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)]Read More

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