Are these ratios equivalent? 18 kittens : 16 puppies 17 kittens : 12 puppies Choices: (A)yes (B)no

Convert to Fraction: Convert the first ratio into a fraction. 18 kittens : 16 puppies can be written as 18/16. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 2. 18/16 = 9/8.Simplify Fraction: Convert the second ratio into a fraction. 17 kittens : 12 puppies can be written as 17/12. This fraction cannot be simplified further as 17 and 12 have no common factors other than 1.Convert to Fraction: Compare the two simplified fractions. First fraction: 9/8 Second fraction: 17/12 To compare, find a common denominator or directly compare their decimal forms. 9/8 = 1.125 17/12 ≈ 1.4167 Since 1.125 is not equal to 1.4167, the ratios are not equivalent.

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Are these ratios equivalent? $\newline$ $18$ kittens : $16$ puppies $\newline$ $17$ kittens : $12$ puppies $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Grade 7

Equivalent ratios: word problems

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Q. Are these ratios equivalent?

\newline

18

kittens :

16

puppies

\newline

17

kittens :

12

puppies

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Convert to Fraction: Convert the first ratio into a fraction. $\newline$ $18$ kittens : $16$ puppies can be written as $\frac{18}{16}$ . $\newline$ Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is $2$ . $\newline$ $\frac{18}{16} = \frac{9}{8}$ .
Simplify Fraction: Convert the second ratio into a fraction. $17$ kittens : $12$ puppies can be written as $\frac{17}{12}$ . This fraction cannot be simplified further as $17$ and $12$ have no common factors other than $1$ .
Convert to Fraction: Compare the two simplified fractions. $\newline$ First fraction: $\frac{9}{8}$ $\newline$ Second fraction: $\frac{17}{12}$ $\newline$ To compare, find a common denominator or directly compare their decimal forms. $\newline$ $\frac{9}{8} = 1.125$ $\newline$ $\frac{17}{12} \approx 1.4167$ $\newline$ Since $1.125$ is not equal to $1.4167$ , the ratios are not equivalent.