How to Calculate the Remainder

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Calculating the remainder is a very important part of any division problem. Calculate the remainder with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: Number Theory Education
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to calculate the remainder. Now, if you are comfortable with how the process of long division works, hopefully, calculating the remainder will be pretty straightforward, as well. Because, generally speaking, long division is the best way to figure out the remainder, and it's always going to be the last number standing, if you will. So, let's do a long division problem, and you'll see how to calculate the remainder that way. So, suppose you want to find one-sixty-five, let's just say, divide by fourteen. Now, to transform it to a long division problem, as you're aware, fourteen goes on the outside. One-sixty-five goes on the inside. So, just treat it like you would a long division problem, and the remainder will take care of itself at the very end. So, fourteen does not go into one, but fourteen goes into sixteen once. So, one times fourteen, that's going to be fourteen. Do the subtraction. Sixteen minus fourteen is going to be two. Bring down the five, of course. And then fourteen goes into twenty-five one time. So, one times fourteen is going to be fourteen. Subtraction, you're going to have eleven. Now, that's as far as you can go, of course. And so, you can do it two ways. You can do remainder eleven, which is the former way of remainder. Or, some folks have opted to write the remainder over the divisors. So, you can think of it as eleven, remainder eleven, or eleven and eleven-fourteenths. But, the bottom line is, calculating the remainder is the number that's left standing when the division is complete. So, I'm Jimmy Chang, and that's a brief tutorial on how to calculate the remainder.


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