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Shawn and Robert are comparing the scout patches they've earned. Shawn has a total of $8$ patches, $5$ of which are explorer patches. Robert has a total of $6$ patches, $3$ of which are explorer patches. Do Shawn and Robert have the same ratio of explorer patches to total patches? $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Compare ratios: word problems

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Q. Shawn and Robert are comparing the scout patches they've earned. Shawn has a total of

8

patches,

5

of which are explorer patches. Robert has a total of

6

patches,

3

of which are explorer patches. Do Shawn and Robert have the same ratio of explorer patches to total patches?

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Calculate Shawn's Ratio: Calculate the ratio of explorer patches to total patches for Shawn. $\newline$ Shawn's ratio: $5$ explorer patches / $8$ total patches = $\frac{5}{8}$
Calculate Robert's Ratio: Calculate the ratio of explorer patches to total patches for Robert. $\newline$ Robert's ratio: $3$ explorer patches / $6$ total patches = $\frac{3}{6}$ = $\frac{1}{2}$
Compare Shawn and Robert's Ratios: Compare the ratios of Shawn and Robert to see if they are the same. $\newline$ Shawn's ratio: $\frac{5}{8}$ $\newline$ Robert's ratio: $\frac{1}{2}$ $\newline$ Since $\frac{5}{8}$ is not equal to $\frac{1}{2}$ , the ratios are different.

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