Question

regina writes the expression $y + 9\cdot \frac{3}{4}$. which expression is equivalent to the one regina writes?\
$(9\cdot 3\div 4)+y$\
$(y + 9)(3\div 4)$\
$9 + y\cdot (3\div 4)$\
none of these

Explanation:

Step1: Simplify Regina's expression

First, calculate the product and division: $9 \cdot \frac{3}{4} = \frac{27}{4}$, so the expression is $y + \frac{27}{4}$.

Step2: Analyze first option

Simplify $(9 \cdot 3 \div 4) + y$: $9 \cdot 3 = 27$, $27 \div 4 = \frac{27}{4}$, so this becomes $\frac{27}{4} + y$, which is the same as $y + \frac{27}{4}$ due to the commutative property of addition.

Step3: Verify other options

• The second option $(y + 9)(3 \div 4)$ expands to $\frac{3}{4}y + \frac{27}{4}$, which is not equivalent.
• The third option $9 + y \cdot (3 \div 4)$ is $9 + \frac{3}{4}y$, which is not equivalent.

Answer:

$(9 \cdot 3 \div 4) + y$