Quotients that are multiples of 10 | Math | 4th grade | Khan Academy

Let's solve 240 divided by three. To solve this, we could take this large three-digit number and divide it by a one-digit number, or we could take what we know about tens and zeros and try to break this up into numbers that might be easier for us to work with.

So, 240, because of the zero on the end, I know is the same as 24 tens or 24 times 10. 24 times 10, anytime we multiply by 10, we'll have the original number, 24, in this case, with a zero on the end: 240. So, 240 is the same as 24 tens or 10 times 24.

We can come back over here and write this number 240 as 24 times 10 and then still have the divided by 3 at the end. So, what we changed was to change 240 or 24 tens to be 24 times 10. What we did not change is the solution; these expressions are still equal. They equal the same number, so we can solve either one to get the same solution.

Down here, we have a little bit simpler of numbers to work with, so I'll work with this one down here. The next thing I'm going to do is look at this multiplication problem: 24 times 10. I know that in multiplication, I can multiply in any order. For example, if I have something like 2 times 3, which is 6, that's the same as 3 times 2, which is also 6. Two threes or three twos is six. We can change the order without changing the answer.

So, over here, let's do that: 10 times 24 divided by 3. We've changed the expression; we've changed what's written here, but we have not changed what it equals. We have not changed the solution. Now I can see a division problem that, for me, is far simpler than this big three-digit division problem up here.

24 divided into groups of three is eight. And with eight, then we'll bring down our times ten, bringing down this 10 and the times sign. We can use the pattern we already know that we talked about up here. When we multiply by 10, we take our whole number, in this case, eight, and we add a zero to the end or 80.

So our solution we came up with is 80, which means our solution to the original expression is also 80. 240 divided by three is eight tens or eighty. One other way we could have thought about this is two hundred forty, as we've already said, is twenty-four tens. If we divide twenty-four tens by three, we end up with eight tens, and eight tens is equal to eighty.

If we have 8 tens, that equals 80. So this is one other way that we could have thought about it—both ways using the zero or our knowledge of tens to break this division problem down, so we didn't have to deal with a large three-digit number, but could deal with simpler, smaller numbers.

Let's try another one. This time, let's do thousands; let's make this one trickier. What about something like 42 hundred or 4200 divided by, let's see, how about seven?

Divided by seven. So here again, we can break this number down. 4200, this number 4200 can be written as 42 times 100 because our pattern tells us when we have a number, like a whole number like 42, and we multiply by a hundred, we keep our whole number of 42, and we add two zeros.

Now, so 42 times 100, and then we still need to have our divided by 7 at the end. Reverse these numbers so that 42 and 7 can be next to each other. 42 divided by 7, because that's a division problem, division factor we might already know. 42 divided in groups of 7 is 6.

And bring down the 100 and the times sign. 100 times 6 is six hundred. So, our solution going back up here to forty-two hundred divided by seven is six hundred, or we could have thought about it again, still thinking about place value but using words here instead of digits.

4200 is 42 hundreds. I can write that out: 42 hundreds. If you divide 42 hundreds into groups of seven or into seven groups, each group will have six hundreds or six hundred in it. So either way, forty-two hundred, four thousand two hundred divided by seven is six hundred.

So here again, we were able to solve a tricky problem—one that had a four-digit number—without using any long division but instead using what we know about place value or hundreds and zeros.