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## 6th grade (Illustrative Mathematics)

### Unit 3: Lesson 9

Lesson 16: Finding the percentage# 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.

## Want to join the conversation?

- this is so hard i still dont under stand this and btw im only in 6th grade and im dumb i vant do it(27 votes)
- Hi!

First of all, you are super smart! Don't be mad at yourself - it will only make you feel worse! Believe that you CAN do it!

I would recommend trying to do this problem this way:

Ok, so let's make the fraction bigger. Twenty times five is 100, but since we have to multiply both parts of the fraction equally, then we multiply 13 by 5 also. This gives us a fraction of 65 over 100, or 65%. Does this make sense?(80 votes)

- Instead of moving the decimal point 2 places to the right, we could have ALSO made 0.65 as 65/100 and since 100 is the same thing as PERCENT, we could write it as 65% too...(12 votes)
- ORRRRRRR you can make it even easier and just do

13/20 since 13 is out of the whole number 20.

I would recommend you write this setup down to make it easier.

so as I said 13/20 because 13 is a part of the whole number which is 20.

soooooo, after that set it up in fraction form.

Let me backtrack a little. so what you're going to do is you're going to set up 13/20 in a fraction form. on the left side before the equal sign. After the = sign, you would put ?/100. why did I choose over a hundred well because that Will be your variable and 100 is a total number that you're going to take from. after that you're going to cross multiply or as you would call the butterfly effect so what you're going to do is going to multiply 13 * 100 fraction that is after equal signs of 13 * 100 and that will give you 1300. Ater that your going to * 20 which is the denominator of 13. the whole number 1300* the variable or? XYZ whatever it doesn't really matter then you're going to do 13* 100 which is 1300. then you multiply 20 by the variable in this case X. after you multiply 20*X, that should give you 20x. so the setup now should be 1300 is equal to or = to 20x.

Since you multiplied now do the opposite, divide. whatever sign you use first do the oppisite of that next. So if you add then subtract, if you times then divide, and vise versa!

now you have to divide with whatever the denominator number is in this case the number would be 20 you have to divide both sides by the denominator which is 20. equal number so that would be 20 so you would divide 1300 divided by 20 that should give you 65. Then 20X / 20, it would be 1 or in this case 1X or just X.

Your answer should be X=65

Hopefully, this helped everyone. The butterfly effect is very easy or in other words, cross multiplication.(8 votes)

- it not clear on how you get percent(10 votes)
- Try a diff video, if that dosn't work. Can you explain what you don't get.-w-(7 votes)

- When you divide by 10 or 100 etc, you move the digits. So the
*place value*is changing, not the decimal point.(10 votes) - Wouldn't you be able to just do 13 divided by 2 over 10 and get 65%?(6 votes)
- 13/2 over 10 = 0.65

To get to a percent, you must then multiply by 100

0.65 * 100 = 65%(7 votes)

- Mr sal can u answer my question his is hard(5 votes)
- At2:11I think Sal should have said forget the numerator(5 votes)
- He actually said, "to get the denominator from 20 to 100 you would multiply by 5" so he is correct, the person who transcribed the video just made a little mistake.(4 votes)

- Instead of moving the decimal point 2 places to the right, we could have ALSO made 0.65 as 65/100 and since 100 is the same thing as PERCENT, we could write it as 65% too...(5 votes)
- Wouldn't it be easier to just multiply 20 by 5 to get 100, and then multiply 13 by five to get 65? Then we could do 65 out of 100, which would get us to 65%.(4 votes)
- That's a way to do it, and that's what Sal did around2:15(2 votes)

- i don't get this 12 is 60% of what number(2 votes)
- Translate to math 12 is (verbs are equal) 60 % (either divide by 100 or move decimal two places to left) of (multiply) what number (often use x for unknown number). This gives 12 = 60/100 x or 12 = .6 x. Can you solve from there?(5 votes)

## 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%.