Question

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

$\frac{6}{10},\frac{2}{5}$

Short answer

The pair of ratios$\frac{6}{10},\frac{2}{5}$ are not equivalent ratios because $\frac{6}{10}\ne \frac{2}{5}$.

Step-by-step solution

Step-1. Define equivalent ratios.

Equivalent ratios are two ratios which have same relationship between the numbers.

Step-2. Simplify the ratios.

Simplify both the ratios by dividing them with the common factor, if there is any.

$\begin{array}{c}\frac{6}{10}=\frac{2\times 3}{2\times 5}\\ =\frac{3}{5}\end{array}$

And,

$\begin{array}{c}\frac{2}{5}=\frac{2\times 1}{5\times 1}\\ =\frac{2}{5}\end{array}$

Step-3. State the conclusion.

As, both the results are not equal, that is., $\frac{3}{5}\ne \frac{2}{5}$, therefore, no, the given ratios are not equivalent.