Question

select the correct answer. choose the number sentence that illustrates the distributive property of multiplication over addition. \bigcirc\\; 3\times(9 + 5)=(3\times9)\times(3\times5) \bigcirc\\; 3\times(9 + 5)=(3\times9)+(3\times5) \bigcirc\\; 3\times(9 + 5)=(3\times9)+5

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: \(3\times(9 + 5)=(3\times9)\times(3\times5)\)

The right - hand side is a multiplication of two products, which is not the form of the distributive property. The distributive property should result in a sum of two products, not a product of two products.

• Second option: \(3\times(9 + 5)=(3\times9)+(3\times5)\)

Here, \(a = 3\), \(b = 9\) and \(c = 5\). It follows the form \(a\times(b + c)=a\times b+a\times c\) of the distributive property of multiplication over addition.

• Third option: \(3\times(9 + 5)=(3\times9)+5\)

In this case, the \(5\) on the right - hand side is not multiplied by \(3\), so it does not follow the distributive property. The correct form should have both \(9\) and \(5\) multiplied by \(3\) and then added.

Answer:

\(3\times(9 + 5)=(3\times9)+(3\times5)\) (the second option)