In a school orchestra, 2/5 of the students are string players. Of the string players, 5/8 are girls. What fraction of all the students in the orchestra are girls who play string instruments.
(2/5) * (5/8) = 10/40 = 1/4
Well, it seems like we have a math puzzle here! Let's break it down together.
First, we know that 2/5 of the students are string players. So, if we imagine there are a total of 100 students in the orchestra, we can say that 2/5 of them, or 40 students, are string players.
Now, out of these 40 string players, we are told that 5/8 of them are girls. To find how many girls that is, we can multiply 40 by 5/8, which gives us 25.
So, out of our initial group of 100 students, we found that 25 of them are girls who play string instruments. To express this as a fraction, we can write it as 25/100.
However, we can simplify that fraction further. Both the numerator and denominator of 25/100 can be divided by 25, which gives us 1/4.
Hence, the fraction of all the students in the orchestra who are girls who play string instruments is 1/4.
Remember, math can be fun, especially when we add a pinch of humor to it!
To find the fraction of all the students in the orchestra who are girls and play string instruments, we need to multiply the fraction of string players by the fraction of girls among the string players.
First, let's find the fraction of string players in the orchestra. We are told that 2/5 of the students are string players. So, if there are X total students in the orchestra, (2/5)X of them are string players.
Next, we need to find the fraction of girls among the string players. We are given that 5/8 of the string players are girls. So, if (2/5)X is the number of string players, then (5/8) * (2/5)X of them are girls who play string instruments.
To find the fraction of all the students in the orchestra who are girls and play string instruments, we multiply the fraction of string players by the fraction of girls among the string players:
(2/5)X * (5/8) * (2/5)
Simplifying this expression:
(2/5) * (5/8) * (2/5)
= (2 * 5 * 2) / (5 * 8 * 5)
= 20 / 200
= 1/10
Therefore, 1/10 of all the students in the orchestra are girls who play string instruments.