Methods to Check Multi-Digit Multiplication Problems

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You can check your work on multi-digit multiplication problems in a few very specific ways. Learn about methods to check multi-digit multiplication problems with help from a tutor in high school mathematics in this free video clip.

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Hi, I'm Charlie Kasov. I'm a math teacher and today we're going to learn methods to check multi-digit multiplication problems. Now, what I'm going to do is I'm going to put a multiplication problem on the board and I'm going to solve it, and then show you how I would check it over. So, let's take the numbers three hundred and twelve times four hundred and forty-five. Not that it takes that much deciding. Just a little bit, you know. I like my four hundred and forty numbers. So, three hundred and twelve times four hundred forty-five. We're always going to start with the ones. So, the thing is, when we say start with the ones, we have the ones place here, which is two. We have the ones place here, which is five. But really we're talking about the bottom line. So, we're going to start with the one here. We're going to multiply two times five, so that's ten, so we put a zero, and we carry. One times five, which is five plus one, so that's six. And then three times five, and that's fifteen. So, the last one we don't have to carry. We just write it out. So, now we have fifteen hundred and sixty. So, the next thing we do is we're going to move over to the four, to the tens place. And if we do that, we automatically start with a zero here. So, we're going to go two times four, which is eight. One times four, which is four. And three times four, which is twelve. So, now we have twelve thousand four hundred and eighty. And then we're going to go to the hundreds place. And again, we're going to move over, so we're going to move over to zeros. And we have two times four, which is eight. One times four, which is four. And three times four, which is twelve. So, now we have a hundred and twenty-four thousand eight hundred. Now, we have to add everything up. So, we add all our zeros. We add six plus eight is fourteen. So, again, with addition, we're going to carry the one. So, five plus one is six plus four is ten plus eight is eighteen, carry the one. One plus one is two plus two is four plus four is eight. And then one plus two is three, and then one. So, we have a hundred and thirty-eight thousand eight hundred and forty. Now, how do we check this? One way we can do it is to draw straight lines all the way down. Maybe just here. And one of the most important things that you have to do when you're checking your multiplication is count the number of digits in the bottom line, and we have one, two, three. So, we know we need at least three lines of multiplication here, or exactly three. This one doesn't have to start with a zero. It just happened to 'cause we had two times five. This one has to start with a zero, and this line has to start with two zeros. So, the way you check is first line, no zeros. But again in this case, we happen to have one. This second line, one zero, third line, two zeros. And, of course, fourth line would be three zeros. And it's always one less zero, one fewer zero than the number of lines. So, I'm Charlie Kasov, and you just learned some methods to check your multi-digit multiplication problems. Thanks a lot.

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