Dividing whole numbers by 10 | Math | 4th grade | Khan Academy

Dividing by 10, a lot like multiplying by 10, creates a pattern with numbers. So let's dig in and look at dividing by 10. Look at what happens when we divide by 10 and see if we can figure out that pattern and maybe even how it relates to the pattern for multiplying by 10.

Let's take a fairly simple one to start. Let's say something like 30 divided by 10. One way to think about this is we're taking the number thirty, and we're dividing it into groups of ten. So let's see how many groups of ten it takes to make thirty. One group of ten is ten, so that's not enough. Plus a second group is 20, plus a third group is 30. So 30 can be thought of as 10 plus 10 plus 10, or 3 groups of 10.

So if we divide 30 by 10, divide 30 into groups of 10, we end up with three groups. Let's try another one, maybe something slightly trickier. Maybe let's go with a hundred ten divided by ten. And again, we're dividing. We're taking 110 and dividing it into groups of ten. So let's see how many groups of ten it takes to get to a hundred ten.

There's one ten, plus another is twenty, thirty, forty, fifty. Another ten gets us to 60, 70, 80. We're getting closer. 90, 100, and 110. So this right here is how many groups of 10 it takes us to get to 110. So let's see how many groups is that: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Our solution is eleven. If we have a hundred ten and we divide it into groups of ten, we end up with eleven groups.

Well, let's look at these first two. Let's pause here and see if we see a pattern. 30 divided by 10 was 3; 110 divided by 10 was 11. So what happened? What happened to the 30 and the 110 to get these quotients? What happened is the zero. The zero on the end was taken off. Our solution is the same but with the zero taken off the end. Here again, the solution is the same with a zero taken off the end.

And if we remember for multiplication, it was the opposite. If we had 2 times 10 instead of dividing times 10, our solution was 20, or a 2, our original number with a zero added to the end. Remembering another one, something like 13 times 10, our product, our solution, is a 13, the original number with a zero added to the end.

So in multiplication, when we multiply by 10, we add a zero to our whole number at the end. And when we divide, when we do the opposite by 10, we take off a zero from the end of our whole number. So knowing that pattern, let's try one more, maybe one where we don't work out all the tens but just try to use the pattern to solve it.

If we had something like say seven thousand divided by ten, well our solution is going to be seven thousand but with a zero taken off of the end because we're dividing by ten. So instead of seven thousand, we would have seven hundred. Seven thousand divided into groups of ten would be seven hundred groups of ten. So our solution is seven hundred.

Let's take this all a step further, and let's think about what dividing by ten is doing to these numbers—to thirty, to one hundred ten, to seven thousand—in terms of their place value. So here's a place value chart. Let's use it to look at one of the numbers we already tried, something like 30.

And when we divided 30 by 10, remember what happened to the three? Instead of being three tens, our solution was three ones. The three moved one place value to the right, and the 0 really did too. It would move after a decimal, which would be 3.0, which is the same as 3, which is the reason we didn't need to write that 0. The reason that we could cross it off. So our number, instead of being three tens, when we divided by ten, became three ones.

Let's look at a little bit trickier of one we also tried: seven thousand. So that would be seven thousands, zero hundreds, zero tens, and zero ones. And when we divided by ten, our seven in our thousands place became seven hundreds, and the zero hundreds became zero tens, and zero tens became zero ones. And that last zero we were able to cross off and moved after the decimal, so 7000 divided by 10 was 700. Again, everything moved one place value to the right.

So there's two ways to think about dividing by 10. We could either say you drop a zero off the end, or we could say that you move every digit one place value to the right. Let's think about it again in terms of place value with a new number.

Let's try something like 630. If we divide 630 by 10, we're going to move everything one place value to the right. So the six hundreds will become six tens. Six tens, three tens will become three ones, and the zero ones will move after the decimal. So we can say that 630 divided by 10 is equal to sixty three, or six tens and three ones.

So again, two ways to think about dividing by ten: either we can cross off a zero, or we move every digit, each digit one place value to the right.