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Last weekend, Erin went skiing at Snowy Peak Mountain. On Saturday, she skied $3$ hard slopes and $4$ easy slopes. On Sunday, she skied $4$ hard slopes and $5$ easy slopes. Did Erin ski the same ratio of hard slopes to easy slopes on both days? $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Compare ratios: word problems

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Q. Last weekend, Erin went skiing at Snowy Peak Mountain. On Saturday, she skied

3

hard slopes and

4

easy slopes. On Sunday, she skied

4

hard slopes and

5

easy slopes. Did Erin ski the same ratio of hard slopes to easy slopes on both days?

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Calculate ratio Saturday: Calculate the ratio of hard slopes to easy slopes for Saturday: $\newline$ Number of hard slopes: $3$ $\newline$ Number of easy slopes: $4$ $\newline$ Ratio of hard slopes to easy slopes = $\frac{3}{4}$
Calculate ratio Sunday: Calculate the ratio of hard slopes to easy slopes for Sunday: $\newline$ Number of hard slopes: $4$ $\newline$ Number of easy slopes: $5$ $\newline$ Ratio of hard slopes to easy slopes = $\frac{4}{5}$
Compare ratios: Compare the ratios from Saturday and Sunday: $\newline$ Saturday's ratio: $\frac{3}{4}$ $\newline$ Sunday's ratio: $\frac{4}{5}$ $\newline$ Check if $\frac{3}{4}$ is equal to $\frac{4}{5}$ : $\newline$ To compare, find a common denominator or simplify the fractions. Common denominators for $4$ and $5$ is $20$ . $\newline$ $\frac{3}{4}$ as a fraction with denominator $20$ : $(3 \times 5) / (4 \times 5) = \frac{15}{20}$ $\newline$ $\frac{4}{5}$ as a fraction with denominator $20$ : $\frac{4}{5}$ $2$ $\newline$ Since $\frac{4}{5}$ $3$ is not equal to $\frac{4}{5}$ $4$ , the ratios are not the same.

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