Using suitable rearrangement

Question:

Using suitable rearrangement and find the sum:

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

(b) -5 + (7/10) + (3/7) + (-3) + (5/45) + (-4/5)

Solution:

First rearrange the rational numbers and add the numbers with same denominator.

= (4/7) + (3/7) – (4/9) – (13/9)

= ((4 + 3)/7) – ((4 + 13)/9)

= (7/7) – (17/9)

= 1 – (17/9)

= (9 – 17)/9

= -8/9

(b) -5 + (7/10) + (3/7) + (-3) + (5/45) + (-4/5)

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

= 8 + [(7-8)/10] + [(6 + 5)/14]

= – 8 – (1/10) + (11/14)

LCM of 1, 10 and 14 is 70

= (-560 – 7 + 55)/70

= -512/70

= – 256/35

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