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Rose has a playlist with $40$ rock songs and $28$ country songs. What is the ratio of country songs to rock songs on the playlist?

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Compare ratios: word problems

Full solution

Q. Rose has a playlist with

40

rock songs and

28

country songs. What is the ratio of country songs to rock songs on the playlist?

Identify Songs Count: Identify the number of country songs and rock songs on the playlist. $\newline$ Number of country songs: $28$ $\newline$ Number of rock songs: $40$
Calculate Ratio: Calculate the ratio of country songs to rock songs. $\newline$ Ratio of country songs to rock songs = Number of country songs / Number of rock songs = $\frac{28}{40}$
Find GCD: Simplify the ratio by finding the greatest common divisor (GCD) of $28$ and $40$ . GCD of $28$ and $40$ is $4$ .
Simplify Ratio: Divide both terms of the ratio by the GCD to simplify the ratio. $\newline$ Simplified ratio = $(28 \div 4) / (40 \div 4) = 7 / 10$

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