# Fraction

## Exercise 2.3

Question 1: Find the following:

(a) 1/4 of (a) 1/4 (b) 3/5 (c) 4/3

Answer: 1/4 of 1/4=1/4xx1/4=(1)/(16)

1/4 of 3/5=1/4xx3/5=(3)/(20)

1/4 of 4/3=1/4xx4/3=1/3

(b) 1/7 of (a) 2/9 (b) 6/5 (c) (3)/(10)

Answer: 1/7 of 2/9=1/7xx2/9=(2)/(63)

1/7 of 6/5=1/7xx6/5=(6)/(35)

1/7 of (3)/(10)=1/7xx(3)/(10)=(3)/(70)

Question 2: Multiply and reduce to the lowest form:

(a) 2/3xx2\2/3

Answer: 2/3xx2\2/3=2/3xx8/3

=(16)/(9)=1\7/9

(b) 2/7xx7/9

Answer: 2/7xx7/9=(14)/(63)

(c) 3/8xx6/4

Answer: 3/8xx6/4=(3xx3)/(4xx4)=(9)/(16)

(d) 9/5xx3/5

Answer: 9/5xx3/5=(27)/(25)=1\(2)/(27)

(e) 1/3xx(15)/(8)

Answer: 1/3xx(15)/(8)=5/8

(f) (11)/(2)xx(3)/(10)

Answer: (11)/(2)xx(3)/(10)=(33)/(20)

(g) 4/5xx(12)/(7)

Answer: 4/5xx(12)/(7)=(48)/(35)=1\(13)/(35)

Question 3: Multiply the following fractions:

(a) 2/5xx5\1/4

Answer: 2/5xx5\1/4=2/5xx(21)/(4)

=(21)/(10)=2\(1)/(10)

(b) 6\2/5xx7/9

Answer: 6\2/5xx7/9=(32)/(5)xx7/9

=(224)/(45)=4\(44)/(45)

(c) 3/2xx5\1/3

Answer: 3/2xx5\1/3=3/2xx(16)/(3)=8

(d) 5/6xx2\3/7

Answer: 5/6xx2\3/7=5/6xx(17)/(7)

=(85)/(42)=2\(1)/(42)

(e) 3\2/5xx4/7

Answer: 3\2/5xx4/7=(17)/(5)xx4/7

=(68)/(35)=1\(33)/(35)

(f) 2\3/5xx4/7

Answer: 2\3/5xx4/7=(13)/(5)xx4/7

=(52)/(35)=1\(17)/(35)

(g) 3\4/7xx3/5

Answer: 3\4/7xx3/5=(25)/(7)xx3/5

=(5xx3)/(7)=(15)/(7)=2\1/7

Question 4:Which is greater:

(a) 2/7 of 3/4 or 3/5 of 5/8

Answer: 2/7 of 3/4=2/7xx3/4=(3)/(14)

3/5 of 5/8=3/5xx5/8=3/8

Now, LCM of denominators = 56

Hence, (3)/(14)=(3xx4)/(14xx4)=(12)/(56)

3/8=(3xx7)/(8xx7)=(21)/(56)

It is clear that: (21)/(56)>(12)/(56)

So, 3/5 of 5/8>2/7 of 3/4

(b) 1/2 of 6/7 or 2/3 of 3/7

Answer: 1/2 of 6/7=1/2xx6/7=3/7

2/3 of3/7=2/3xx3/7=2/7

Denominator is same in both cases.

Hence, 3/7>2/7

So, 1/2 of 6/7 > 2/3 of 3/7

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.

Answer: There are three saplings after the first sapling. Hence, distance between the first and the last sapling:

3xx3/4=9/4=2\1/4 m

Question 6: Lipika reads a book for 1 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?

Answer: Number of hours in 6 days can be calculated as follows:

6xx1\3/4=6xx7/4=(21)/(2)=10\1/2 hr

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?

Answer: Total distance can be calculated as follows:

16xx2\3/4=16xx(11)/(4)=44 km

Question 8: Fill in the blank and provide the simplest form of number obtained for the blank space

(a) 2/3xx[ ]=(10)/(30)

Answer: The required number in blank can be obtained as follows:

(10)/(30)÷2/3=(10)/(30)xx3/2=1/2

(b) 3/5xx[ ]=(24)/(75)

Answer: The required number in blank can be obtained as follows:

(24)/(75)÷3/5=(24)/(75)xx5/3=(8)/(25)