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?
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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