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Computing the Remainder

Computing the Remainder

Author: Morris Goldstein

In this lesson you will learn how to compute the remainder of integer division using a calculator.

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Using a Calculator to Find the Remainder

What is 12581divided by 32?

Any calculator will quickly provide the answer 393.15625...simple enough.

How about what is the remainder when 12581 is divided by 32?  Reach for your calculator, where's the remainder function on your trusty TI-83, TI-84 or whatever calculating device you cherish?   Can't find it can you because it's not there?  The operation you are actually trying to perform is mathematically called the modulus which does exist on some calculators, Excel and programming languages.

With a few extra key strokes, you can use any calculator to get the remainder of integer division.  Let's take a look at the result we obtained previously:

     12581 / 32 = 393.15625

what does it mean?  One way to think about it is that if I have 12,581 "things" (like marbles) and I group them into 32 groups each having the same number of marbles, each group would contain 393 marbles.  Would there be any left over?  How many?  That is the remainder.

The decimal part of the answer (0.15625) is actually a fraction that represents the remainder (or what's left over).  So how can we convert this decimal quantity into something that represents the remainder?  Multiply it by the divisor, 32 in this case:

   0.15625 * 32 = 5

The answer above (5) is the remainder, it is the amount left over.  

Here's the recipe you can use on your calculator:

1.  Perform the division as you normally would on a calculator

2  Subtract the number to the left of the decimal (the integer part, 393 in this case)

3.  Multiply the result by the divisor (the number you are dividing by, 32 in this case)

4.  The result is the remainder.