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Common fractions and decimals | Math | 4th Grade | Khan Academy

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Common fractions and decimals | Math | 4th Grade | Khan Academy

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We need to calculate 9.005 minus 3.6, or we could view it as 9 and 5 thousandths minus 3 and 6 tenths. Whenever you do a subtracting decimals problem, the most important thing, and this is true when you're adding decimals as well, is you have to line up the decimals. So this is 9.005 minus 3.6. So we've lined up the decimals, and now we're ready to subtract. Now we can subtract. So we start up here. We have 5 minus nothing. You can imagine this 3.6, or this 3 and 6 tenths, we could add two zeroes right here, and it would be the same thing as 3 and 600 thousandths, which is the same thing as 6 tenths. And when you look at it that way, you'd say, OK, 5 minus 0 is nothing, and you just write a 5 right there. Or you could have said, if there's nothing there, it would have been 5 minus nothing is 5. Then you have 0 minus 0, which is just 0. And then you have a 0 minus 6. And you can't subtract 6 from 0. So we need to get something into this space right here, and what we essentially are going to do is regroup. We're going to take one 1 from the 9, so let's do that. So let's take one 1 from the 9, so it becomes an 8. And we need to do something with that one 1. We're going to put it in the tenths place. Now remember, one whole is equal to 10 tenths. This is the tenths place. So then this will become 10. Sometimes it's taught that you're borrowing the 1, but you're really taking it, and you're actually taking 10 from the place to your left. So one whole is 10 tenths, we're in the tenths place. So you have 10 minus 6. Let me switch colors. 10 minus 6 is 4. You have your decimal right there, and then you have 8 minus 3 is 5. So 9.005 minus 3.6 is 5.405.

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Subtracting decimals: 9.005 - 3.6 (video) | Khan Academy

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We need to calculate 9.005 minus 3.6, or we could view it as 9 and 5 thousandths minus 3 and 6 tenths. Whenever you do a subtracting decimals problem, the most important thing, and this is true when you're adding decimals as well, is you have to line up the decimals.

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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.

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Multiplying decimals example (video) | Khan Academy

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