Fractions - Exercise 6.9 Class 6 Notes | EduRev

Mathematics (Maths) Class 6

Class 6 : Fractions - Exercise 6.9 Class 6 Notes | EduRev

 Page 1


 
 
 
 
 
 
Exercise 6.9                                                                               page: 6.35 
1. Add: 
(i) 3/4 and 5/6 
(ii) 7/10 and 2/15 
(iii) 8/13 and 2/3 
(iv) 4/5 and 7/15 
Solution: 
 
(i) 3/4 and 5/6 
It can be written as 
3/4 + 5/6 
We know that the LCM of 4 and 6 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(3 × 3)/ (4 × 3)] + [(5 × 2)/ (6 × 2)] 
On further calculation 
= 9/12 + 10/ 12 
We get 
= (9 + 10)/ 12 = 19/12 
 
(ii) 7/10 and 2/15 
It can be written as 
7/10 + 2/15 
We know that the LCM of 10 and 15 is 30 
In order to convert fraction into equivalent fraction having 30 as denominator 
= [(7 × 3)/ (10 × 3)] + [(2 × 2)/ (15 × 2)] 
On further calculation 
= 21/30 + 4/ 30 
We get 
= (21 + 4)/ 30 = 25/30 = 5/6 
 
(iii) 8/13 and 2/3 
It can be written as 
8/13 + 2/3 
We know that the LCM of 13 and 3 is 39 
In order to convert fraction into equivalent fraction having 39 as denominator 
= [(8 × 3)/ (13 × 3)] + [(2 × 13)/ (3 × 13)] 
On further calculation 
= 24/39 + 26/39 
We get 
= (24 + 26)/ 39 = 50/39 
 
(iv) 4/5 and 7/15 
It can be written as 
4/5 + 7/15 
We know that the LCM of 5 and 15 is 1 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(4 × 3)/ (5 × 3)] + [(7 × 1)/ (15 × 1)] 
On further calculation 
= 12/15 + 7/ 15 
Page 2


 
 
 
 
 
 
Exercise 6.9                                                                               page: 6.35 
1. Add: 
(i) 3/4 and 5/6 
(ii) 7/10 and 2/15 
(iii) 8/13 and 2/3 
(iv) 4/5 and 7/15 
Solution: 
 
(i) 3/4 and 5/6 
It can be written as 
3/4 + 5/6 
We know that the LCM of 4 and 6 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(3 × 3)/ (4 × 3)] + [(5 × 2)/ (6 × 2)] 
On further calculation 
= 9/12 + 10/ 12 
We get 
= (9 + 10)/ 12 = 19/12 
 
(ii) 7/10 and 2/15 
It can be written as 
7/10 + 2/15 
We know that the LCM of 10 and 15 is 30 
In order to convert fraction into equivalent fraction having 30 as denominator 
= [(7 × 3)/ (10 × 3)] + [(2 × 2)/ (15 × 2)] 
On further calculation 
= 21/30 + 4/ 30 
We get 
= (21 + 4)/ 30 = 25/30 = 5/6 
 
(iii) 8/13 and 2/3 
It can be written as 
8/13 + 2/3 
We know that the LCM of 13 and 3 is 39 
In order to convert fraction into equivalent fraction having 39 as denominator 
= [(8 × 3)/ (13 × 3)] + [(2 × 13)/ (3 × 13)] 
On further calculation 
= 24/39 + 26/39 
We get 
= (24 + 26)/ 39 = 50/39 
 
(iv) 4/5 and 7/15 
It can be written as 
4/5 + 7/15 
We know that the LCM of 5 and 15 is 1 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(4 × 3)/ (5 × 3)] + [(7 × 1)/ (15 × 1)] 
On further calculation 
= 12/15 + 7/ 15 
 
 
 
 
 
 
We get 
= (12 + 7)/ 15 = 19/15 
 
2. Subtract: 
(i) 2/7 from 19/21 
(ii) 21/25 from 18/20 
(iii) 7/16 from 2 
(iv) 4/15 from 2 1/5 
Solution: 
 
(i) 2/7 from 19/21 
It can be written as 
19/21 – 2/7 
We know that LCM of 21 and 7 is 21 
In order to convert fraction into equivalent fraction having 21 as denominator 
= [(19 × 1)/ (21 × 1)] - [(2 × 3)/ (7 × 3)] 
On further calculation 
= 19/21 - 6/21 
We get 
= (19 - 6)/21 = 13/21 
 
(ii) 21/25 from 18/20 
It can be written as 
18/20 – 21/25 
We know that LCM of 20 and 25 is 100 
In order to convert fraction into equivalent fraction having 100 as denominator 
= [(18 × 5)/ (20 × 5)] - [(21 × 4)/ (25 × 4)] 
On further calculation 
= 90/100 - 84/100 
We get 
= (90 - 84)/100 = 6/100 = 3/50 
 
(iii) 7/16 from 2 
It can be written as 
2/1 – 7/16 
We know that LCM of 1 and 16 is 16 
In order to convert fraction into equivalent fraction having 16 as denominator 
= [(16 × 2)/ (16 × 1)] - [(7 × 1)/ (16 × 1)] 
On further calculation 
= 32/16 - 7/16 
We get 
= (32 - 7)/16 = 25/16 
 
(iv) 4/15 from 2 1/5 
It can be written as 
11/5 – 4/15  
We know that LCM of 5 and 15 is 15 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(11 × 3)/ (5 × 3)] - [(4 × 1)/ (15 × 1)] 
Page 3


 
 
 
 
 
 
Exercise 6.9                                                                               page: 6.35 
1. Add: 
(i) 3/4 and 5/6 
(ii) 7/10 and 2/15 
(iii) 8/13 and 2/3 
(iv) 4/5 and 7/15 
Solution: 
 
(i) 3/4 and 5/6 
It can be written as 
3/4 + 5/6 
We know that the LCM of 4 and 6 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(3 × 3)/ (4 × 3)] + [(5 × 2)/ (6 × 2)] 
On further calculation 
= 9/12 + 10/ 12 
We get 
= (9 + 10)/ 12 = 19/12 
 
(ii) 7/10 and 2/15 
It can be written as 
7/10 + 2/15 
We know that the LCM of 10 and 15 is 30 
In order to convert fraction into equivalent fraction having 30 as denominator 
= [(7 × 3)/ (10 × 3)] + [(2 × 2)/ (15 × 2)] 
On further calculation 
= 21/30 + 4/ 30 
We get 
= (21 + 4)/ 30 = 25/30 = 5/6 
 
(iii) 8/13 and 2/3 
It can be written as 
8/13 + 2/3 
We know that the LCM of 13 and 3 is 39 
In order to convert fraction into equivalent fraction having 39 as denominator 
= [(8 × 3)/ (13 × 3)] + [(2 × 13)/ (3 × 13)] 
On further calculation 
= 24/39 + 26/39 
We get 
= (24 + 26)/ 39 = 50/39 
 
(iv) 4/5 and 7/15 
It can be written as 
4/5 + 7/15 
We know that the LCM of 5 and 15 is 1 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(4 × 3)/ (5 × 3)] + [(7 × 1)/ (15 × 1)] 
On further calculation 
= 12/15 + 7/ 15 
 
 
 
 
 
 
We get 
= (12 + 7)/ 15 = 19/15 
 
2. Subtract: 
(i) 2/7 from 19/21 
(ii) 21/25 from 18/20 
(iii) 7/16 from 2 
(iv) 4/15 from 2 1/5 
Solution: 
 
(i) 2/7 from 19/21 
It can be written as 
19/21 – 2/7 
We know that LCM of 21 and 7 is 21 
In order to convert fraction into equivalent fraction having 21 as denominator 
= [(19 × 1)/ (21 × 1)] - [(2 × 3)/ (7 × 3)] 
On further calculation 
= 19/21 - 6/21 
We get 
= (19 - 6)/21 = 13/21 
 
(ii) 21/25 from 18/20 
It can be written as 
18/20 – 21/25 
We know that LCM of 20 and 25 is 100 
In order to convert fraction into equivalent fraction having 100 as denominator 
= [(18 × 5)/ (20 × 5)] - [(21 × 4)/ (25 × 4)] 
On further calculation 
= 90/100 - 84/100 
We get 
= (90 - 84)/100 = 6/100 = 3/50 
 
(iii) 7/16 from 2 
It can be written as 
2/1 – 7/16 
We know that LCM of 1 and 16 is 16 
In order to convert fraction into equivalent fraction having 16 as denominator 
= [(16 × 2)/ (16 × 1)] - [(7 × 1)/ (16 × 1)] 
On further calculation 
= 32/16 - 7/16 
We get 
= (32 - 7)/16 = 25/16 
 
(iv) 4/15 from 2 1/5 
It can be written as 
11/5 – 4/15  
We know that LCM of 5 and 15 is 15 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(11 × 3)/ (5 × 3)] - [(4 × 1)/ (15 × 1)] 
 
 
 
 
 
 
On further calculation 
= 33/15 - 4/15 
We get 
= (33 - 4)/15 = 29/15 
 
3. Find the difference of: 
(i) 13/24 and 7/16 
(ii) 5/18 and 4/15 
(iii) 1/12 and 3/4 
(iv) 2/3 and 6/7 
Solution: 
 
(i) 13/24 and 7/16 
It can be written as 
13/24 – 7/16 
We know that LCM of 24 and 16 is 48 
In order to convert fraction into equivalent fraction having 48 as denominator 
= [(13 × 2)/ (24 × 2)] - [(7 × 3)/ (16 × 3)] 
On further calculation 
= 26/48 - 21/48 
We get 
= (26 - 21)/48 = 5/48 
 
(ii) 5/18 and 4/15 
It can be written as 
5/18 – 4/15 
We know that LCM of 18 and 15 is 90 
In order to convert fraction into equivalent fraction having 90 as denominator 
= [(5 × 5)/ (18 × 5)] - [(4 × 6)/ (15 × 6)] 
On further calculation 
= 25/90 - 24/90 
We get 
= (25 - 24)/90 = 1/90 
 
(iii) 1/12 and 3/4 
It can be written as 
3/4 – 1/12 
We know that LCM of 4 and 12 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(3 × 3)/ (4 × 3)] - [(1 × 1)/ (12 × 1)] 
On further calculation 
= 9/12 - 1/12 
We get 
= (9 - 1)/12 = 8/12 = 2/3 
 
(iv) 2/3 and 6/7 
It can be written as 
6/7 – 2/3 
We know that LCM of 7 and 3 is 21 
In order to convert fraction into equivalent fraction having 48 as denominator 
Page 4


 
 
 
 
 
 
Exercise 6.9                                                                               page: 6.35 
1. Add: 
(i) 3/4 and 5/6 
(ii) 7/10 and 2/15 
(iii) 8/13 and 2/3 
(iv) 4/5 and 7/15 
Solution: 
 
(i) 3/4 and 5/6 
It can be written as 
3/4 + 5/6 
We know that the LCM of 4 and 6 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(3 × 3)/ (4 × 3)] + [(5 × 2)/ (6 × 2)] 
On further calculation 
= 9/12 + 10/ 12 
We get 
= (9 + 10)/ 12 = 19/12 
 
(ii) 7/10 and 2/15 
It can be written as 
7/10 + 2/15 
We know that the LCM of 10 and 15 is 30 
In order to convert fraction into equivalent fraction having 30 as denominator 
= [(7 × 3)/ (10 × 3)] + [(2 × 2)/ (15 × 2)] 
On further calculation 
= 21/30 + 4/ 30 
We get 
= (21 + 4)/ 30 = 25/30 = 5/6 
 
(iii) 8/13 and 2/3 
It can be written as 
8/13 + 2/3 
We know that the LCM of 13 and 3 is 39 
In order to convert fraction into equivalent fraction having 39 as denominator 
= [(8 × 3)/ (13 × 3)] + [(2 × 13)/ (3 × 13)] 
On further calculation 
= 24/39 + 26/39 
We get 
= (24 + 26)/ 39 = 50/39 
 
(iv) 4/5 and 7/15 
It can be written as 
4/5 + 7/15 
We know that the LCM of 5 and 15 is 1 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(4 × 3)/ (5 × 3)] + [(7 × 1)/ (15 × 1)] 
On further calculation 
= 12/15 + 7/ 15 
 
 
 
 
 
 
We get 
= (12 + 7)/ 15 = 19/15 
 
2. Subtract: 
(i) 2/7 from 19/21 
(ii) 21/25 from 18/20 
(iii) 7/16 from 2 
(iv) 4/15 from 2 1/5 
Solution: 
 
(i) 2/7 from 19/21 
It can be written as 
19/21 – 2/7 
We know that LCM of 21 and 7 is 21 
In order to convert fraction into equivalent fraction having 21 as denominator 
= [(19 × 1)/ (21 × 1)] - [(2 × 3)/ (7 × 3)] 
On further calculation 
= 19/21 - 6/21 
We get 
= (19 - 6)/21 = 13/21 
 
(ii) 21/25 from 18/20 
It can be written as 
18/20 – 21/25 
We know that LCM of 20 and 25 is 100 
In order to convert fraction into equivalent fraction having 100 as denominator 
= [(18 × 5)/ (20 × 5)] - [(21 × 4)/ (25 × 4)] 
On further calculation 
= 90/100 - 84/100 
We get 
= (90 - 84)/100 = 6/100 = 3/50 
 
(iii) 7/16 from 2 
It can be written as 
2/1 – 7/16 
We know that LCM of 1 and 16 is 16 
In order to convert fraction into equivalent fraction having 16 as denominator 
= [(16 × 2)/ (16 × 1)] - [(7 × 1)/ (16 × 1)] 
On further calculation 
= 32/16 - 7/16 
We get 
= (32 - 7)/16 = 25/16 
 
(iv) 4/15 from 2 1/5 
It can be written as 
11/5 – 4/15  
We know that LCM of 5 and 15 is 15 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(11 × 3)/ (5 × 3)] - [(4 × 1)/ (15 × 1)] 
 
 
 
 
 
 
On further calculation 
= 33/15 - 4/15 
We get 
= (33 - 4)/15 = 29/15 
 
3. Find the difference of: 
(i) 13/24 and 7/16 
(ii) 5/18 and 4/15 
(iii) 1/12 and 3/4 
(iv) 2/3 and 6/7 
Solution: 
 
(i) 13/24 and 7/16 
It can be written as 
13/24 – 7/16 
We know that LCM of 24 and 16 is 48 
In order to convert fraction into equivalent fraction having 48 as denominator 
= [(13 × 2)/ (24 × 2)] - [(7 × 3)/ (16 × 3)] 
On further calculation 
= 26/48 - 21/48 
We get 
= (26 - 21)/48 = 5/48 
 
(ii) 5/18 and 4/15 
It can be written as 
5/18 – 4/15 
We know that LCM of 18 and 15 is 90 
In order to convert fraction into equivalent fraction having 90 as denominator 
= [(5 × 5)/ (18 × 5)] - [(4 × 6)/ (15 × 6)] 
On further calculation 
= 25/90 - 24/90 
We get 
= (25 - 24)/90 = 1/90 
 
(iii) 1/12 and 3/4 
It can be written as 
3/4 – 1/12 
We know that LCM of 4 and 12 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(3 × 3)/ (4 × 3)] - [(1 × 1)/ (12 × 1)] 
On further calculation 
= 9/12 - 1/12 
We get 
= (9 - 1)/12 = 8/12 = 2/3 
 
(iv) 2/3 and 6/7 
It can be written as 
6/7 – 2/3 
We know that LCM of 7 and 3 is 21 
In order to convert fraction into equivalent fraction having 48 as denominator 
 
 
 
 
 
 
= [(6 × 3)/ (7 × 3)] - [(2 × 7)/ (3 × 7)] 
On further calculation 
= 18/21 - 14/21 
We get 
= (18 - 14)/21 = 4/21 
 
4. Subtract as indicated: 
(i) 8/3 – 5/9 
(ii) 4 2/5 – 2 1/5 
(iii) 5 6/7 – 2 2/3 
(iv) 4 3/4 – 2 1/6 
Solution: 
 
(i) 8/3 – 5/9 
It can be written as 
8/3 – 5/9 
We know that LCM of 3 and 9 is 9 
In order to convert fraction into equivalent fraction having 9 as denominator 
= [(8 × 3)/ (3 × 3)] - [(5 × 1)/ (9 × 1)] 
On further calculation 
= 24/9 - 5/9 
We get 
= (24 - 5)/9 = 19/9  
 
(ii) 4 2/5 – 2 1/5 
It can be written as 
22/5 – 11/5 
We get 
= (22 - 11)/5 = 11/5  
 
(iii) 5 6/7 – 2 2/3 
It can be written as 
41/7 – 8/3 
We know that LCM of 7 and 3 is 21 
In order to convert fraction into equivalent fraction having 21 as denominator 
= [(41 × 3)/ (7 × 3)] - [(8 × 7)/ (3 × 7)] 
On further calculation 
= 123/21 - 56/21 
We get 
= (123 - 56)/21 = 67/21  
 
(iv) 4 3/4 – 2 1/6 
It can be written as 
19/4 – 13/6 
We know that LCM of 4 and 6 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(19 × 3)/ (4 × 3)] - [(13 × 2)/ (6 × 2)] 
Page 5


 
 
 
 
 
 
Exercise 6.9                                                                               page: 6.35 
1. Add: 
(i) 3/4 and 5/6 
(ii) 7/10 and 2/15 
(iii) 8/13 and 2/3 
(iv) 4/5 and 7/15 
Solution: 
 
(i) 3/4 and 5/6 
It can be written as 
3/4 + 5/6 
We know that the LCM of 4 and 6 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(3 × 3)/ (4 × 3)] + [(5 × 2)/ (6 × 2)] 
On further calculation 
= 9/12 + 10/ 12 
We get 
= (9 + 10)/ 12 = 19/12 
 
(ii) 7/10 and 2/15 
It can be written as 
7/10 + 2/15 
We know that the LCM of 10 and 15 is 30 
In order to convert fraction into equivalent fraction having 30 as denominator 
= [(7 × 3)/ (10 × 3)] + [(2 × 2)/ (15 × 2)] 
On further calculation 
= 21/30 + 4/ 30 
We get 
= (21 + 4)/ 30 = 25/30 = 5/6 
 
(iii) 8/13 and 2/3 
It can be written as 
8/13 + 2/3 
We know that the LCM of 13 and 3 is 39 
In order to convert fraction into equivalent fraction having 39 as denominator 
= [(8 × 3)/ (13 × 3)] + [(2 × 13)/ (3 × 13)] 
On further calculation 
= 24/39 + 26/39 
We get 
= (24 + 26)/ 39 = 50/39 
 
(iv) 4/5 and 7/15 
It can be written as 
4/5 + 7/15 
We know that the LCM of 5 and 15 is 1 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(4 × 3)/ (5 × 3)] + [(7 × 1)/ (15 × 1)] 
On further calculation 
= 12/15 + 7/ 15 
 
 
 
 
 
 
We get 
= (12 + 7)/ 15 = 19/15 
 
2. Subtract: 
(i) 2/7 from 19/21 
(ii) 21/25 from 18/20 
(iii) 7/16 from 2 
(iv) 4/15 from 2 1/5 
Solution: 
 
(i) 2/7 from 19/21 
It can be written as 
19/21 – 2/7 
We know that LCM of 21 and 7 is 21 
In order to convert fraction into equivalent fraction having 21 as denominator 
= [(19 × 1)/ (21 × 1)] - [(2 × 3)/ (7 × 3)] 
On further calculation 
= 19/21 - 6/21 
We get 
= (19 - 6)/21 = 13/21 
 
(ii) 21/25 from 18/20 
It can be written as 
18/20 – 21/25 
We know that LCM of 20 and 25 is 100 
In order to convert fraction into equivalent fraction having 100 as denominator 
= [(18 × 5)/ (20 × 5)] - [(21 × 4)/ (25 × 4)] 
On further calculation 
= 90/100 - 84/100 
We get 
= (90 - 84)/100 = 6/100 = 3/50 
 
(iii) 7/16 from 2 
It can be written as 
2/1 – 7/16 
We know that LCM of 1 and 16 is 16 
In order to convert fraction into equivalent fraction having 16 as denominator 
= [(16 × 2)/ (16 × 1)] - [(7 × 1)/ (16 × 1)] 
On further calculation 
= 32/16 - 7/16 
We get 
= (32 - 7)/16 = 25/16 
 
(iv) 4/15 from 2 1/5 
It can be written as 
11/5 – 4/15  
We know that LCM of 5 and 15 is 15 
In order to convert fraction into equivalent fraction having 15 as denominator 
= [(11 × 3)/ (5 × 3)] - [(4 × 1)/ (15 × 1)] 
 
 
 
 
 
 
On further calculation 
= 33/15 - 4/15 
We get 
= (33 - 4)/15 = 29/15 
 
3. Find the difference of: 
(i) 13/24 and 7/16 
(ii) 5/18 and 4/15 
(iii) 1/12 and 3/4 
(iv) 2/3 and 6/7 
Solution: 
 
(i) 13/24 and 7/16 
It can be written as 
13/24 – 7/16 
We know that LCM of 24 and 16 is 48 
In order to convert fraction into equivalent fraction having 48 as denominator 
= [(13 × 2)/ (24 × 2)] - [(7 × 3)/ (16 × 3)] 
On further calculation 
= 26/48 - 21/48 
We get 
= (26 - 21)/48 = 5/48 
 
(ii) 5/18 and 4/15 
It can be written as 
5/18 – 4/15 
We know that LCM of 18 and 15 is 90 
In order to convert fraction into equivalent fraction having 90 as denominator 
= [(5 × 5)/ (18 × 5)] - [(4 × 6)/ (15 × 6)] 
On further calculation 
= 25/90 - 24/90 
We get 
= (25 - 24)/90 = 1/90 
 
(iii) 1/12 and 3/4 
It can be written as 
3/4 – 1/12 
We know that LCM of 4 and 12 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(3 × 3)/ (4 × 3)] - [(1 × 1)/ (12 × 1)] 
On further calculation 
= 9/12 - 1/12 
We get 
= (9 - 1)/12 = 8/12 = 2/3 
 
(iv) 2/3 and 6/7 
It can be written as 
6/7 – 2/3 
We know that LCM of 7 and 3 is 21 
In order to convert fraction into equivalent fraction having 48 as denominator 
 
 
 
 
 
 
= [(6 × 3)/ (7 × 3)] - [(2 × 7)/ (3 × 7)] 
On further calculation 
= 18/21 - 14/21 
We get 
= (18 - 14)/21 = 4/21 
 
4. Subtract as indicated: 
(i) 8/3 – 5/9 
(ii) 4 2/5 – 2 1/5 
(iii) 5 6/7 – 2 2/3 
(iv) 4 3/4 – 2 1/6 
Solution: 
 
(i) 8/3 – 5/9 
It can be written as 
8/3 – 5/9 
We know that LCM of 3 and 9 is 9 
In order to convert fraction into equivalent fraction having 9 as denominator 
= [(8 × 3)/ (3 × 3)] - [(5 × 1)/ (9 × 1)] 
On further calculation 
= 24/9 - 5/9 
We get 
= (24 - 5)/9 = 19/9  
 
(ii) 4 2/5 – 2 1/5 
It can be written as 
22/5 – 11/5 
We get 
= (22 - 11)/5 = 11/5  
 
(iii) 5 6/7 – 2 2/3 
It can be written as 
41/7 – 8/3 
We know that LCM of 7 and 3 is 21 
In order to convert fraction into equivalent fraction having 21 as denominator 
= [(41 × 3)/ (7 × 3)] - [(8 × 7)/ (3 × 7)] 
On further calculation 
= 123/21 - 56/21 
We get 
= (123 - 56)/21 = 67/21  
 
(iv) 4 3/4 – 2 1/6 
It can be written as 
19/4 – 13/6 
We know that LCM of 4 and 6 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(19 × 3)/ (4 × 3)] - [(13 × 2)/ (6 × 2)] 
 
 
 
 
 
 
On further calculation 
= 57/12 - 26/12 
We get 
= (57 - 26)/12 = 31/12  
 
5. Simplify: 
(i) 2/3 + 3/4 + 1/2 
(ii) 5/8 + 2/5 + 3/4 
(iii) 3/10 + 7/15 + 3/5 
(iv) 3/4 + 7/16 + 5/8 
(v) 4 2/3 + 3 1/4 + 7 1/2 
(vi) 7 1/3 + 3 2/3 + 5 1/6 
(vii) 7 + 7/4 + 5 1/6 
(viii) 5/6 + 3 + 3/4 
(ix) 7/18 + 5/6 + 1 1/12 
Solution: 
 
(i) 2/3 + 3/4 + 1/2 
We know that the LCM of 3, 4 and 2 is 12 
In order to convert fraction into equivalent fraction having 12 as denominator 
= [(2 × 4)/ (3 × 4)] + [(3 × 3)/ (4 × 3)] + [(1 × 6)/ (2 × 6)] 
On further calculation 
= 8/12+ 9/12 + 6/12 
We get 
= (8 + 9 + 6)/ 12 = 23/12 
 
(ii) 5/8 + 2/5 + 3/4 
We know that the LCM of 8, 5 and 4 is 40 
In order to convert fraction into equivalent fraction having 40 as denominator 
= [(5 × 5)/ (8 × 5)] + [(2 × 8)/ (5 × 8)] + [(3 × 10)/ (4 × 10)] 
On further calculation 
= 25/40 + 16/40 + 30/40 
We get 
= (25 + 16 + 30)/ 40 = 71/40 
 
(iii) 3/10 + 7/15 + 3/5 
We know that the LCM of 10, 15 and 5 is 30 
In order to convert fraction into equivalent fraction having 30 as denominator 
= [(3 × 3)/ (10 × 3)] + [(7 × 2)/ (15 × 2)] + [(3 × 6)/ (5 × 6)] 
On further calculation 
= 9/30+ 14/30 + 18/30 
We get 
= (9 + 14 + 18)/ 30 = 41/30 
 
(iv) 3/4 + 7/16 + 5/8 
We know that the LCM of 4, 16 and 8 is 16 
In order to convert fraction into equivalent fraction having 16 as denominator 
= [(3 × 4)/ (4 × 4)] + [(7 × 1)/ (16 × 1)] + [(5 × 2)/ (8 × 2)] 
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