Are the ratios 17:16 and 10:8 equivalent? Choices: (A)yes (B)no

Simplify Ratio: Simplify the ratio 17:16. Calculation: The ratio 17:16 is already in its simplest form because 17 and 16 are relatively prime (no common factors other than 1).Simplify Ratio: Simplify the ratio 10:8. Calculation: Divide both terms by their greatest common divisor, which is 2. 10 ÷ 2 = 5, 8 ÷ 2 = 4. So, the simplest form of 10:8 is 5:4.Compare Ratios: Compare the simplified ratios. Comparison: The simplest form of 17:16 is 17:16, and the simplest form of 10:8 is 5:4. Since 17:16 ≠ 5:4, the ratios are not equivalent.

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Are the ratios $17:16$ and $10:8$ 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

17:16

and

10:8

equivalent?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Simplify Ratio: Simplify the ratio $17:16$ . $\newline$ Calculation: The ratio $17:16$ is already in its simplest form because $17$ and $16$ are relatively prime (no common factors other than $1$ ).
Simplify Ratio: Simplify the ratio $10:8$ . $\newline$ Calculation: Divide both terms by their greatest common divisor, which is $2$ . $\newline$ $10 \div 2 = 5$ , $8 \div 2 = 4$ . $\newline$ So, the simplest form of $10:8$ is $5:4$ .
Compare Ratios: Compare the simplified ratios. $\newline$ Comparison: The simplest form of $17:16$ is $17:16$ , and the simplest form of $10:8$ is $5:4$ . $\newline$ Since $17:16 \neq 5:4$ , the ratios are not equivalent.