Fraction NCERT 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` of`3/7=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)`