Question

Justify each step.

$\begin{array}{c}\frac{3a}{2}=\frac{6}{5}\\ 3a=\frac{12}{5}\\ a=\frac{4}{5}\end{array}$

Short answer

$\frac{3a}{2}=\frac{6}{5}$Given

$3a=\frac{12}{5}$Multiplication property of equality

$a=\frac{4}{5}$Division property of equality

Step-by-step solution

Step 1. Apply the multiplication property of equality.

If $a=b$, then$ca=ab$.

Step 2. Description of step.

Multiply each side of $\frac{3a}{2}=\frac{6}{5}$by 2 and simplify.

$\begin{array}{c}2\times \frac{3a}{2}=2\times \frac{6}{5}\\ 3a=\frac{12}{5}\end{array}$

Step 3. Apply division property of equality.

If $a=b$and $c\ne 0$, then $\frac{a}{c}=\frac{b}{c}$.

Step 4. Description of step.

Divide each side of the equation obtained in steps 2 by 3 to find the value of a.

$\begin{array}{c}\frac{3a}{3}=\frac{\frac{12}{5}}{3}\\ a=\frac{4}{5}\end{array}$

Therefore, the value of a is $\frac{4}{5}$.