Question

envmath-grade 7-lesson quiz topic 4-4 - copy
1 which expression is equivalent to this expression?
\\( \frac{3}{4}(4h - 6) \\)
\\( \circ 3h - \frac{9}{2} \\)
\\( \circ 4h + \frac{9}{2} \\)
\\( \circ 3h - 6 \\)
\\( \circ 4h + 6 \\)

Explanation:

Step1: Apply Distributive Property

The distributive property states that \( a(b + c)=ab+ac \). For the expression \( \frac{3}{4}(4h - 6) \), we distribute \( \frac{3}{4} \) to both terms inside the parentheses.

$$ \frac{3}{4}(4h)-\frac{3}{4}(6) $$

Step2: Simplify Each Term

• For the first term \( \frac{3}{4}(4h) \): \( \frac{3}{4}\times4h = 3h \) (since \( \frac{3}{4}\times4 = 3 \)).
• For the second term \( \frac{3}{4}(6) \): \( \frac{3}{4}\times6=\frac{18}{4}=\frac{9}{2} \).

So the simplified expression is \( 3h-\frac{9}{2} \).

Answer:

\( 3h - \frac{9}{2} \) (the first option among the choices, likely labeled as "3h - 9/2" visually)