Using suitable rearrangement find the sum:
(a) 4/7 + (-4/9) + 3/7 + (-13/9)
(b) -5 + 7/10 + 3/7 + (-3) + 5/14 + -4/5

Solution:

(a)4/7 + (-4/9) + 3/7 + (-13/9)

We evaluate by grouping the like fractions.

= 4/7 - 4/9 + 3/7 - 13/9

= (4/7 + 3/7) + (-4/9 - 13/9)

= 7/7 + -17/9

= 1 - 17/9

= 9/9 - 17/9

= (9 - 17)/9

= -8/9

(b) -5 + 7/10 + 3/7 + (-3) + 5/14 + -4/5

= -5 - 3 + 6/14 + 5/14 + 7/10 - 8/10

= -8 + 11/14 - 1/10

= -560/70 + 55/70 -7/70

= -512/70

= -256/35

✦ Try This: Using suitable rearrangement find the sum: 4/7 + 2/7 + 1/7 - 3/7

= 4/7 + 2/7 + 1/7 - 3/7

= (4 + 2 + 1 - 3)/7

= 4/7

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1

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NCERT Exemplar Class 8 Maths Chapter 1 Problem 102

Using suitable rearrangement find the sum: (a) 4/7 + (-4/9) + 3/7 + (-13/9), (b) -5 + 7/10 + 3/7 + (-3) + 5/14 + -4/5

Summary:

Using suitable rearrangement find the sum: (a) 4/7 + (-4/9) + 3/7 + (-13/9) = -8/9, (b) -5 + 7/10 + 3/7 + (-3) + 5/14 + -4/5 = -256/35

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☛ Related Questions:

• Verify -(-x) = x for (i) when x = 3/5, (ii) x = -7/9, (iii) x = 13/-15
• Give one example each to show that the rational numbers are closed under addition, subtraction and m . . . .
• Verify the property x + y = y + x of rational numbers by taking (a) x = 1/2, y = 1/2, (b) x = -2/3, . . . .