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Are these ratios equivalent? $\newline$ $7$ ounces every $4$ days $\newline$ $14$ ounces every $8$ days $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Equivalent ratios: word problems

Full solution

Q. Are these ratios equivalent?

\newline

7

ounces every

4

days

\newline

14

ounces every

8

days

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Identify Given Quantities: Step $1$ : Identify the quantities given in the problem. $\newline$ We have two ratios to compare: $\newline$ - $7$ ounces every $4$ days $\newline$ - $14$ ounces every $8$ days
Simplify First Ratio: Step $2$ : Simplify the first ratio. $\newline$ To simplify $7$ ounces every $4$ days, we divide both the numerator ( $7$ ounces) and the denominator ( $4$ days) by their greatest common divisor, which is $1$ . $\newline$ Simplified ratio = $\frac{7}{4}$
Simplify Second Ratio: Step $3$ : Simplify the second ratio. $\newline$ To simplify $14$ ounces every $8$ days, we divide both the numerator ( $14$ ounces) and the denominator ( $8$ days) by their greatest common divisor, which is $2$ . $\newline$ Simplified ratio = $\frac{14}{8} = \frac{7}{4}$
Compare Simplified Ratios: Step $4$ : Compare the simplified ratios. $\newline$ Both simplified ratios are $\frac{7}{4}$ . Therefore, the ratios are equivalent.

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