A. What fraction of the band are woodwinds?
First, find common denominators for the first two. Let's use 15.
6/15 is brass (5x3=15, and 2x3=6)
5/15 is percussion (3x5=15, and 1x5=5)
Now, we add the two and subtract them from the whole.
6/15 + 5/15 = 11/15
15/15 - 11/15 = 4/15
4/15 of the band is woodwinds.
B. One half of the woodwinds are clarinets. What fraction of the band is clarinets?
To find this, we take our 4/15 and divide it by two. Thankfully, the numerator is an even number, so it splits in half easily.
4/15 divided by 2 = 2/15
2/15 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?
First, find 1/8 of the number of brass instruments.
6/15 of the band is brass.
We need to make this an equivalent fraction that is divisible by 8.
Both 6 and 8 go into 24, so we'll multiply our fraction by 4, since 6x4=24
The new fraction is
24/60
Now, we divide that fraction by 8, to find 1/8 of the brass instruments.
24/8=3
3/60 of the band is tubas.
To find the number of tubas out of a 240 instrument band, we multiply the fraction of tubas by the whole band.
3/60 x 240 = 12
There are 12 tubas in the band.
