The rule a(b + c) = ab + ac illustrates which property?

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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

The rule a(b + c) = ab + ac illustrates which property?

Explanation:
This shows how multiplication distributes over addition. The outside factor multiplies each addend inside the parentheses, which is the distributive property: a(b + c) = ab + ac. For example, with a = 3, b = 4, and c = 5, 3(4 + 5) = 3×9 = 27, and 3×4 + 3×5 = 12 + 15 = 27, so both sides are equal. This principle is used to expand expressions and to simplify or factor algebraic expressions. The other properties don’t describe distributing over a sum: the commutative property is about the order of multiplication (ab = ba), the transitive property is about chains of equality (if a = b and b = c, then a = c), and the reciprocal property involves numbers that multiply to 1.

This shows how multiplication distributes over addition. The outside factor multiplies each addend inside the parentheses, which is the distributive property: a(b + c) = ab + ac. For example, with a = 3, b = 4, and c = 5, 3(4 + 5) = 3×9 = 27, and 3×4 + 3×5 = 12 + 15 = 27, so both sides are equal. This principle is used to expand expressions and to simplify or factor algebraic expressions. The other properties don’t describe distributing over a sum: the commutative property is about the order of multiplication (ab = ba), the transitive property is about chains of equality (if a = b and b = c, then a = c), and the reciprocal property involves numbers that multiply to 1.

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