Q55. - Algebra 1

Question

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

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

Step-by-Step Solution

Answer

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

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

$\begin{array}{l} \frac{27}{45}=\frac{3\times 9}{5\times 9}\\ \Rightarrow \frac{27}{45}=\frac{3}{5}\end{array}$

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

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