Q2. - Algebra 1

Question

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

$\frac{7}{8},\frac{42}{48}$

Step-by-Step Solution

Answer

Yes, the pair of ratios $\frac{7}{8},\frac{42}{48}$ are equivalent ratios because $\frac{7}{8}=\frac{42}{48}$.

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.

$$\begin{gathered} \frac{7}{8}=\frac{7\times 1}{8\times 1} \\ =\frac{7}{8} \end{gathered}$$

And,

$$\begin{gathered} \frac{42}{48}=\frac{7\times \cancel{6}}{8\times \cancel{6}} \\ =\frac{7}{8} \end{gathered}$$

Step-3. State the conclusion.

As, both the results are equal, that is., $\frac{7}{8}=\frac{7}{8}$, therefore, yes, the given ratios are equivalent ratios.