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, rewrite the multiplication and division:
$$y + 9 \cdot \frac{3}{4} = y + \frac{27}{4}$$
Or using division notation: $y + (9 \cdot 3 \div 4)$

Step2: Analyze first option

Simplify the first expression:
$$(9 \cdot 3 \div 4) + y = \frac{27}{4} + y$$
By the commutative property of addition, $a + b = b + a$, so this matches Regina's expression.

Step3: Verify other options

• Second option: $(y+9)(3\div4) = \frac{3}{4}y + \frac{27}{4}$, which is not equivalent.
• Third option: $9 + y \cdot (3\div4) = 9 + \frac{3}{4}y$, which is not equivalent.

Answer:

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