ¼ by 4/3
(1/4) × (4/3) = 4/12
4/12 = 1/3
(ii) 1/7 of
(a) 2/9
Multiply 1/7 by 2/9
(1/7) × (2/9) = 2/63
(b) 6/5
Multiply 1/7 by 6/5
(1/7) × (6/5) = 6/35
(c) 3/10
Multiply 1/7 by 3/10
(1/7) × (3/10) = 3/70
Question 2. Multiply and reduce to lowest form (if possible):
(i) (2/3) × 2(2/3)
(ii) (2/7) × (7/9)
(iii) (3/8) × (6/4)
(iv) (9/5) × (3/5)
(v) (1/3) × (15/8)
(vi) (11/2) × (3/10)
(vii) (4/5) × (12/7)
(i) (2/3) × 2(2/3)
Convert mixed number to improper fraction: 2(2/3) = 8/3
Multiply (2/3) by (8/3)
(2/3) × (8/3) = 16/9
16/9 = 1(7/9)
(ii) (2/7) × (7/9)
Multiply (2/7) by (7/9)
(2/7) × (7/9) = 14/63
14/63 = 2/9
(iii) (3/8) × (6/4)
Multiply (3/8) by (6/4)
(3/8) × (6/4) = 18/32
18/32 = 9/16
(iv) (9/5) × (3/5)
Multiply (9/5) by (3/5)
(9/5) × (3/5) = 27/25
(v) (1/3) × (15/8)
Multiply (1/3) by (15/8)
(1/3) × (15/8) = 15/24
=15/24 = 5/8
(vi) (11/2) × (3/10)
Multiply (11/2) by (3/10)
(11/2) × (3/10) = 33/20
=33/20 = 1(13/20)
(vii) (4/5) × (12/7)
Multiply (4/5) by (12/7)
(4/5) × (12/7) = 48/35
48/35 = 1(13/35)
Here are the step-by-step solutions:
Question 3. Multiply the following fractions:
(i) (2/5) × 5 ¼
(ii)6(2/5) × (7/9)
(iii) (3/2) × 5(1/3)
(iv) (5/6) × 2(3/7)
(v) 3(2/5) × (4/7)
(vi)2(3/5) × 3
(vi)3(4/7) × (3/5)
(i) (2/5) × 5 ¼
Convert mixed number to improper fraction: 5 ¼ = 21/4
Multiply (2/5) by (21/4)
(2/5) × (21/4) = 42/20
42/20 = 2(1/10)
(ii) 6(2/5) × (7/9)
Convert mixed number to improper fraction: 6(2/5) = 32/5
Multiply (32/5) by (7/9)
(32/5) × (7/9) = 224/45
(iii) (3/2) × 5(1/3)
Convert mixed number to improper fraction: 5(1/3) = 16/3
Multiply (3/2) by (16/3)
(3/2) × (16/3) = 48/6
48/6 = 8
(iv) (5/6) × 2(3/7)
Convert mixed number to improper fraction: 2(3/7) = 17/7
Multiply (5/6) by (17/7)
(5/6) × (17/7) = 85/42
85/42 = 2(1/42)
(v) 3(2/5) × (4/7)
Convert mixed number to improper fraction: 3(2/5) = 17/5
Multiply (17/5) by (4/7)
(17/5) × (4/7) = 68/35
68/35 = 1(33/35)
(vi) 2(3/5) × 3
Convert mixed number to improper fraction: 2(3/5) = 13/5
Multiply (13/5) by 3
(13/5) × 3 = 39/5
39/5 = 7(4/5)
(vii) 3(4/7) × (3/5)
Convert mixed number to improper fraction: 3(4/7) = 25/7
Multiply (25/7) by (3/5)
(25/7) × (3/5) = 75/35
75/35 = 2(5/35) = 2(1/7)
Question 4. Which is greater:
(i) (2/7) of (3/4) or (3/5) of (5/8)
(ii) (1/2) of (6/7) or (2/3) of (3/7)
(i) (2/7) of (3/4) or (3/5) of (5/8)
Calculate (2/7) × (3/4) = 6/28 = 3/14
Calculate (3/5) × (5/8) = 15/40 = 3/8
Compare 3/14 and 3/8
– Result: 3/8 is greater than 3/14
(ii) (1/2) of (6/7) or (2/3) of (3/7)
Calculate (1/2) × (6/7) = 6/14 = 3/7
Calculate (2/3) × (3/7) = 6/21 = 2/7
Compare 3/7 and 2/7
– Result: 3/7 is greater than 2/7
Question 5. Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is ¾ m. Find the distance between the first and the last sapling.
Distance between the first and the last sapling:
There are 4 saplings, so there are 3 gaps between them.
Each gap is ¾ m.
Total distance = Number of gaps × Distance per gap
Total distance = 3 × ¾ m = 2 ¼ m
Question 6. Lipika reads a book for 1(3/4) hours every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
Total hours Lipika reads a book:
Lipika reads for 1(3/4) hours each day.
Convert mixed number to improper fraction: 1(3/4) = 7/4 hours
She reads the book for 6 days.
Total hours = Daily reading hours × Number of days
Total hours = (7/4) × 6 = 42/4 hours
42/4 = 10 ½ hours
Question 7. A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2 ¾ litres of petrol.
Distance covered using 2 ¾ litres of petrol:
A car runs 16 km on 1 litre of petrol.
Convert mixed number to improper fraction: 2 ¾ = 11/4 litres
Distance covered = Petrol consumption × Distance per litre
Distance covered = (11/4) × 16 km = 44 km
Question 8.
(a) (i) provide the number in the box [ ], such that (2/3) × [ ] = (10/30)
(ii) The simplest form of the number obtained in [ ] is
(b) (i) provide the number in the box [ ], such that (3/5) × [ ] = (24/75)
(ii) The simplest form of the number obtained in [ ] is
Question 8. Finding the number in the box [ ]:
(a)
(i) (2/3) × [ ] = (10/30)
Rearrange the equation: [ ] = (10/30) ÷ (2/3)
Simplify and solve: [ ] = (10/30) × (3/2) = 15/30
(ii) Simplest form of the number obtained in [ ] = 15/30 = 1/2
(b)
(i) (3/5) × [ ] = (24/75)
Rearrange the equation: [ ] = (24/75) ÷ (3/5)
Simplify and solve: [ ] = (24/75) × (5/3) = 40/75
(ii) Simplest form of the number obtained in [ ] = 40/75 = 8/15
