While I was teaching my students I stumbled on that question because I have a serious headache. I need help because I am starting to grade papers.
Five-eighths of the marching band members are seniors and 1/5 of the marching band are juniors. What fraction of the marching band members are freshmen and sophomores?
Sofar you have 5/8 + 1/5
= 25/40 + 8/40
= 33/40
which leaves 7/40 of the band to consist of freshmen and sophs
Thank you Reiny
To solve this problem, you need to find the fraction of marching band members that are freshmen and sophomores.
Let's start by finding the fraction of seniors in the marching band. We are given that five-eighths (5/8) of the band members are seniors.
To find the fraction of juniors, we know that 1/5 of the marching band are juniors.
Now, to find the fraction of freshmen and sophomores, we need to subtract the fractions of seniors and juniors from 1 (since the total is 1 or 100%).
So, the fraction of freshmen and sophomores can be calculated as:
1 - (fraction of seniors + fraction of juniors)
Since the fraction of seniors is 5/8 and the fraction of juniors is 1/5, we can substitute these values into the equation:
1 - (5/8 + 1/5)
To add these fractions, we need to have a common denominator. The least common multiple of 8 and 5 is 40.
Converting the fractions to have a common denominator:
1 - (25/40 + 8/40)
Next, adding the fractions:
1 - (33/40)
Finally, subtracting the fraction:
7/40
Therefore, the fraction of marching band members that are freshmen and sophomores is 7/40.