To find which expression correctly applies the distributive property to show equivalent expressions for the total number of bracelets Mrs. Adenan sold (which is \(63 + 36\)), we need to check if the right-hand side of each expression correctly equals \(99\) (the sum of \(63\) and \(36\)) and if the distributive property is being applied correctly.
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Checking \(63 + 36 = (3)(21) + (9)(4)\): \[ (3)(21) = 63 \quad \text{and} \quad (9)(4) = 36 \quad \Rightarrow \quad 63 + 36 = 63 + 36 , \text{(True)} \]
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Checking \(63 + 36 = (7)(9) + (12)(3)\): \[ (7)(9) = 63 \quad \text{and} \quad (12)(3) = 36 \quad \Rightarrow \quad 63 + 36 = 63 + 36 , \text{(True)} \]
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Checking \(63 + 36 = 9(7 + 4)\): \[ 7 + 4 = 11 \quad \Rightarrow \quad 9(11) = 99 , \text{(False)} \]
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Checking \(63 + 36 = 3(21 + 9)\): \[ 21 + 9 = 30 \quad \Rightarrow \quad 3(30) = 90 , \text{(False)} \]
Based on this analysis, the expressions that correctly apply the distributive property and show equivalent expressions for the total number of bracelets sold are:
- \(63 + 36 = (3)(21) + (9)(4)\)
- \(63 + 36 = (7)(9) + (12)(3)\)
Therefore, both the first and second expressions are correct. The preferred simplest representation that shows the distributive property of the total is:
\(63 + 36 = (3)(21) + (9)(4)\) or \(63 + 36 = (7)(9) + (12)(3)\).
1 answer