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?

Answer 1

A) The fraction of the prize winners were​ women is $\frac{12}{577}$

B) The fraction of the prize winners were​ men is $\frac{565}{577}$

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,

$\text{Fraction women } = \frac{24}{1154}\\\\\text{Reduce to lowest terms }\\\\\text{Fraction women } = \frac{12}{577}$

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,

$\text{Fraction men } = \frac{1130}{1154}\\\\\text{Reduce to lowest terms }\\\\\text{Fraction men } = \frac{565}{577}$

Thus the fractions are found