Are the ratios 4:3 and 9:12 equivalent? Choices: (A)yes (B)no

Simplify 4:3: Step 1: Simplify the ratio 4:3. 4:3 is already in its simplest form because the greatest common divisor of 4 and 3 is 1.Simplify 9:12: Step 2: Simplify the ratio 9:12. Divide both terms by their greatest common divisor, which is 3. 9 ÷ 3 = 3, 12 ÷ 3 = 4, so the simplest form of 9:12 is 3:4.Compare simplified ratios: Step 3: Compare the simplified ratios. The simplified form of 4:3 is 4:3, and the simplified form of 9:12 is 3:4. Since 4:3 does not equal 3:4, the ratios are not equivalent.

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Are the ratios $4:3$ and $9:12$ equivalent? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Math Problems

Grade 7

Identify equivalent ratios

Full solution

Q. Are the ratios

4:3

and

9:12

equivalent?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Simplify $4$ : $3$ : Step $1$ : Simplify the ratio $4:3$ . $\newline$ $4:3$ is already in its simplest form because the greatest common divisor of $4$ and $3$ is $1$ .
Simplify $9:12$ : Step $2$ : Simplify the ratio $9:12$ . $\newline$ Divide both terms by their greatest common divisor, which is $3$ . $\newline$ $9 \div 3 = 3$ , $12 \div 3 = 4$ , so the simplest form of $9:12$ is $3:4$ .
Compare simplified ratios: Step $3$ : Compare the simplified ratios. $\newline$ The simplified form of $4:3$ is $4:3$ , and the simplified form of $9:12$ is $3:4$ . Since $4:3$ does not equal $3:4$ , the ratios are not equivalent.