2/3 OF STUDENTplay piano 1/2 of the students who play the piano also play the violin 1/4 of those students also play flute what fraction of students plays all three instruments
2/3 + 1/2 + 1/4 = 17/12
Mixed fraction:
1 5/12
1/4 * 1/2 * 2/3 = 1/12
how can more than all of the students do anything?
15/12
To find the fraction of students who play all three instruments, we need to calculate the intersection of the three groups: those who play piano, those who play violin, and those who play flute.
Let's break it down step by step:
1. Suppose there are 100 students in total. We can use this number for easier calculation.
2. From the given information, 2/3 of the students play the piano. So the number of students who play piano is (2/3) * 100 = 66.
3. Out of the piano players, 1/2 also play the violin. So the number of students who play both piano and violin is (1/2) * 66 = 33.
4. From the piano and violin players, 1/4 also play the flute. So the number of students who play all three instruments is (1/4) * 33 = 8.25.
Note: We have calculated a fraction of a student, which doesn't make sense in this context because we're dealing with whole numbers of students. Therefore, we need to consider the nearest whole number. Since we can't have a fraction of a student, we must round down to the nearest whole number, making it 8.
5. Finally, let's express our answer as a fraction of the total number of students. So the fraction of students who play all three instruments is 8 out of 100, which can be simplified to 8/100 or 2/25.
Therefore, 2/25 of the students play all three instruments (piano, violin, and flute).