Question

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

$\frac{3}{7},\frac{18}{42}$

Short answer

Yes, the pair of ratios $\frac{3}{7},\frac{18}{42}$are equivalent ratios because $\frac{3}{7}=\frac{18}{42}$.

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.

$\begin{array}{c}\frac{3}{7}=\frac{3\times 1}{7\times 1}\\ =\frac{3}{7}\end{array}$

And,

$\begin{array}{c}\frac{18}{42}=\frac{\cancel{6}\times 3}{\cancel{6}\times 7}\\ =\frac{3}{7}\end{array}$

Step-3. State the conclusion.

As, both the results are equal, that is., $\frac{3}{7}=\frac{3}{7}$, therefore, yes, the given ratios are equivalent.