Word problem about multiplying and subtracting fractions

by Moises Villalpando
(San Diego, CA)

Your job is to sweep 3/4 of the school's cafeteria. Your friend agrees to help you and sweeps 1/3 of your part. What fraction of the entire floor your friend agreed to sweep? What fraction of the entire cafeteria floor you will have to sweep?

Solution:

Your friend will help you with 1/3 of your part. This can be written as 1/3 of 3/4 or 1/3 times 3/4.

1/3 times 3/4 = 3/12 = 1/4

So, your friend will complete 1/4 of the job.

Your part now is 3/4 - 1/4 = 2/4 = 1/2

You will sweep only half the cafeteria.


Alternatively, you could write 3/4 = 1/4 + 1/4 + 1/4

and then argue that you have 3 jobs to do consisted of 1/4, 1/4, and 1/4.

If your friend takes 1 out of these 3 jobs, it means 1/4.

Then, you are left with 1/4 + 1/4, which is equal to 2/4 or 1/2