Video: Subtracting a Decimal from an Integer

Calculate the following: 90 − 70.8.

04:39

Video Transcript

Calculate the following. 90 take away 70.8.

In this question, we’re being asked to subtract a decimal from a whole number. Notice how the number 70.8 has got one more decimal place than the number 90. Now, the point of this video is to show how we can subtract decimals with one decimal place using the column method. And we will go on to show that method. But using the column method isn’t always the most efficient or the quickest way we can find an answer. And so, we’ll go through the column method. And then, we’re going to go through another method that might be a little bit more efficient.

When using the column method, we need to make sure that we write both numbers vertically on top of each other so that the digits are in the correct columns. Notice how the second number has got a digit in the tenths column. To make it easier for us to subtract, we can make sure that we write a digit in the tenths column for the first number too. We know there are zero-tenths, so we can write a zero there, doesn’t affect the number.

The other thing to remember, which is very easy to forget, is to put a decimal point in our answer. We need to make sure this lines up with the other two decimal points. But if we do this at the start, before we start subtracting, we know it’s going to definitely be there, and we won’t forget it.

First, we’ll look at the tenths column. What’s zero take away eight? We can’t do this because eight is more than zero. So, normally, what we do is look at the next column along and exchange to help us. But there’s nothing in the next column along. So, we need to go all the way along to the tens column. We will take one 10 and we’ll exchange it for 10 ones. We now have eight 10s instead of nine 10s, and 10 ones.

Now, we’ve got something in the ones column. We can exchange here. We’ll take one lot of one and exchange it for ten-tenths. So, instead of 10 ones, we now have nine ones. We have ten-tenths. Now, we can subtract the tenths.

Remember that exchanging like this is really another way of partitioning the first number. We did have the number 90, which was nine 10s. We now have a number that seems to say eight 10s, nine ones, and ten-tenths. But that’s exactly the same as 90. We’ve just split it up in another way, and it helps us now to subtract.

Let’s subtract the tenths. ten-tenths take away eight-tenths leaves us with two-tenths. Onto the ones, nine take away zero is still nine. And eight 10s take away seven 10s leaves us with one 10. And that’s how to use the column method to find the answer to 90 take away 70.8.

But we did say this is not perhaps the most efficient method we could use. A quicker way is to start with 70.8 and to count up until we get to 90. The column method involved a fair amount of exchanging. This method is perhaps a little quicker. We can start with 70.8. And first, we can add to make the nearest whole number. And we do this by adding 0.2. 70.8 plus 0.2 equals 71.

Now, we can count on to make the nearest 10. 71 plus nine equals 80. And then, finally, we can add another 10 to take us to 90. So, altogether, we’ve added 10, nine, and 0.2. In other words, we’ve added one 10, nine ones, and two-tenths. And our answer has one 10, nine ones, and two-tenths in it. So, whether we use the column method or choose to use a mental method instead, we can still find the same answer. 90 take away 70.8 equals 19.2.

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