Two fifths of the instruments in the marching band are brass, one third are percussion, and the rest are woodwinds. What fraction of the band is woodwinds?

Answer 1

#4/15# of the band's instruments are woodwinds.

We need a common denominator to equate the #2/5#, and the #1/3# fractions. Clearly, we could express the fractions as #"fifteenths"#.
And thus #2/5-=6/15#, and #1/3-=5/15#.
The balance are woodwind instruments, i.e. #1-6/15-5/15=4/15#.
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Answer 2

To find the fraction of the marching band that is woodwinds, subtract the fractions representing the brass and percussion instruments from 1 (since the total fractions of the band must add up to 1).

[ 1 - \frac{2}{5} - \frac{1}{3} = 1 - \frac{6}{15} - \frac{5}{15} = 1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15} ]

So, (\frac{4}{15}) of the band is woodwinds.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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