Question

select the correct answer. choose the number sentence that illustrates the distributive property of multiplication over add 6×(5 + 8) = (6 × 5) + 8 6×(5 + 8) = (6 + 5) × (6 + 8) 6×(5 + 8) = (6 × 5) + (6 × 8)

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: \(6\times(5 + 8)=(6\times5)+8\). Here, only \(5\) is multiplied by \(6\), but \(8\) is not, so it does not follow the distributive property.
• Second option: \(6\times(5 + 8)=(6 + 5)\times(6 + 8)\). This is incorrect as it is not the form of the distributive property (it resembles a wrong expansion, more like a misapplication of something else).
• Third option: \(6\times(5 + 8)=(6\times5)+(6\times8)\). This matches the distributive property formula \(a\times(b + c)=(a\times b)+(a\times c)\) where \(a = 6\), \(b = 5\), and \(c = 8\).

Answer:

\(6\times(5 + 8)=(6\times5)+(6\times8)\) (the third option)