Verify associative property of addition for the given rational numbers. a) 3/2, 1/4, 7/6
Answers
Step-by-step explanation:
1/2, 2/3 and -1/6
Show that:
1/2 + (2/3 + (-1/6) = (1/2 + 2/3) + (-1/6)
∵ 1/2 + (2/3 + (-1/6)
∴ LCM of 3 and 6 = 6
= 1/2 + (2 × 2/3 × 2) + (-1 × 1/6 ×1)
= 1/2 + (4/6 – 1/6)
= 1/2 + [(4-1)/6]
=1/2 + (3/6)
= (1 × 3/2 × 3) + (3 × 1/6 × 1) (∵ LCM of 2 and 6 = 3)
= (3 + 3)/6 = 6/6 = 1
And, (1/2 + 2/3) + (-1/6)
∴ LCM of 2 and 3 = 6
= (1 × 3/2 × 3) + (2 × 2/3 × 2) + (-1/6)
= (3 + 4)/6 + -1/6
= (7 – 1)/6 = 6/6 = 1
∴ 1/2 + (2/3 + (-1/6) = (1/2 + 2/3) + (-1/6)
This verifies associative property of the addition of rational numbers.
(ii) -2/5, 4/15 and -7/10
Show that:
-2/5 + (4/15 + (-7/10) = (-2/5 + 4/15) + (-7/10)
∵ -2/5 + (4/15 + (-7/10)
∴ LCM of 15, 10 = 2 × 3 × 5 = 30
= -2/5 + (4 × 2/15 × 2) + (-7 × 3/10 × 3)
(∵ LCM of 15 and 10 = 30)
= -2/5 + [(8 – 21)/30]
= -2/5 – 13/30 = (-2 × 6/5 × 6) – (13 × 1/30 × 1)
= (-12 -13)/30 = -25/30 = -5/6
And, (-2/5 + 4/15) + -7/10
∴ LCM of 5 and 15 = 3 × 5 = 15
= (-2 × 3/5 × 3) + (4 × 1/15 ×1) + -7/10
∴ LCM of 5 and 15 = 15
= (-6 + 4)/15 + (-7/10)
= -2/15 + (-7/10)
= (-2 × 2/15 × 2) – (7 × 3/10 × 3)
= -4/30 – 21/30 = -25/30 = -5/6
∴ -2/5 + (4/15 + (-7/10) = (-2 /5 + 4/15) + (-7/10)
This verifies associative property of the addition of rational numbers.
Answer:
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