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
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