Which property shows that (ab)c = a(bc)?

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Study for the GACE Elementary Education II Test. Prep with flashcards and multiple-choice questions, each with hints and explanations. Get ready for your exam!

Multiple Choice

Which property shows that (ab)c = a(bc)?

Explanation:
The idea is that numbers can be grouped in multiplication without changing the result. This is the associative property of multiplication: (ab)c = a(bc) for any numbers a, b, and c. You can see it works by example: with a = 2, b = 3, c = 4, (2×3)×4 = 6×4 = 24 and 2×(3×4) = 2×12 = 24. Since both expressions yield the same product, the grouping doesn’t affect the outcome. This differs from the distributive property, which relates multiplication to addition (a(b + c) = ab + ac), from the commutative property, which concerns swapping order (ab = ba), and from the identity property, which says multiplying by 1 doesn't change the number.

The idea is that numbers can be grouped in multiplication without changing the result. This is the associative property of multiplication: (ab)c = a(bc) for any numbers a, b, and c. You can see it works by example: with a = 2, b = 3, c = 4, (2×3)×4 = 6×4 = 24 and 2×(3×4) = 2×12 = 24. Since both expressions yield the same product, the grouping doesn’t affect the outcome. This differs from the distributive property, which relates multiplication to addition (a(b + c) = ab + ac), from the commutative property, which concerns swapping order (ab = ba), and from the identity property, which says multiplying by 1 doesn't change the number.

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