Question

select the correct answer. choose the number sentence that illustrates the distributive property of multiplication over addition. \bigcirc \\ 2\times(5 + 4)=(2\times5)+4 \bigcirc \\ 2\times(5 + 4)=(2\times5)+(2\times4) \bigcirc \\ 2\times(5 + 4)=(2 + 5)\times(2 + 4)

Explanation:

Step1: Recall 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: \(2\times(5 + 4)=(2\times5)+4\). Here, the 2 is not distributed to the 4 (since we have \(+4\) instead of \(+ (2\times4)\)), so this is incorrect.
• Second option: \(2\times(5 + 4)=(2\times5)+(2\times4)\). Here, \(a = 2\), \(b = 5\), \(c = 4\), and it follows \(a\times(b + c)=(a\times b)+(a\times c)\), so this is correct.
• Third option: \(2\times(5 + 4)=(2 + 5)\times(2 + 4)\). This does not follow the distributive property (it's a wrong expansion), so this is incorrect.

Answer:

\(2\times(5 + 4)=(2\times5)+(2\times4)\) (the second option)