Question

A prize was awarded to 24 women and 1130 men. a. What fraction of the prize winners were​ women? b. What fraction were​ men?

simplify each

Answer 1

A) The fraction of the prize winners were​ women is
`(12)/(577)`

B) The fraction of the prize winners were​ men is
`(565)/(577)`

Solution:

Given that, A prize was awarded to 24 women and 1130 men

Therefore, Women + men = 24 + 1130 = 1154

A) What fraction of the prize winners were​ women?

The fraction of the prize winners were​ women is found by dividing the total women by total men and women

`\text{Fraction women } = \frac{\text{Number of women}}{\text{Total men and women}}`

Total men and women = 1154

Number of women = 24

Thus, we get,

`\text{Fraction women } = (24)/(1154)\\\\\text{Reduce to lowest terms }\\\\\text{Fraction women } = (12)/(577)`

b.) What fraction were​ men?

The fraction of the prize winners were​ men is found by dividing the total men by total men and women

`\text{Fraction women } = \frac{\text{Number of men}}{\text{Total men and women}}`

Total men and women = 1154

Number of men = 1130

Thus, we get,

`\text{Fraction men } = (1130)/(1154)\\\\\text{Reduce to lowest terms }\\\\\text{Fraction men } = (565)/(577)`

Thus the fractions are found