Two fifths of the instruments in the marching band are brass, one third are percussion, and the rest are woodwinds. A)What fraction of the band is woodwinds?
B)One half of the woodwinds are clarinets. What fraction of the band is clarinets?
C)One eighth of the brass instruments are tubas. If there are 240 instruments in the band, how many are tubas?
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2/5 + 1/3 = 6/15 + 5/15 = 11/15
That leaves 4/15 as woodwinds.
So, 2/15 are clarinets
2/5 * 240 * 1/8 = 12 are tubas
To answer these questions, we first need to find the number of instruments in each category.
Let's assume there are 240 instruments in the marching band.
A) Fraction of the band that is woodwinds:
Two-fifths of the band are brass instruments, one-third are percussion, so the remaining fraction should be woodwinds.
Fraction of the band that is woodwinds = 1 - (2/5 + 1/3)
To find the common denominator, we need to multiply the denominators (5 and 3), which gives us 15.
Fraction of the band that is woodwinds = 1 - (6/15 + 5/15) = 1 - 11/15 = 4/15
Therefore, 4/15 of the band consists of woodwinds.
B) Fraction of the band that is clarinets:
One-half of the woodwinds are clarinets, and we know that 4/15 of the band is woodwinds.
Fraction of the band that is clarinets = (1/2) * (4/15)
To multiply fractions, we simply multiply the numerators and denominators:
Fraction of the band that is clarinets = (1/2) * (4/15) = 4/30 = 2/15
Therefore, 2/15 of the band consists of clarinets.
C) Number of tubas in the band:
One-eighth of the brass instruments are tubas, and we know there are a total of 240 instruments in the band.
Number of tubas = (1/8) * (2/5) * 240
To find the number of tubas, we multiply the fraction of brass instruments (2/5) by the fraction of tubas in the brass instruments (1/8), and multiply the result by the total number of instruments (240):
Number of tubas = (1/8) * (2/5) * 240 = (1 * 2 * 240) / (8 * 5) = 480 / 40 = 12
Therefore, there are 12 tubas in the band.