Quotients that are multiples of 10

- [Voiceover] 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 10s, about zeroes and 10s, 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 10s, or 24 times 10. 24 times 10, any time we multiply by 10, will have the original number, 24 in this case, with a zero on the end, 240. So 240 is the same as 24 10s, or 10 times 24. So we can come back over here and write this number 240 as 24 times 10, and then still have the divided by three at the end. So what we changed was we changed 240, or 24 10s, 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. And 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 gonna do is look at this multiplication problem, 24 times 10, and I know that in multiplication, I can multiply in any order. For example, if I have something like two times three, which is six, that's the same as three times two, which is also six. 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 three. So 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. And 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, that's eight, and then we'll bring down our times 10, bringing down this 10 and the times sign, and then 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 80, which means our solution to the original expression is also 80. 240 divided by three is eight 10s, or 80. One other way we could've thought about this is 240, as we've already said, is 24 10s. If we divide 24 10s by three, we end up with eight 10s, and eight 10s is equal to 80. If we have eight 10s, that equals 80. So this is one other way that we could've thought about it, both ways using the zero or our knowledge of 10s 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 4,200, divided by, and let's see, how about seven, divided by seven. So here, again we can break this number down. 42 hundred, this number 42 hundred, or 4,200, 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 100, we keep our whole number of 42 and we add two zeroes now. So 42 times 100, and then we still need to have our divided by seven at the end. Reverse these numbers so that 42 and seven can be next to each other, 42 divided by seven, because that's a division problem, a division factor we might already know. 42 divided into groups of seven is six, and bring down the 100 and the times sign, 100 times six is 600. So our solution, going back up here to 4,200 divided by seven, is 600. Or we could've thought about it again, still thinking about place value but using words here instead of digits, 4,200 is 42 hundreds, 42, I can write that out, 42 hundreds, and if you divide 42 hundreds into groups of seven or into seven groups, each group will have six hundreds, or 600 in it. So either way, 42 hundred, 4,200 divided by seven is 600. 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 zeroes.