using a circle graph of 1/3 percussion, 2/5 brass, 4/15 woodwind and also a circle graph of 1/3 woodwind, 1/6 percussion, 1/2 brass. Both bands combine as one band. A. What fraction of the band members will play brass instruments? B. what fraction of band members will play a percussion instrument? c. What fraction of the band members will play a woodwind instrument?
I think for A. my answer is 14 4/5. For B. I think I will multiply 42 times 1/2 and my answer is 21. C. I think my answer is to multiply and my answer is 25 1/5. Are these correct?
Yes, your answers are correct. 14 4/5 for A, 21 for B, and 25 1/5 for C.
To solve this problem, you'll need to find the intersection of the fractions represented by the two circle graphs.
A. Fraction of band members playing brass instruments:
To find the fraction of band members playing brass instruments, you need to find the intersection between the two fractions representing brass instruments in the two circle graphs. The first graph represents 2/5 brass instruments, and the second graph represents 1/2 brass instruments.
To find the intersection, you can multiply the fractions together:
(2/5) * (1/2) = 2/10 = 1/5
So the fraction of band members playing brass instruments is 1/5.
B. Fraction of band members playing percussion instruments:
Similarly, you'll need to find the intersection between the fractions representing percussion instruments in the two circle graphs. The first graph represents 1/3 percussion instruments, and the second graph represents 1/6 percussion instruments.
(1/3) * (1/6) = 1/18
So the fraction of band members playing percussion instruments is 1/18.
C. Fraction of band members playing woodwind instruments:
Again, find the intersection between the fractions representing woodwind instruments in the two circle graphs. The first graph represents 4/15 woodwind instruments, and the second graph represents 1/3 woodwind instruments.
(4/15) * (1/3) = 4/45
So the fraction of band members playing woodwind instruments is 4/45.
To summarize:
A. Fraction of band members playing brass instruments: 1/5
B. Fraction of band members playing percussion instruments: 1/18
C. Fraction of band members playing woodwind instruments: 4/45
Let's calculate the fractions step-by-step to find the correct answers:
A. To find the fraction of band members who will play brass instruments, we can add the fractions from both circle graphs that represent brass:
1/3 (per the first graph) + 1/2 (per the second graph)
To add these fractions, we need a common denominator. The least common multiple of 3 and 2 is 6, so let's convert the fractions:
1/3 = 2/6 (multiplying numerator and denominator by 2)
1/2 = 3/6 (multiplying numerator and denominator by 3)
Now we can add:
2/6 + 3/6 = 5/6
Therefore, 5/6 of the band members will play brass instruments.
B. To find the fraction of band members who will play a percussion instrument, we can add the fractions from the first graph:
1/3 (per the first graph) + 1/6 (per the second graph)
Again, let's find a common denominator:
1/3 = 2/6 (multiplying numerator and denominator by 2)
1/6 = 1/6 (no need to change)
Adding these fractions:
2/6 + 1/6 = 3/6
Simplifying the fraction, we get:
3/6 = 1/2
Therefore, 1/2 of the band members will play a percussion instrument.
C. To find the fraction of band members who will play a woodwind instrument, we can add the fractions from both circle graphs that represent woodwind:
4/15 (per the first graph) + 1/3 (per the second graph)
Let's find a common denominator:
4/15 = 8/30 (multiplying numerator and denominator by 2)
1/3 = 10/30 (multiplying numerator and denominator by 10)
Adding these fractions:
8/30 + 10/30 = 18/30
Simplifying the fraction:
18/30 = 3/5
Therefore, 3/5 of the band members will play a woodwind instrument.
Based on these calculations, the correct answers are:
A. 5/6
B. 1/2
C. 3/5