Question

3/7 of 8th graders play sports. is 3/5 of the 8th graders that play sports are boys, what fraction of the 8th graders are boys

Answer 1

To determine the fraction of 8th graders who are boys and play sports, we multiply 3/7, the fraction that plays sports, by 3/5, the fraction of those who are boys, resulting in 9/35.

Step-by-step explanation:

To find what fraction of the 8th graders are boys who play sports, we will use two steps. First, we calculate the fraction of 8th graders who play sports: 3/7 of 8th graders.

In the second step, we find out what fraction of these sports-playing 8th graders are boys. We are told that 3/5 of the sports-playing 8th graders are boys. To find the overall fraction of 8th graders who are boys and play sports, we multiply the two fractions:

• Calculate the total number of 8th graders who play sports: 3/7 of the total.
• Multiply that result by 3/5 to find the fraction that are boys: (3/7) × (3/5).

The calculation would then be:

(3/7) × (3/5) = 9/35.

Thus, 9/35 of the 8th graders are boys who play sports.

Answer 2

`(9)/(35)` is the fraction of 8th graders who are boys.

Step-by-step explanation:

Let total number of 8th graders =
`x`

Given that,
`(3)/(7)` of 8th graders play sports

`\Rightarrow` 8th graders who play sports =
`(3)/(7) * x`

Also, Given that,
`(3)/(5)` of 8th graders that play sports are boys

Number of 8th graders that play sports, and are boys =
`(3)/(5) * \text{Number of 8th graders who play sports}`

`\Rightarrow (3)/(5) * (3)/(7) * x\\\Rightarrow (9)/(35) * x`

Hence, the answer is:

`(9)/(35)` is the fraction of 8th graders who are boys.