Division of Fractions: NCERT Exercise 2.4
Fractions and Decimals 7th Math
Division of Fractions: NCERT Exercise 2.4
Reciprocals of a Number
The non–zero numbers whose product with each other is 1, are called the reciprocals of each other.
Example (1)
Solution :
Reciprocal of 2 is `1/2`
When we multiply the 2 with `1/2` the result is 1.
i.e. `cancel2xx1/cancel2 ` = 1
Similarly, reciprocal of `1/4` is 4
And `1/cancel4xxcancel4` = 1
Similarly, reciprocal of `3/4` is equal to `4/3`
And `cancel3/cancel4xxcancel4/cancel3` = 1
Similarly, reciprocal of `5/6` is equal to `6/5`
And their produc, `cancel5/cancel6xxcancel6/cancel5` = 1
Division of Fractions
Division of whole number by a fraction
To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.
Example Divide 3 by `4/5`
Solution :
Here reciprocal of `4/5` is equal to `5/4`
Thus, `3-:4/5 = 3xx5/4`
`=(3xx5)/4`
`=15/4` Answer
Example (2)
Solution :
Divide 5 by `2/3`
Here reciprocal of `2/3` is equal to `3/2`
Thus, `5-: 2/3 = 5xx3/2`
`=(5xx3)/2`
`= 15/2` Answer
Division of a fraction by a whole number
To divide a fraction by a whole, multiply that fraction by the reciprocal of that whole number.
Example (1) Divide `1/2` by 3
Solution :
Here, given, `1/2-:3`
The reciprocal of 3 is equal to `1/3`
Thus, `1/2xx1/3`
`=(1xx1)/(2xx3)`
`=1/6` Answer
Example (2) Divide `1/5` by 7
Solution :
Here we have to divide `1/5` by 7
The reciprocal of 7 is equal to `1/7`
Thus, `1/5-:7`
`=1/5xx1/7`
`=(1xx1)/(5xx7)`
`=1/35` Answer
Division of fraction by another fraction
To divide a fraction by any fraction, multiply that fraction by the reciprocal of that fraction.
Example (1) Divide `1/2` by `2/3`
Solution :
The reciprocal of `2/3` is equal to `3/2`
Thus, `1/2-:2/3`
`=1/2xx3/2`
`=(1xx3)/(2xx3)`
`=3/6` Answer
Example (2) Divide `5/4` by `3/4`
Solution :
The reciprocal of `3/4` is equal to `4/3`
Thus, `5/4-:3/4`
`=5/cancel4xxcancel4/3`
`=5/3` Answer
Solution of NCERT Exercise 2.4
Question (1) Find
(i) `12-: 3/4`
Solution :
Given, to find `12-: 3/4`
We know that, to divide a whole number by any fraction, we have to multiply that whole number by the reciprocal of that fraction.
Thus, here the reciprocal of `3/4` is equal to `4/3`
Thus, `12-: 3/4`
`=cancel12 4xx4/cancel3`
= 4 × 4
= 16 Answer
(ii) `14-:5/6`
Solution :
Given, `14-:5/6`
We know that, to divide a whole number by any fraction, we have to multiply that whole number by the reciprocal of that fraction.
Thus, here the reciprocal of `5/6` is equal to `6/5`
Thus, `14-:5/6`
`=14xx6/5`
`=(14xx6)/5`
`=84/5`
`=16 4/5` Answer
(iii) `8-:7/3`
Solution :
Given, `8-:7/3`
We know that, to divide a whole number by any fraction, we have to multiply that whole number by the reciprocal of that fraction.
Thus, here the reciprocal of `7/3` is equal to `3/7`
Thus, `8-:7/3`
`=8xx3/7`
`=(8xx3)/7`
`=24/7`
`=3 3/7` Answer
(iv) `4-:8/3`
Solution :
Given, `4-:8/3`
We know that, to divide a whole number by any fraction, we have to multiply that whole number by the reciprocal of that fraction.
Thus, here the reciprocal of `8/3` is equal to `3/8`
Thus, `4-:8/3`
`=cancel4xx3/(cancel8 2)`
`=(1xx3)/2`
`=3/2`
`=1 1/2` Answer
(v) `3-:2 1/3`
Solution :
Given, `3-:2 1/3`
`=3-:7/3`
We know that, to divide a whole number by any fraction, we have to multiply that whole number by the reciprocal of that fraction.
Thus, here the reciprocal of `7/3` is equal to `3/7`
`=3xx3/7`
`=(3xx3)/7`
`=9/7`
`=1 2/7` Answer
(vi) `5-:3 4/7`
Solution :
Given, `5-:3 4/7`
`=5-:25/7`
We know that, to divide a whole number by any fraction, we have to multiply that whole number by the reciprocal of that fraction.
Thus, here the reciprocal of `25/7` is equal to `7/25`
`=cancel5xx7/(cancel25 5)`
`=7/5`
`=1 2/5` Answer
Question (2) Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) `3/7`
Solution :
Given, `3/7`
Thus, reciprocal = ?
The reciprocal of `3/7` is equal to `7/3`
`=7/3`. This is a improper fraction Answer
(ii) `5/8`
Solution :
Given, `5/8`
Thus, reciprocal = ?
The reciprocal of given fraction
`=8/5`
Since, denominator is smaller than numerator, thus it is an improper fraction.
Thus, `8/5`, improper fraction. Answer
(iii) `9/7`
Solution :
Given, `9/7`
Thus, reciprocal = ?
The reciprocal of given fraction
`=7/9`
Since here numerator is smaller than denominator, thus it is a proper fraction.
Thus, `7/9`, proper fraction Answer
(iv) `6/5`
Solution :
Given, `6/5`
Thus, reciprocal = ?
The reciprocal of given fraction is equal to `5/6`
Since here numerator is greater than denominator, thus it is an improper fraction.
Thus, `5/6`, improper fraction Answer
(v) `12/7`
Solution :
Given, `12/7`
Thus, reciprocal = ?
The reciprocal of given fraction
`=7/12`
Since, here numerator is smaller than denominator, thus it is a proper fraction.
Thus, `7/12`, proper fraction Answer
(vi) `1/8`
Solution :
Given, `1/8`
Thus, reciprocal = ?
The reciprocal of given fraction
`=8/1=8`
Thus, 8, whole number Answer
(vii) `1/11`
Solution :
Given, `1/11`
Thus, reciprocal = ?
The reciprocal of given fraction = 8
Thus, 8, whole number Answer
Question (3) Find:
(i) `7/3-:2`
Solution :
Given, `7/3-:2`
The reciprocal of 2 is equal to `1/2`
Thus, `7/3-:2`
`=7/3xx1/2`
`=(7xx1)/(3xx2)`
`=7/6`
`=1 1/6` Answer
(ii) `4/9-:5`
Solution :
Given, `4/9-:5`
The reciprocal of 5 `=1/5`
Thus, `4/9-:5`
`=4/9xx1/5`
`=(4xx1)/(9xx5)`
`=4/45` Answer
(iii) `6/13-:7`
Solution :
Given, `6/13-:7`
The reciprocal of `7=1/7`
Thus, `6/13-:7`
`=6/13xx1/7`
`=(6xx1)/(13xx7)`
`=6/91` Answer
(iv) `4 1/3-:3`
Solution :
Given, `4 1/3-:3`
`=13/3-:3`
The reciprocal of `3=1/3`
Thus, `13/3-:3`
`=13/3xx1/3`
`=(13xx1)/(3xx3)`
`=13/9`
`=1 4/9` Answer
(v) `3 1/2-:4`
Solution :
Given, `3 1/2-:4`
`=7/2-:4`
The reciprocal of `4=1/4`
`=7/2xx1/4`
`=(7xx1)/(2xx4)`
`=7/8` Answer
(vi) `4 3/7-:7`
Solution :
Given, `4 3/7-:7`
`=31/7-:7`
The reciprocal of `7=1/7`
`=31/7xx1/7`
`=(31xx1)/(7xx7)`
`=31/49` Answer
Question (4) Find :
(i) `2/5-:1/2`
Solution :
Given, `2/5-:1/2`
The reciprocal of `1/2=2/1`
`=2/5xx2/1`
`=(2xx2)/(5xx1)`
`=4/5` Answer
(ii) `4/9-:2/3`
Solution :
Given, `4/9-:2/3`
The reciprocal of `2/3=3/2`
`=4/9xx2/3`
`=(4xx2)/(9xx3)`
`=8/27` Answer
(iii) `3/7-:8/7`
Solution :
Given, `3/7-:8/7`
The reciprocal of `8/7=7/8`
`=3/cancel7xxcancel7/8`
`=3/8` Answer
(iv) `2 1/3-:3/5`
Solution :
Given, `2 1/3-:3/5`
`=7/3-:3/5`
The reciprocal of `3/5=5/3`
`=7/3xx5/3`
`=(7xx5)/(3xx3)`
`=35/9`
`=3 8/9` Answer
(v) `3 1/2-:8/3`
Solution :
Given, `3 1/2-:8/3`
`=7/2-:8/3`
The reciprocal of `8/3=3/8`
`=7/2xx3/8`
`=(7xx3)/(2xx8)`
`=21/16`
`=1 5/16` Answer
(vi) `2/5-:1 1/2`
Solution :
Given, `2/5-:1 1/2`
`=2/5-:3/2`
The reciprocal of `3/2=2/3`
`=2/5xx2/3`
`=(2xx2)/(5xx3)`
`=4/15` Answer
(vii) `3 1/5-:1 2/3`
Solution :
Given, `3 1/5-:1 2/3`
`=16/5-:5/3`
The reciprocal of `5/3=3/5`
`=16/5xx3/5`
`=(16xx3)/(5xx5)`
`=48/25`
`=1 23/25` Answer
(viii) `2 1/5-:1 1/5`
Solution :
Given, `2 1/5-:1 1/5`
`=11/5-:6/5`
The reciprocal of `6/5=5/6`
`=cancel6/cancel5xxcancel5/cancel6`
=1 Answer
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