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# Simplifying rates and ratios

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.