Question

Determine whether each pair of ratios are equivalent ratios. Write yes or no.

$\frac{27}{45},\frac{3}{5}$

Short answer

The ratios$\frac{27}{45},\frac{3}{5}$ are equivalent ratios.

Step-by-step solution

Step 1. Given information.

We have a pair of ratios $\frac{27}{45},\frac{3}{5}$.

To show that given pair of ratios are equivalent ratios or not.

Step 2. Apply concept.

We find the simplified form of the given both ratios if simplified form of the both ratios

are same then the pair of ratios are equivalent.

Step 3. Calculation.

Solving each ratio:

$\frac{3}{5}$is already in simplest form and

role="math" localid="1643049566461" $\begin{array}{l}\frac{27}{45}=\frac{3\times 9}{5\times 9}\\ \Rightarrow \frac{27}{45}=\frac{3}{5}\end{array}$

$\frac{3}{5}$is also simplest form of the $\frac{27}{45}$.

Therefore, the ratios$\frac{27}{45},\frac{3}{5}$ are equivalent ratios.