1 Answers
To show that rational numbers are associative under multiplication, we need to demonstrate that the two expressions you provided are equal.
Let's evaluate the expressions:
a = (2/3) × ((6/7) × (3/7))
b = ((2/3) × (6/7)) × (3/5)
Expression a:
a = (2/3) × ((6/7) × (3/7))
a = (2/3) × (18/49) (simplify the inner multiplication)
a = 36/147 (multiply the numerators and denominators)
a = 4/7 (simplify the fraction)
Expression b:
b = ((2/3) × (6/7)) × (3/5)
b = (12/21) × (3/5) (simplify the inner multiplication)
b = 36/105 (multiply the numerators and denominators)
b = 12/35 (simplify the fraction)
As a and b do not yield the same result, the given expressions do not show that rational numbers are associative under multiplication.
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