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Are the ratios $3:1$ and $9:3$ equivalent? $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Identify equivalent ratios

Full solution

Q. Are the ratios

3:1

and

9:3

equivalent?

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Simplify $3:1$ : Step $1$ : Simplify the ratio $3:1$ . $\newline$ $3:1$ is already in its simplest form because $3$ and $1$ have no common factors other than $1$ .
Simplify $9:3$ : Step $2$ : Simplify the ratio $9:3$ . $\newline$ Divide both terms by their greatest common divisor, which is $3$ . $\newline$ $9 \div 3 = 3$ , and $3 \div 3 = 1$ , so the simplest form of $9:3$ is $3:1$ .
Compare simplified ratios: Step $3$ : Compare the simplified ratios. $\newline$ Both ratios, $3:1$ from step $1$ and $3:1$ from step $2$ , are the same.

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