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## Algebra basics

### Unit 1: Lesson 8

Operations with decimals- Adding decimals: 9.087+15.31
- Adding decimals: 0.822+5.65
- Adding decimals: thousandths
- Subtracting decimals: 9.57-8.09
- Subtracting decimals: 39.1 - 0.794
- Subtracting decimals: thousandths
- Multiplying decimals example
- Multiplying challenging decimals
- Decimal multiplication place value
- Dividing decimals with hundredths
- Dividing by a multi-digit decimal
- Dividing decimals: hundredths

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# Multiplying decimals example

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product. For example, if we multiply 7.61✕9.2, we will have 3 digits behind the decimal in our product because there are 3 digits behind the decimals in the factors. Created by Sal Khan and Monterey Institute for Technology and Education.

## Video transcript

We're asked to multiply 32.12,
or 32 and 12 hundredths, times 0.5, or just 5 tenths. Now when you multiply decimals,
you multiply them the exact same way you would
multiply whole numbers, and then you count the number of
spaces behind the decimal you have in your two numbers you're
multiplying, and you're going to have that many spaces
in your product. Let me show you what
I'm talking about. So let's just multiply
these two characters. So we have 32.12 times 0.5. And when you write them out, you
can just push both of them all the way to the right. You could almost ignore
the decimal. Right now, you should write the
decimal where they belong, but you can almost pretend that
this is 3,212 times 5, and then we'll worry about
the decimals in a second. So let's get started. So if we were just multiplying
5 times 3,212, we would say, well, 5 times 2 is 10. Regroup the 1. 5 times 1 is 5, plus 1 is 6. 5 times 2 is 10. Regroup the 1. And then finally, you have 5
times 3 is 15, plus 1 is 16. And then we don't have
any other places. If we were just doing this as
05, we wouldn't multiply 0 times this whole thing. We would just get 0 anyway. So just 5 times 3,212 gives
us this number. But now we want to care
about the decimals. We just have to count the total
number of spaces or places we have behind the
decimal point in the two numbers we're multiplying. So we have one, two, three
spaces, or three numbers, to the right of the decimals in
the two numbers that we're multiplying. So we need that many numbers to
the right of the decimal in our answer. So we go one, two, three, put
the decimal right over there. So 32.12 times 0.5 is 16.060. And this trailing zero right
here we can ignore, because it's really not adding any
information there. So we could just write
this as 16.06. The last thing you want to do
is just make sure that this makes sense. You have a number that's
almost 32, and we're multiplying it by 0.5. Remember, 0.5 is the same thing
as 5 over 10, which is the same thing as 1/2. So we're really multiplying
32.12 times 1/2. We're trying to figure out what
one half of 32.12 is. And half of 32 is 16, and half
of 0.12 0.06, so this makes complete sense.