Are these ratios equivalent? $8 : 5 items $17 : 17 items Choices: (A)yes (B)no

Simplify Ratio 1: Simplify the first ratio. The first ratio is $8 : 5$. This ratio is already in its simplest form because the greatest common divisor (GCD) of 8 and 5 is 1. Calculation: GCD(8, 5) = 1.Simplify Ratio 2: Simplify the second ratio. The second ratio is $17 : 17$. This can be simplified by dividing both terms by 17. Calculation: $17 ÷ 17 = 1$ and $17 ÷ 17 = 1$, so the simplified ratio is $1 : 1$.Compare Simplified Ratios: Compare the simplified ratios. The simplified first ratio is $8 : 5$ and the simplified second ratio is $1 : 1$. Since $8/5 ≠ 1/1$, the ratios are not equivalent.

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Are these ratios equivalent? $\newline$ $8 : 5$ items $\newline$ $17 : 17$ items $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Grade 6

Equivalent ratios: word problems

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Q. Are these ratios equivalent?

\newline

8 : 5

items

\newline

17 : 17

items

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Simplify Ratio $1$ : Simplify the first ratio. $\newline$ The first ratio is $\$8 : 5\$$ . This ratio is already in its simplest form because the greatest common divisor (GCD) of $8$ and $5$ is $1$ . $\newline$ Calculation: $\text{GCD}(8, 5) = 1$ .
Simplify Ratio $2$ : Simplify the second ratio. $\newline$ The second ratio is $17 : 17$ . This can be simplified by dividing both terms by $17$ . $\newline$ Calculation: $17 \div 17 = 1$ and $17 \div 17 = 1$ , so the simplified ratio is $1 : 1$ .
Compare Simplified Ratios: Compare the simplified ratios. The simplified first ratio is $8 : 5$ and the simplified second ratio is $1 : 1$ . Since $\frac{8}{5} \neq \frac{1}{1}$ , the ratios are not equivalent.