Question

select the correct answer.
choose the number sentence that illustrates the distributive property of multiplication over addition.

• $6×(5 + 4)=(6×5)+(6×4)$
• $6×(5 + 4)=(6×5)+4$
• $6×(5 + 4)=(6 + 5)×(6 + 4)$

Explanation:

Step1: Recall Distributive Property

The distributive property of multiplication over addition states that \( a \times (b + c) = (a \times b) + (a \times c) \) for any real numbers \( a \), \( b \), and \( c \).

Step2: Analyze Each Option

• First Option: \( 6 \times (5 + 4) = (6 \times 5) + (6 \times 4) \). Here, \( a = 6 \), \( b = 5 \), \( c = 4 \), which matches the distributive property formula \( a \times (b + c) = (a \times b) + (a \times c) \).
• Second Option: \( 6 \times (5 + 4) = (6 \times 5) + 4 \). This does not follow the distributive property because the second term should be \( 6 \times 4 \), not \( 4 \).
• Third Option: \( 6 \times (5 + 4) = (6 + 5) \times (6 + 4) \). This is not the distributive property; it incorrectly distributes multiplication as addition in the factors.

Answer:

A. \( 6 \times (5 + 4) = (6 \times 5) + (6 \times 4) \)