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At a school for performance art students 2 5 of the girls study music, 3 5 of the girls study dance, and 1 6 of the girls study music and dance. What fraction of those who study music also study dance? A) 1 5 B) 1 6 C) 2 30 D) 5 12

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sqdancefan

Answer:

  D)  5/12

Step-by-step explanation:

Suppose there are 30 girls at the school. Then the proportions tell you that 12 of them study music, and 5 of them study both music and dance.

Then 5 of the 12 girls who study music also study dance. That fraction is 5/12.

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We chose 30 because it is the least common multiple of the denominators of the fractions (2/5, 3/5, 1/6) in the problem statement.

Of course, you know that 2/5·30 = 12, and 1/6·30 = 5.

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