Question

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

$\frac{9}{11},\frac{81}{99}$

Short answer

Yes, the pair of ratios$\frac{9}{11},\frac{81}{99}$ are equivalent ratios because $\frac{9}{11}=\frac{81}{99}$.

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.

$\begin{array}{c}\frac{9}{11}=\frac{9\times 1}{11\times 1}\\ =\frac{9}{11}\end{array}$

And,

$\begin{array}{c}\frac{81}{99}=\frac{\cancel{9}\times 9}{\cancel{9}\times 11}\\ =\frac{9}{11}\end{array}$

Step-3. State the conclusion.

As, both the results are equal, that is., $\frac{9}{11}=\frac{9}{11}$, therefore, yes, the given ratios are equivalent.