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Are the ratios $1:3$ and $4:12$ equivalent? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Identify equivalent ratios

Full solution

Q. Are the ratios

1:3

and

4:12

equivalent?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Simplify $1:3$ : Simplify the ratio $1:3$ . The ratio $1:3$ is already in its simplest form.
Simplify $4:12$ : Simplify the ratio $4:12$ . $\newline$ Divide both terms by their greatest common divisor, which is $4$ . $\newline$ $4 \div 4 = 1$ and $12 \div 4 = 3$ . $\newline$ So, the simplest form of $4:12$ is $1:3$ .
Compare simplified forms: Compare the simplified forms of both ratios. $\newline$ The simplified form of the first ratio is $1:3$ . $\newline$ The simplified form of the second ratio is also $1:3$ . $\newline$ Since both simplified forms are the same, the ratios $1:3$ and $4:12$ are equivalent.

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