What is: 3/4 + (1/3 / 1/6) - (-1/2) = a

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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