Question

select the correct answer. choose the number sentence that illustrates the distributive property of multiplication over addition. 5×(7 + 2)=(5 + 7)×(5 + 2) 5×(7 + 2)=(5×7)+2 5×(7 + 2)=(5×7)+(5×2)

Explanation:

Step1: Recall the 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: \( 5 \times (7 + 2)=(5 + 7) \times (5 + 2) \)

This does not follow the distributive property. It incorrectly distributes 5 to both 7 and 2 by adding 5 to them instead of multiplying.

• Second option: \( 5 \times (7 + 2)=(5 \times 7)+2 \)

This is incorrect because it only multiplies 5 with 7 and then adds 2, but it should multiply 5 with both 7 and 2 and then add the results.

• Third option: \( 5 \times (7 + 2)=(5 \times 7)+(5 \times 2) \)

This follows the distributive property \( a\times(b + c)=(a\times b)+(a\times c) \) where \( a = 5 \), \( b = 7 \), and \( c = 2 \).

Answer:

\( 5 \times (7 + 2) = (5 \times 7) + (5 \times 2) \) (the third option)