SOLUTION: I don't know how or if I should convert these fractions to solve this word problem. Could you explan it to me? 2/3 of the people working at Happy Homes Realty are sal

Question 23495: I don't know how or if I should convert these fractions to solve this word problem. Could you explan it to me?
2/3 of the people working at Happy Homes Realty are sales agents and the rest are clerical workers. If 5/8 of the agents are women and 4/7 of the clerical workers are men, find the fraction of the people in the office who are male agents, female agents, male clerical workers, and female clerical workers.
My mom thinks that I have to change the fractions into percents, then when I find the answer that I have to convert them back to fractions. Do I?
Yours Truly,
Confused

Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
Fractions, decimals and % are all the same.... does not matter which you use. Seeing as how the Q is in fractions, stick to this (plus it is less work to do..why bother converting to % just to convert back again? Madness :-) )

So, think of a tree:

Agents (2/3) --> 5/8 Women
Agents (2/3) --> 3/8 Men
Clerical (1/3) --> 3/7 Women
Clerical (1/3) --> 4/7 Men
So,
agents AND women --> (2/3)*(5/8) = 5/12
agents AND men --> (2/3)*(3/8) = 1/4
clerical AND women --> (1/3)*(3/7) = 1/7
clerical AND men --> (1/3)*(4/7) = 4/21
Add up all the 4 final fractions on a calculator..should equal to 1..ie EVERYBODY :-)
jon.

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