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## Chapter 2 Fractions and Decimals Exercise 2.3

Question 1: Find:
(i) 1/4 of (a) 1/4 (b) 3/5 (c) 4/3

(a) 1/4
= 1/4 × 1/4
= 1/4 × 1/4
= 1 × 1/4 × 4
= 1/16

(b) 3/5
= 1/4 × 3/5
= 1/4 × 3/5
= 1 × 3/4 × 5
= 3/20

(c) 4/3
= 1/4 × 4/3
= 1/4 × 4/3
= 1 × 4/4 × 3
= 4/12
= 1/3

(ii) 1/7 of (a) 2/9 (b) 6/5 (c) 3/10
(a) 2/9
= 1/7 × 2/9
= 1/7 × 2/9
= 1 × 2/7 × 9
= 2/63

(b) 6/5
= 1/7 × 6/5
= 1/7 × 6/5
= 1 × 6/7 × 5
= 6/35

(c) 3/10
= 1/7 × 3/10
= 1/7 × 3/10
= 1 × 3/7 × 10
= 3/70

Question 2: Multiply and reduce to lowest form (if possible):
(i) (2/3) × 2 2/3
= 2 2/3 = 8/3
= 2/3 × 8/3
= 2 × 8/3 × 3
= 16/9
= 1 7/9

(ii) (2/7) × (7/9)
= 2 × 7/7 × 9
= 2 × 1/1 × 9
= 2/9

(iii) (3/8) × (6/4)
= 3 × 6/8 × 4
= 3 × 3/4 × 4
= 9/16

(iv) (9/5) × (3/5)

= 9 × 3/5 × 5
= 27/25
= 1 2/25

(v) (1/3) × (15/8)

= 1 × 15/3 × 8
= 1 × 5/1 × 8
= 5/8

(vi) (11/2) × (3/10)

= 11 × 3/2 × 10
= 33/20
= 1 13/20

(vii) (4/5) × (12/7)

= 4 × 12/5 × 7
= 48/35
= 1 13/35

Question 3: Multiply the following fractions:
(i) (2/5) × 5 1/4

= 5 1/4 = 21/4
= 2/5 × 21/4
= 2 × 21/5 × 4
= 1 × 21/5 × 2
= 21/10
= 2 1/10

(ii) 6 2/5 × (7/9)
= 6 2/5 = 32/5
= 32/5 × 7/9
= 32 × 7/5 × 9
= 224/45
= 4 44/45

(iii) (3/2) × 5 1/3
= 5 1/3 = 16/3
= 3/2 × 16/3
= 3 × 16/2 × 3
= 1 × 8/1 × 1
= 8

(iv) (5/6) × 2 3/7
= 2 3/7 = 17/7
= 5/6 × 17/7
= 5 × 17/6 × 7
= 85/42
= 2 1/42

(v) 3 2/5 × (4/7)
= 3 2/5 = 17/5
= 17/5 × 4/7
= 17 × 4/5 × 7
= 68/35
= 1 33/35

(vi) 2 3/5 × 3
= 2 3/5 = 13/5
= 13/5 × 3/1
= 13 × 3/5 × 1
= 39/5
= 7 4/5

(vi) 3 4/7 × (3/5)
= 3 4/7 = 25/7
= 25/7 × 3/5
= 25 × 3/7 × 5
= 5 × 3/7 × 1
= 15/7
= 2 1/7

Question 4: Which is greater?
(i) (2/7) of (3/4) or (3/5) of (5/8)
= 2/7 × 3/4 and 3/5 × 5/8
= 2/7 × 3/4
= 2 × 3/7 × 4
= 1 × 3/7 × 2
= 3/14
= 3/5 × 5/8
= 3 × 5/5 × 8
= 3 × 1/1 × 8
= 3/8
LCM of 8, 14 = 56
= 3/14 × 4/4 = 12/56
= 3/8 × 7/7 = 21/56
Comparing 12/56 [] 21/56
= 12/56 < 21/56
= 3/14 < 3/8

(ii) (1/2) of (6/7) or (2/3) of (3/7)
= 1/2 × 6/7 and 2/3 × 3/7
= 1/2 × 6/7
= 1 × 6/2 × 7
= 1 × 3/1 × 7
= 3/7
= 2/3 × 3/7
= 2 × 3/3 × 7
= 2 × 1/1 × 7
= 2/7
Comparing 3/7 [] 2/7
= 3/7 > 2/7

Question 5: Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is 3/4 m. Find the distance between the first and the last sapling.
The distance between two adjacent saplings = 3/4 m
Number of saplings planted by Saili in a row = 4
Number of gap in saplings = 3/4 × 4 = 3
The distance between the first and the last saplings = ?
= 3 × 3/4
= 9/4 m
= 2 1/4 m
Therefore, the distance between the first and the last saplings is 2 1/4 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?
Time taken by Lipika to read a book = 1 3/4 hours (7/4 hours)
Number of days she took to read the entire book = 6 days
Total number of hours required by her to complete the book = 7/4 × 6
= 7/2 × 3
= 21/2
= 10 1/2 hours
Therefore, the total number of hours required by her to complete the book is 10 1/2 hours.

Question 7: A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2 3/4 litres of petrol.
The total number of distance travelled by a car in 1 litre of petrol = 16 km
Total quantity of petrol = 2 3/4 litre (11/4 litre)
Total distance travelled by car in 11/4 litres of petrol = ?
= 11/4 × 16
= 11 × 4
= 44 km
Therefore, total distance travelled by car in 11/4 litres of petrol is 44 km.

Question 8: (a) (i) provide the number in the box [ ], such that (2/3) × [ ] = (10/30)
Let the number be x.
= 2/3 × x = 10/30
= x = 10/30 × 3/2
= x = 10 × 3/30 × 2
= x = 5 × 1/10 × 1
= x = 5/10
Therefore, the required number in the box is 5/10.

(ii) The simplest form of the number obtained in [ ] is

Let the number in the box be 5/10.
The simplest form of 5/10 = 1/2

(b) (i) provide the number in the box [ ], such that (3/5) × [ ] = (24/75)

Let the number be x.
= 3/5 × x = 24/75
= x = 24/75 × 5/3
= x = 24 × 5/75 × 3
= x = 8 × 1/15 × 1
= x = 8/15
Therefore, the required number in the box is 8/15.

(ii) The simplest form of the number obtained in [ ] is