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## Equivalent representations of percent problems

## Video transcript

Let's see if we can figure
out what 30% of 6 is. So one way of thinking
about 30%-- this literally means 30 per 100. So you could view
this as 30/100 times 6 is the same thing as 30% of 6. Or you could view this
as 30 hundredths times 6, so 0.30 times 6. Now we could solve
both of these, and you'll see that we'll
get the same answer. If you do this multiplication
right over here, 30/100-- and you
could view this times 6/1-- this is equal to 180/100. And let's see. We can simplify. We can divide the numerator
and the denominator by 10. And then we can divide the
numerator and the denominator by 2. And we will get 9/5, which is
the same thing as 1 and 4/5. And then if we wanted to write
this as a decimal, 4/5 is 0.8. And if you want to
verify that, you could verify that
5 goes into 4-- and there's going
to be a decimal. So let's throw some
decimals in there. It goes into 4 zero times. So we don't have to
worry about that. It goes into 40 eight times. 8 times 5 is 40. Subtract. You have no remainder, and
you just have 0's left here. So 4/5 is 0.8. You've got the 1 there. This is the same
thing as 1.8, which you would have gotten
if you divided 5 into 9. You would've gotten 1.8. So 30% of 6 is equal to 1.8. And we can verify it
doing this way as well. So if we were to multiply
0.30 times 6-- let's do that. And I could just write that
literally as 0.3 times 6. Well, 3 times 6 is 18. I have only one digit
behind the decimal amongst both of these
numbers that I'm multiplying. I only have the 3 to the
right of the decimal. So I'm only going
to have one number to the right of
the decimal here. So I just count one number. It's going to be 1.8. So either way you think about
it or calculate it, 30% of 6 is 1.8.