Question

Two thirds of the students in the orchestra play string instruments. Half of the students who play string instruments play violins. What fraction of all the students in the orchestra play violins?

Answer 1

To find the fraction of orchestra students who play violins, we multiply two thirds by one half, resulting in one third of all students.

Step-by-step explanation:

To determine what fraction of all the students in the orchestra play violins, we need to calculate the fraction of students who play string instruments and then find half of that, since half of the string players play violins. According to the question, two thirds of the students play string instruments. If half of these students play violins, we simply multiply two thirds by one half.

Here is the calculation step-by-step:

1. Determine the fraction of orchestra members playing string instruments: 2/3.
2. Calculate half of the string instrument players to find the fraction that play violins: 1/2 of 2/3.
3. Multiply the fractions:
   2/3 × 1/2 = 2/6 = 1/3.

Therefore, one third of all the students in the orchestra play violins.