Question

Last season, Emille's soccer team had a win-loss ratio of 9 to 12, and Grant's soccer team had a win-loss ratio of 10 to 15.

Whose team had a higher ratio of wins to losses? Use complete sentences to explain your reasoning.

Answer 1

Emille's soccer team

Explanation:

You want to know the higher win/loss ratio of Emille's 9/12 or Grant's 10/15.

Comparison

One way to compare the fractions is to subtract one from the other:

9/12 -10/15 = (9·15 -12·10)/(12·15) = (135 -120)/(12·15) = 1/12

This is a positive number, so the fraction 9/12 is higher.

Emille's team's win/loss ratio is higher because subtracting the win/loss ratio of Grant's team gives a positive result.

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Additional comment

Grant's team's ratio reduces to 2/3, which can be expressed as 8/12. This is clearly lower than 9/12.