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What is 15/11?

```
Date: 27 Apr 1995 13:16:46 -0400
From: Lindsay Pickett
Subject: (none)

Dear Dr. Math,

My name is Lindsay Pickett.  We are learning division.
What is 15/11?
```

```
From: Dr. Sydney
Date: 9 May 1995 22:21:15 -0400

Dear Lindsay,

Hello there!  I'm so glad you wrote us!  I wish we could have written back
sooner, but we've been swamped with work here.  How is the division going?

I guess the best approach to a problem like this is to write it out in long
division:
___
11|15

Then ask yourself, how many times does 11 go into 1 (the first digit of
15)?  Since 11 is bigger than 1, it goes in zero times, right?  So, now ask
yourself, how many times does 11 go into 15 (the first two and only two
digits of 15)?  Multiply 11 by the number of times it goes into 15, and
subtract this number from 15.  The resulting number will be your remainder.
So, your answer here will be the number of times 11 goes into 15 with a
remainder of whatever the difference between 15 and that number multiplied
by 11 is.

But what does remainder really mean?  Let's look at a simpler example.
Suppose we divide 4 by 3.  Then our calculation looks like this:
_1_
3|4
-3
---
1

So, we would say 4 divided by 3 is 1 remainder 1 or 1 R. 1, right?  But what
does that second one mean?  Let's think about what we are really trying to
figure out.  When we divide 4 by 3, we want to know what number times 3 will
give us 4, right?  We know that 3 times 1 is 3 and that 3 times 2 is 6, so
our intuition (and actually lengthy proofs that we need not get into!) tells
us that the number we are looking for is in between 1 and 2.  So, the number
we are looking for is 1 plus a fraction.  The remainder tells us what that
fraction is.  Since the remainder is 1 and we are dividing by 3, what the
remainder portion of our answer tells us is that we have 1 third left over.
So, in this case the answer 1 remainder 1 is equivalent to 1 and one third.

Of course this will change depending on what numbers you are dividing.  Can
you figure out what 3 divided by 2 is in terms of remainder and in the terms
I described above?  If this seems confusing, don't worry, you'll study it in
great detail later on, but feel free to write back with any questions!

--Sydney, "Dr. Math"
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Associated Topics:
Elementary Division

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