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We're asked to multiply 32.12, or 32 and 12 hundredths, times

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0.5, or just 5 tenths.

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Now when you multiply decimals, you multiply them

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the exact same way you would multiply whole numbers, and

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then you count the number of spaces behind the decimal you

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have in your two numbers you're multiplying, and you're

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going to have that many spaces in your product.

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Let me show you what I'm talking about.

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So let's just multiply these two characters.

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So we have 32.12 times 0.5.

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And when you write them out, you can just push both of them

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all the way to the right.

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You could almost ignore the decimal.

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Right now, you should write the decimal where they belong,

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but you can almost pretend that this is 3,212 times 5,

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and then we'll worry about the decimals in a second.

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So let's get started.

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So if we were just multiplying 5 times 3,212, we would say,

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well, 5 times 2 is 10.

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Regroup the 1.

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5 times 1 is 5, plus 1 is 6.

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5 times 2 is 10.

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Regroup the 1.

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And then finally, you have 5 times 3 is 15, plus 1 is 16.

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And then we don't have any other places.

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If we were just doing this as 05, we wouldn't multiply 0

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times this whole thing.

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We would just get 0 anyway.

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So just 5 times 3,212 gives us this number.

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But now we want to care about the decimals.

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We just have to count the total number of spaces or

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places we have behind the decimal point in the two

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numbers we're multiplying.

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So we have one, two, three spaces, or three numbers, to

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the right of the decimals in the two numbers that we're

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multiplying.

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So we need that many numbers to the right of the decimal in

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our answer.

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So we go one, two, three, put the decimal right over there.

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So 32.12 times 0.5 is 16.060.

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And this trailing zero right here we can ignore, because

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it's really not adding any information there.

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So we could just write this as 16.06.

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The last thing you want to do is just make sure that this

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makes sense.

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You have a number that's almost 32, and we're

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multiplying it by 0.5.

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Remember, 0.5 is the same thing as 5 over 10, which is

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the same thing as 1/2.

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So we're really multiplying 32.12 times 1/2.

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We're trying to figure out what one half of 32.12 is.

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And half of 32 is 16, and half of 0.12 0.06, so this makes

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complete sense.

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