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Solve
(a) 2/3 + 1/7
(b) 3/10 + 7/15
(c) 4/9 + 2/7
(d) 5/7 + 1/3
(e) 2/5 + 1/6
(f) 4/5 + 2/3
(g) 3/4 - 1/3
(h) 5/6 - 1/3
(i) 2/3 + 3/4 + 1/2
(j) 1/2 + 1/3 + 1/6
(k) \(1{\dfrac{1}{3}}\) + \(3{\dfrac{2}{3}}\)
(l) \(4{\dfrac{2}{3}}\) + \(3{\dfrac{1}{4}}\)
(m) 16/5 - 7/5
(n) 4/3 - 1/2

Solution:

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) \(1{\dfrac{1}{3}}\) + \(3{\dfrac{2}{3}}\)
= 1 + 1/3 + 3 + 2/3 = 4 + 1/3 + 2/3
= 4 + 1/3 + 2/3 = 4 + 3/3
= 4 + 1 = 5

(l) \(4{\dfrac{2}{3}}\) + \(3{\dfrac{1}{4}}\)
= 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

You can also use the Fraction Calculator to check your answer.

NCERT Solutions for Class 6 Maths Chapter 7 Exercise 7.6 Question 1

Solve (a) 2/3 + 1/7 (b) 3/10 + 7/15 (c) 4/9 + 2/7 (d) 5/7 + 1/3 (e) 2/5 + 1/6 (f) 4/5 + 2/3 (g) 3/4 - 1/3 (h) 5/6 - 1/3 (i) 2/3 + 3/4 + 1/2 (j) 1/2 + 1/3 + 1/6 (k) \(1{\dfrac{1}{3}}\) + \(3{\dfrac{2}{3}}\) (l) \(4{\dfrac{2}{3}}\) + \(3{\dfrac{1}{4}}\) (m) 16/5 - 7/5 (n) 4/3 - 1/2

Summary:

The required answer for all the given problems is a. 17/21 b. 23/30 c. 46/63 d. 22/21 e. 17/30 f. 22/15 g. 5/12 h. 1/2 i. 23/12 j.1 k. 5 l. 95/12 m. 9/5 n. 5/6

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