Question

identify the pair of expressions below that are equivalent.
$(6 * h) + 10$ and $(h * 6) + 10$
$(5 + 7) \div h$ and $5 + (7 \div h)$
$h * (11 + 4)$ and $11 * (4 + h)$
$5 + 2 * h$ and $(5 + 2) * h$

Explanation:

Step1: Analyze Commutative Property of Multiplication

The commutative property of multiplication states that \(a\times b = b\times a\). For the first pair \((6 h)+10\) and \((h 6)+10\), by the commutative property of multiplication, \(6\times h=h\times 6\), so \((6\times h) + 10=(h\times 6)+10\).

Step2: Analyze the Second Pair

For \((5 + 7)\div h\) and \(5+(7\div h)\), \((5 + 7)\div h=\frac{5 + 7}{h}=\frac{5}{h}+\frac{7}{h}\), while \(5+(7\div h)=5+\frac{7}{h}\). These are not equal.

Step3: Analyze the Third Pair

\(h\times(11 + 4)=h\times15 = 15h\), and \(11\times(4 + h)=44+11h\). These are not equal.

Step4: Analyze the Fourth Pair

\(5+2\times h=5 + 2h\), and \((5 + 2)\times h=7h\). These are not equal.

Answer:

\((6 h)+10\) and \((h 6)+10\)