Are the ratios 16:12 and 5:4 equivalent? Choices: (A)yes (B)no

Simplify Ratio Calculation: Step 1: Simplify the ratio 16:12. Calculation: Divide both terms by their greatest common divisor, which is 4. 16 ÷ 4 = 4, 12 ÷ 4 = 3. So, the simplest form of 16:12 is 4:3.Check Ratio Simplification: Step 2: Check the simplest form of the ratio 5:4. Calculation: The ratio 5:4 is already in its simplest form because the greatest common divisor of 5 and 4 is 1. So, the simplest form of 5:4 remains 5:4.Compare Simplified Ratios: Step 3: Compare the simplest forms of both ratios. The simplest form of 16:12 is 4:3, and the simplest form of 5:4 is 5:4. Since 4:3 is not equal to 5:4, the ratios 16:12 and 5:4 are not equivalent.

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Are the ratios $16:12$ and $5:4$ 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

16:12

and

5:4

equivalent?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Simplify Ratio Calculation: Step $1$ : Simplify the ratio $16:12$ . Calculation: Divide both terms by their greatest common divisor, which is $4$ . $16 \div 4 = 4$ , $12 \div 4 = 3$ . So, the simplest form of $16:12$ is $4:3$ .
Check Ratio Simplification: Step $2$ : Check the simplest form of the ratio $5:4$ . $\newline$ Calculation: The ratio $5:4$ is already in its simplest form because the greatest common divisor of $5$ and $4$ is $1$ . $\newline$ So, the simplest form of $5:4$ remains $5:4$ .
Compare Simplified Ratios: Step $3$ : Compare the simplest forms of both ratios. $\newline$ The simplest form of $16:12$ is $4:3$ , and the simplest form of $5:4$ is $5:4$ . $\newline$ Since $4:3$ is not equal to $5:4$ , the ratios $16:12$ and $5:4$ are not equivalent.