Division problems that work out nicely
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Canceling zeros when dividing
- [Voiceover] Let's solve 350 divided by 50. So, one way to think about this is if we had 350 of something, let's say, something delicious like brownies. If we had 350 brownies and we were dividing them into groups of 50, how many groups of 50 could we get? Well, one idea is to count by 50's until we get to 350 and see how many groups there are. One group of 50 would be 50, plus another group of 50 would be 100, plus another group of 50 is 150, another one will be 200, 200 plus 50 is 250, plus another 50 is 300, and plus one more 50 is 350. So, when we added all these 50's, these groups of 50, 50, 100, 150, 200, 250, 300, 350, we ended up with 350. So, 350 can be divided into this many groups of 50, and how many groups is this? One, two, three, four, five, six, seven. So, 350 divided into groups of 50 is seven. Now, let's look at that quotient, that solution of seven and let's say something. If we had simply divided 35 by five, we would have also gotten seven. 35 divided into groups of five is also equal to seven. So, in a way, these zeroes didn't matter, they didn't affect our answer. We were able to cancel them out. Having the zero in the first number is cancelled out by having that zero in the second number. And, let's look at why that is. Let's think about why that is. Division is really the same as a fraction. So, if we wrote this as a fraction, let's say 350 over 50, well this fraction bar right here is the same as the division sign up here. 350 divided by 50 is the same as 350 over 50. And, when we have a fraction like this fraction down here, we can simplify it. In this case, because there's zeroes on the end, we know they're both multiples of 10, so we can divide them both by 10. We can divide our numerator and our denominator by 10. And, when we divide whole numbers by 10, we have a trick we can use, a pattern, really, which is that the whole number, in this case 350, when it's divided by 10 we drop a zero from the end. So, 350 divided by 10 is 35. 350 could be divided into 10 groups of 35. And, then 50 divided by 10 will be the same thing. When we divided 50 by 10, we drop that zero off the end, or another way to think about it is 50 divided into groups of 10 would make five groups. And, then we end up with our simplified fraction of 35 fifths or 35 divided by five, which is the same thing here. So, in both of these cases, we can see that 350 divided by 50 is the same as 35 divided by 5. So, when both whole numbers, when we're dividing whole numbers and they both end in zeroes, we can cancel those zeroes. Basically, we're factoring out a 10. We're taking the 10, the divided by 10 out of both of them, out of both numbers. So, we can cancel those zeroes which leaves us with smaller numbers and at least for me, I find division a lot simpler when I'm working with smaller numbers. Let's try a few more. Let's try one like 420 divided by 70. So, we can see we have two whole numbers, both end in zero. So, we're gonna cancel those zeroes, basically we're dividing a ten out of both numbers and end up with a simpler division problem of 42 divided by seven. 42 divided by seven equals six, therefore 420 divided by 70 also equals six. And, here's one last one. What is we had 5600 divided by 80? So, the first thing I notice is I have zeroes at the end of both of my whole numbers. If I cancel out this one, I can cancel out one on the other side. I can't cancel both of 'em over here, there were two, with cancelling we have to cancel the same amount of zeroes on both sides, and now we end up with 560 divided by eight. This leaves us with a new division problem that's still a little bit tricky, but easier than dividing by 80. So, here we can think of 560 as 56 10's because of the zero on the end, and 56 10's or 560 could be rewritten as 10 times 56. Theses are equivalent. 560 and 10 times 56, because 10 times 56 is a 56 with a zero on the end. And, rewriting it this way makes it so now I have a division problem right here, 56 divided by 8 that we can solve, 56 divided by eight is seven, and then we still have this 10 and the times sign and 10 times seven equals 70. So, our solution here, when we divided 560 by eight was 70, so that means our solution up here for 5600 divided by 80 is also 70. Because, when we cancel zeroes and divide, we still get the same solution. But, remember, we have to cancel the same amount of zeroes in each number, here we couldn't cancel both zeroes. If we cancel one zero in the dividend, we can cancel one zero in the divisor. And, another thing to remember about this trick, first thing to remember is we need to cancel the same amount of zeroes, and the second, the zeroes have to be at the end of the problem. So, if we had a division problem, something for example like 506 divided by 20, here we cannot cancel the zeroes, we cannot cancel the zeroes because this zero is not on the end. So, the new problem this would give us, 56 divided by two, is not equivalent, does not equal the top division problem. So, we can't cancel zeroes, that does not work. We cannot cancel zeroes unless they are at the end of the problem, and we cancel the same amount in both the dividend and the divisor.