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Simplifying Rates and Ratios. Created by Sal Khan and Monterey Institute for Technology and Education.
Video transcript
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.