Dividing whole numbers by 10

- [Voiceover] 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 and look at 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 30 and we're dividing it into groups of 10. So let's see how many groups of 10 it takes to make 30. One group of 10 is 10, 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 three 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 110 divided by 10. And again, we're dividing, we're taking 110 and dividing it into groups of 10. So let's see how many groups of 10 it takes to get to 110. Here's one 10, plus another is 20, 30, 40, 50, another 10 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. One, two, three, four, five, six, seven, eight, nine, 10, 11, our solution is 11. If we have 110 and we divide it into groups of 10, we end up with 11 groups. Let's look at these first two, let's pause here and see if we see a pattern. 30 divide by 10 was three, 110 divided by 10 was 11, so what happened to the 30 in the 110 to get these quotients? And 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 two times 10 instead of dividing, times 10, our solution was 20, or two, our original number, with a zero added to the end. Remember, in 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, 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 10s, but just try to use the pattern to solve it. If we had somethig like, say, 7,000 divided by 10, well, our solution is going to be 7,000 but with a zero taken off of the end because we're dividing by 10, so instead of 7,000 we would have 700. 7,000 divided into groups of 10 would be 700 groups of 10, so our solution is 700. Let's take this all a step further and let's think about what dividing by 10 is doing to these numbers, to 30, to 110, to 7,000, 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 10s, our solution was three ones. The three moved one place value to the right, and the zero really did too, it would move after a decimal, which would be 3.0, which is the same as three, which is the reason we didn't need to write that zero, the reason that we could cross it off. So our number, instead of being three 10s, when we divided by 10, became three ones. Let's look at a little bit trickier of one. We also tried 7,000, so that would be seven thousands, zero hundreds, zero 10s, and zero ones, and when we divided by 10, our seven in our thousands place became seven hundreds, and the zero hundreds became zero 10s, and zero 10s became zero ones. And that last zero we were able to cross off and move to after the decimal. So 7,000 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 10s, three 10s 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 63, or six 10s and three ones. So again, two ways to think about dividing by 10. Either we can cross off a zero, or we move every digit, each digit one place value to the right.