On a certain legislative committe, 3/8 of the committee members are Republicans. If 2/3 of the members are men and 3/5 of the men are Democrats, what fraction of the members are Democratic women?
The common denominator of all those fractions is 120.
So, say there are 120 members
Then 45 are R, 75 are D
Also, 80 are men, so 48 are Dm.
That leaves 75-48=23 Dw
So, 23/120 are Dw
To find the fraction of the members who are Democratic women, we need to calculate the intersection of two different fractions: the fraction of committee members who are men and the fraction of men who are Democrats.
1. Fraction of committee members who are men:
We are given that 2/3 of the members are men. This means that for every 3 committee members, 2 are men. So, the fraction of committee members who are men is 2/3.
2. Fraction of men who are Democrats:
We are given that 3/5 of the men are Democrats. This means that for every 5 men, 3 are Democrats. So, the fraction of men who are Democrats is 3/5.
Now, let's find the fraction of the members who are Democratic women:
1. Fraction of committee members who are Democrats:
Since 3/8 of the committee members are Republicans, the fraction of committee members who are Democrats can be calculated as 1 - 3/8. Simplifying this expression gives us 5/8.
2. Fraction of committee members who are Democratic women:
To find this fraction, we multiply the fraction of committee members who are men (2/3) by the fraction of men who are Democrats (3/5). This is equivalent to (2/3) * (3/5) = 6/15.
Therefore, the fraction of the members who are Democratic women is 6/15, which can be simplified to 2/5.