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- Simplify the rate of cans of soda compared to people.
- So this ratio here says that we have 92 cans of soda for
- every 28 people.
- What we want to do is simplify this, and really just putting
- this ratio, or this fraction, in simplest form.
- So the best way to do that is just to figure out what is the
- largest number, or the largest common factor, of both 92 and
- 28, and divide both of these numbers by that common factor.
- So let's figure out what it is.
- And to do that, let's just take the prime factorization
- of 92, and then we'll do the prime factorization of 28.
- So 92 is 2 times 46, which is 2 times 23.
- And 23 is a prime number, so we're done.
- 92 is 2 times 2 times 23.
- And if we did the prime factorization of 28, 28 is 2
- times 14, which is 2 times 7.
- So we can rewrite the 92 cans of soda as 2 times 2 times 23
- cans of soda for every 2 times 2 times 7 people.
- Now, both of these numbers have a 2 times 2 in it, or
- they're both divisible by 4.
- That is their greatest common factor.
- So let's divide both the top number and the
- bottom number by 4.
- So if you divide the top number by 4, or if you divide
- it by 2 times 2, it will cancel out right over there.
- And then if you do the bottom number divided by 4, or 2
- times 2, it will cancel out with that 2 times 2.
- And we are left with 23 cans of soda for every 7 people, or
- 7 people for every 23 cans of soda.
- And we're done!
- We've simplified the rate of cans, or the ratio of cans, of
- soda compared to people.
- I guess they're considering this a rate, so maybe they're
- saying how quickly do 7 people consume cans over some period,
- or you can view it as a ratio.
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