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 women is $\frac{12}{577}$

b) The fraction of men is $\frac{565}{577}$

Step-by-step explanation:

a)

In this part of the problem, we are asked to find what fraction of the prize winners are women.

We have:

$w=24$ (number of prizes awarded to women)

$m=1130$ (number of prizes awarded to men)

First of all, we calculate the total number of prizes awarded:

$p=w+m=24+1130=1154$

Now we find the fraction of prize winners who were women, which is given by:

$p(w) = \frac{w}{p}=\frac{24}{1154}$

And we can simplify by dividing both numerators and denominators by 2,

$p(w)=\frac{24}{1154}=\frac{12}{577}$

b)

The total number of prizes awarded is

$p=1154$

The number of prizes assigned to men is

$m=1130$

Therefore, the fraction of prize winners who were men is

$p(m)=\frac{m}{p}=\frac{1130}{1154}=\frac{565}{577}$

where we simplified the fraction by dividing both the numerator and the denominator by 2.

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