Answer:
We will use the concepts of fractions to solve this.
(a) 2/3 + 1/7
LCM of 3 and 7 = 21
(2 × 7 + 1 × 3) / 21 = (14 + 3) / 21
= 17/21
(b) 3/10 + 7/15
LCM of 10 and 15 = 30
= (3 × 3 + 7 × 2) / 30 = (14 + 9) / 30
= 23/30
(c) 4/9 + 2/7
LCM of 9 and 7 = 63
= (4 × 7 + 2 × 9) / 63 = (28 + 18) / 63
= 46/63
(d) 5/7 + 1/3
LCM of 7 and 3 = 21
= (5 × 3 + 1 × 7) / 21 = (15 + 7) / 21
= 22/21
(e) 2/5 + 1/6
LCM of 5 and 6 = 30
= (2 × 6 + 1 × 5) / 30 = (12 + 5) / 30
= 17/30
(f) 4/5 + 2/3
LCM of 5 and 3 = 15
= (4 × 3 + 5 × 2) / 15 = (12 + 10) / 15
= 22/15
(g) 3/4 - 1/3
LCM of 4 and 3 = 12
= (3 × 3 + 1 × 4) / 12 = (9-4) / 12
= 5/12
(h) 5/6 - 1/3
LCM of 6 and 3 = 6
= (1 × 5 - 1 × 2) / 6 = (5 - 2) / 6
= 3/6
= 1/2
(i) 2/3 + 3/4 + 1/2
LCM of 3,4 and 2 = 12
= (2 × 4 + 3 × 3 + 1 × 6) /12 = (8 + 9 + 6) / 12
= 23 / 12
(j) 1/2 + 1/3 + 1/6
LCM of 2,3 and 6 = 6
= (1 × 3 + 1 × 2 + 1 × 1) / = (3 + 2 + 1) / 6
= 6 / 6
= 1
(k) 113 + 323
= 1 + 1/3 + 3 + 2/3 = 4 + 1/3 + 2/3
= 4 + 1/3 + 2/3 = 4 + 3/3
= 4 + 1 = 5
(l) 423 + 314
= 4 + 2/3 + 3 + 1/4 = 7 + 2/3 + 1/4
= 7 + (2 × 4 + 1 × 3) / 12
= 7 + 11/12
= 95 / 12
(m) 16/5 - 7/5
= 16 × 1 - 7 × 1 = (16 - 7) / 5
= 9 / 5
(n) 4/3 - 1/2
= (4 × 2 - 1 × 3) / 6
= (8 - 3) / 6
= 5 / 6
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