# 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` 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)`