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# Percent word problem: recycling cans

It's nice to practice conversion problems, but how about applying our new knowledge of percentages to a real life problem like recycling? Hint: don't forget your long division! Created by Sal Khan.

Video transcript

In the United States, 13 out
of every 20 cans are recycled. What percent of
cans are recycled? So 13 out of every
20 are recycled. So 13/20, or 13
over 20, could also be viewed as 13 divided
20, or 13 divided by 20. And if we do this,
we'll get a decimal, and it's fairly straightforward
to convert that decimal into a percentage. So 13 divided 20. We have the smaller
number in this case being divided by the larger number. So we're going to get
a value less than 1. Since we're going to
get a value less than 1, let's put a decimal
right over here. And let's add a
couple of zeroes, as many zeroes as we would need. And we could say, hey, look,
20 goes into 13 zero times. 0 times 20 is 0. And then 13 minus 0 is 13. Now you bring down a 0. 20 goes into 130. Let's see, it goes
in-- 5 times 20 is 100. So 6 times 20 is 120. So it's going to six times. 6 times 20 is 120. You subtract. You get a 10. Let's bring down another 0. 20 goes into 100 five times. 5 times 20 is 100. And we are done. So this, written as
a decimal, is 0.65. So as a decimal, it's 0.65. And if you want to
write it as a percentage you essentially multiply
this number by 100. Or another way you could say
is you shift the decimal point over two spots to the right. So this is going
to be equal to 65%. Now, there's another way
you could have done it. You could have said,
look, percent literally means per hundred. So 13 out of 20 is going to
be equal to what over 100? Well, to go from 20 to a
100-- forget the denominator. To go from 20 to 100,
you would multiply by 5. So let's multiply the
numerator by 5 as well. And 13 times 5, let's see,
that's 15 plus 50, which is 65. So this would have
been a faster way to do it, especially
if you recognize it's pretty easy to
go from 20 to 100. You multiply it by 5. So we would do the
same thing with the 13. And so you would
get 65/100, which is the same thing
as 65 per-- let me write this
percent symbol-- 65%. And just a reminder,
percent literally means per hundred,
65 per hundred, 65%.