Are these ratios equivalent? 8 chairs to 12 benches 10 chairs to 15 benches Choices: (A)yes (B)no

Simplify Ratio: Simplify the first ratio. Original ratio: 8 chairs to 12 benches. Simplified by dividing both terms by 4 (the GCD of 8 and 12). Calculation: 8 ÷ 4 = 2, 12 ÷ 4 = 3. Simplified ratio: 2 chairs to 3 benches.Simplify Ratio: Simplify the second ratio. Original ratio: 10 chairs to 15 benches. Simplified by dividing both terms by 5 (the GCD of 10 and 15). Calculation: 10 ÷ 5 = 2, 15 ÷ 5 = 3. Simplified ratio: 2 chairs to 3 benches.Compare Simplified Ratios: Compare the simplified ratios. First simplified ratio: 2 chairs to 3 benches. Second simplified ratio: 2 chairs to 3 benches. Since both simplified ratios are the same, the original ratios are equivalent.

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Are these ratios equivalent? $\newline$ $8$ chairs to $12$ benches $\newline$ $10$ chairs to $15$ benches $\newline$ 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

chairs to

12

benches

\newline

10

chairs to

15

benches

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Simplify Ratio: Simplify the first ratio. $\newline$ Original ratio: $8$ chairs to $12$ benches. $\newline$ Simplified by dividing both terms by $4$ (the GCD of $8$ and $12$ ). $\newline$ Calculation: $8 \div 4 = 2$ , $12 \div 4 = 3$ . $\newline$ Simplified ratio: $2$ chairs to $3$ benches.
Simplify Ratio: Simplify the second ratio. $\newline$ Original ratio: $10$ chairs to $15$ benches. $\newline$ Simplified by dividing both terms by $5$ (the GCD of $10$ and $15$ ). $\newline$ Calculation: $10 \div 5 = 2$ , $15 \div 5 = 3$ . $\newline$ Simplified ratio: $2$ chairs to $3$ benches.
Compare Simplified Ratios: Compare the simplified ratios. $\newline$ First simplified ratio: $2$ chairs to $3$ benches. $\newline$ Second simplified ratio: $2$ chairs to $3$ benches. $\newline$ Since both simplified ratios are the same, the original ratios are equivalent.