Lesson Video: Adding and Subtracting Decimals Mathematics • 6th Grade

Video Transcript

In this lesson, what we’re gonna be looking at is adding and subtracting decimals. So what we’re gonna do is learn how to add and subtract multidigit decimals. What we expect to have achieved by the end of the lesson is to add decimals with multiple digits, subtract decimals with multiple digits, and use different methods to carry out addition and subtraction on decimals.

So decimals is something that we use in everyday life. A couple of examples are here: our money; we use it in length when we’re looking at the length of something, maybe in meters or centimeters and converting between them and then adding them together or subtracting them. So it is something that is very, very useful in everything we do.

So what we’re gonna do to have a look at how we add and subtract decimals is start straightaway with an example. So in this example, what we’re gonna take a look at is two decimals that have the same number of decimal places.

Calculate 79.529 plus 10.623.

So in this question, what we’re going to be doing is adding two decimals. And we know that because we’ve got decimal points here, which are the little points between our unit and then our tenths. And whenever we’re adding decimals, the best method to use is the column method. But when we’re using the column method, we need to make sure that each of our place values are lined up evenly. And we must also make sure that our decimal points are also aligned. So we can see that we’ve done that, so we’ve got our 79.529 plus 10.623.

So what we do, as with any column addition, is start from the right-hand side. So in this case, we’re gonna be adding our thousandths. So we’ve got nine plus three, which is 12. So we put two underneath the line and then carry the one into the next place value. Then, we have two add two add the one we carried gives us five. Then, we have five add six, which is 11. So once again, we put one in that place value and we carry one to the next place value. Then, next, what we do is we put in our decimal point, which again must be aligned with the two above. So now, we’ve got nine add zero, but then we add the one we carried. So this gives us 10, so we carry one once again. Then, finally, we’ve got seven add one add the one we carried gives us nine. So we’ve got 90.152. So therefore, we can say that 79.529 plus 10.623 is 90.152.

So there we took a look at calculation where we had to add two decimals. Well now let’s take a look at how we’re gonna subtract with another example. So for our first example of subtraction, what we’re gonna look at is subtracting two values that have the same number of decimal places, so that is the number of values after the decimal point.

Calculate 10.651 minus 0.204.

So when we’re gonna subtract two decimals, the easiest and best method is to use column subtraction. But the key is to make sure that each of our place values are lined up and most importantly make sure that our decimal points are lined up, which they are here. So this will help us put every other place value in its place.

So as with any other column subtraction, we start with the right-hand side. So we’ve got one minus four. Well, watch out here for a common mistake! Often people will just see,“Oh, right! We just subtract from the biggest number.” So they do four minus one, which gives us three. But this is not the case; we’re wanting to do one minus four, which we can’t do. So what we need to do is borrow from the next place value. So we borrow from the hundredths. So instead of having five there, we’ve now got four and we bring one down to the thousandths. So now what we have are eleven thousandths rather than just one. So we’ve got 11 minus four, which is seven.

So then we move to the next place value. We have four minus zero, which is four. Then, we have six minus two, which is four again. Then, we make sure our decimal point is in the correct place. Then, we’ve got zero minus zero, which is just zero. And then for the tens column, we’d actually have one minus, and there wasn’t a value there, but I’m just gonna put a zero in. So we can see what the value would be because we’ve got zero 10s in 0.204, so one minus zero which is just one. So therefore, we can say that 10.651 minus 0.204 is equal to 10.447.

So great! We’ve had a look at an addition and a subtraction example. So now, what we’re gonna do is take a look at something where we have a calculation where each number doesn’t have the same number of decimal places.

Solve the following: 736,281.45 plus 3.5.

So the first thing we can see in this calculation is that both of our numbers have a different number of decimal places, so values after the decimal point, because we can see that the first number has two decimal places or two values after the decimal point and the bottom one only has one. However, what has already been done in the question is that the calculation has been set up neatly because what we’ve got is a column addition and we’ve got our decimal points in line.

So now what we’ve done is set up the same calculation, but we’ve just added some zeros in here. And this isn’t necessary, but it’s just to show you that actually each of these place values does have a value of zero.

So starting on the right-hand side, what we have is five add zero, which is five. And what this does is it prevents us doing anything sort of strange where we try and add two values together that aren’t in the same place value. For example, if we thought, “Well! We’ve got to add 45 and five, which will give us 50, so is that gonna be five units?” This wouldn’t be the case. So by putting this extra zero in, we can see clearly that it’s five hundredths add zero hundredths, which gives us five hundredths in our final answer. Then, we have four add five, which is nine.

Our decimal point is in the same line. So it’s in the same line as the other two decimal points. Then, we have one add three, which is four. And then, all the other values remain unchanged, and that’s because we add zeros, so the eight add zero, two add zero, six add zero, et cetera. So therefore, we can say that 736,281.45 add 3.5 is 736,284.95.

So now, we’ve just looked at an example where we’re adding two decimals with different number of decimal places. Now, we’re gonna do the same for subtracting.

Solve the following: 648.3628 minus 434.27.

So what we can see in this question is that we’ve got two numbers: one with four decimal places, the other with two. And that’s the values after the decimal point. The calculation is set up nicely in a column subtraction way with our decimal points aligned, which is very, very important with this kind of question. Okay, but can we do anything else to make it a bit easier for ourselves? So what we can do sometimes to avoid any mistakes that might be made through errors in our method is add zeros in any place values that are blank. So here we’ve got a zero in the thousandths and ten thousandths for the bottom number.

And now what we do is carry out subtraction as we would carry out any column subtraction, starting with the right-hand side. So we’ve got eight minus zero, which is eight, then two minus zero, which is two. Then, we move over to six minus seven, being careful not to get stuck in the common mistake here, which would be to do seven minus six, which gives us one. We have to do six minus seven, which we can’t do. So we’re gonna borrow from the place value to the left. So now, what we’ve done is borrowed one to the tenths. So we’ve got two tenths now.

And now what we’ve got in the hundredths is sixteen hundredths instead of six. So we’ve got 16 minus seven, which is nine. Then, we’ve got two minus two, which is zero. And then, we put the decimal point in exactly the same place that’s aligned. Then, we’ve got eight minus four, which is four; four minus three, which is one; and then finally six minus four. So therefore, we can say that 648.3628 minus 434.27 is 214.0928.

So now, what we’re gonna do is move on to our final example.

Find 657.2436 plus 123.64532.

So to solve this problem, the most common way to do this would be using column addition, and we’re gonna have a look at that in a second. But also, if we saw this kind of problem and wanted to try and solve it mentally, there is a method we could use, because what we could do is first of all take a look at the 657 and the 123. Well, if we add three from the 123 to 657, we get 660. And then, if we add 120, which is what we have left of our 123, to 660, we get 780.

So now, all we need to do is add the decimal parts of our numbers, and we can do that using our place values. So, we’ve got tenths, hundredths, thousandths. And then, we’ve got ten thousandths for the first number and the second number we’ve got a hundred thousandths. So, if we look at the tenths, we’ve got two and six, which is eight. And then the hundredths, we’ve got four plus four, which is eight again. Then, we’re carrying this on for the other place values, and we’d have 892. We get the two because we’d have zero hundred thousandths in our first number and two hundred thousandths in our second number. And this will give us our answer, 780.88892.

Now I did mention that we’re also gonna show you how to do this with a more formal method, which is using column addition. So as with any decimal column subtraction or addition, the key is to line up the decimal points, which I’ve done here. But I’ve also added in a zero where we didn’t have a value in one of the place values in the first number, which is the hundred thousandths. And I’ve just done this just to avoid confusion.

So first of all, starting from the right-hand side, we have zero add two, which is two; then six add three, which is nine; then three add five, which is eight; four add four, which is eight again; then two add six, which is eight again. Then, we’ve got a decimal point, which is lined up. Then, we’ve got seven add three, which is 10. So we’ve put a zero in the units column, and then we carry one into the tens column. Then, we’ve got five add two add the one we carried, which gives us eight. And then finally, we’ve got six add one, which is seven. So therefore, we get the same answer. So we can say that 657.2436 plus 123.64532 is 780.88892.

Now it is worth mentioning, we did a couple of methods here. One of them was a mental method. There is one thing we need to watch out for though. If in the mental method we’d had a number where actually some of our decimals when they’re added together gave us a number bigger than nine, so 10, et cetera — so we have to look at moving and carrying values into the other place values — it would be a bit more complicated. So it’s always, always recommended to use column addition in this kind of problem.

Okay great, so we now looked at all our examples. So let’s have a quick summary of the key points of this lesson. So the first key point we have when adding or subtracting decimals is that when we’re setting up our column addition or subtraction, we need to make sure that the decimal points are lined up so they are in the same line. And this will also line up our different place values.

We also discussed that you may want to add zeros for missing values when we’ve actually got a column addition or subtraction setup. And this is one to keep the place values in the correct line. But also it might avoid you making any mistakes with incorrect calculations, like calculating values that were in different place values.

And the final key point is in fact a key point for any type of column subtraction. And that is, if we’ve got the top number where one of the values is less than the one below it, then we still carry out that as our subtraction. So we’d have four minus seven in our example. And what we do is borrow from the next place value. We would not fall into the trap, which can be a common mistake of doing it the other way around or just thinking, “well, we’ll do the biggest number first, so seven minus four.”