Question

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

• $7×(4 + 3)=(7 + 4)×(7 + 3)$
• $7×(4 + 3)=(7×4)+(7×3)$
• $7×(4 + 3)=(7×4)+3$

Explanation:

Step1: Recall the distributive property

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

Step2: Analyze each option

• First option: \(7\times(4 + 3)=(7 + 4)\times(7 + 3)\) does not follow the distributive property. The right - hand side is incorrect as it is not of the form \((a\times b)+(a\times c)\).
• Second option: \(7\times(4 + 3)=(7\times4)+(7\times3)\) matches the form \(a\times(b + c)=(a\times b)+(a\times c)\) where \(a = 7\), \(b = 4\), and \(c = 3\).
• Third option: \(7\times(4 + 3)=(7\times4)+3\) is incorrect because the \(3\) on the right - hand side is not multiplied by \(7\) as required by the distributive property.

Answer:

\(7\times(4 + 3)=(7\times4)+(7\times3)\) (the second option)