Question

reasoning are the two statements equivalent?

• the ratio of boys to girls is 2 to 3.
• the ratio of girls to boys is 3 to 2.

yes
no
explain your reasoning.

Explanation:

Step1: Define first ratio

Let boys = $B$, girls = $G$.
First statement: $\frac{B}{G} = \frac{2}{3}$

Step2: Define second ratio

Second statement: $\frac{G}{B} = \frac{3}{2}$

Step3: Check equivalence

Take reciprocal of first ratio: $\frac{G}{B} = \frac{3}{2}$, which matches the second ratio.

Answer:

Yes
The two statements are equivalent because the ratio of girls to boys is the reciprocal of the ratio of boys to girls, and $\frac{3}{2}$ is the reciprocal of $\frac{2}{3}$.