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### Long Division

```
Date: 03/16/99 at 22:18:56
From: Daniel
Subject: Division

process step by step.

Thank you.
```

```
Date: 03/17/99 at 12:04:28
From: Doctor Peterson
Subject: Re: Division

Hi, Daniel.

I'm not sure how much you have learned about division; I'll show you
how to divide by a one-digit number. If you need something more
advanced than this, look in our Dr. Math archives for other problems
like what you need to do:

http://mathforum.org/library/drmath/sets/elem_division.html

I'll give you an example problem, and show you how to keep your mind
focused on one part of the problem at a time, so all the numbers
don't get too confusing. You won't write it out in pieces as I will,
but what you do write is a compact way of saying the same thing.
Let's divide 175 by 3:

______
3 ) 175

We take the dividend (175) one digit at a time starting at the left.
If we tried to divide 1 by 3, we would get zero, so let's skip that
and use the first two digits, 17:

___5_
3 ) 17
15
--
2

What I did was to look through the multiplication table for 3 (in my
mind), looking for the biggest multiple of 3 that is less than 17:
3, 6, 9, 12, 15, 18 - since 18 is too big, we use 3 x 5 = 15.
I wrote the 5 on top, above the "ones" digit of the 17 I'm working on,
and wrote the 15 under the 17. Then I subtracted, leaving a remainder
of 2. This says that

17 = 3 x 5 + 2

What we really did just now was to divide 170 by 3, getting only the
number of tens in the quotient:

___50_
3 ) 170
150
---
20

170 = 3 x 50 + 20

That's not the whole problem, though. What do we do with the next
digit of 175, the 5 we left out?

I'll use the remainder, 2, as the tens of a new dividend, by
"bringing down" the next (and last) digit of the dividend:

175
|
v
2-->25

This is really just adding the missing 5 to the remainder of 20. Now
I divide that by 3:

___8_
3 ) 25
24
--
1

I made "25" by combining the remainder, 2, with the next digit, 5,
and divided that by 3 the same way I did before: 25 = 3 x 8 + 1. This
gives us the ones digit of the answer, 8, and a final remainder of 1.

Putting it all together, here's what you actually write down:

___58_
3 ) 175
15
--
25
24
--
1

Do you see that second problem, 25 divided by 3, hidden in there?
When you work on it, you focus on that as if it were a separate
problem by itself, and write the quotient, 8, above the "ones" digit
of the 25.

Putting it all together, the quotient is 58 and the remainder is 1:

175 = 3 x 58 + 1

If it would help you to understand WHY we do it this way, here's a
simple explanation:

Long Division
http://mathforum.org/library/drmath/view/58499.html

You should always check a division. Here's an answer I gave another

Checking Division
http://mathforum.org/library/drmath/view/58807.html

Let's check our answer. I'll do the multiplication "upside down" so
you can see the connection to the way we divided:

3   <--- divisor
x 58   <--- quotient
----
24   <--- notice that 24 and 15 were in your division work!
15    <---
----
174
+  1   <--- remainder
----
175   <--- this matches the dividend, so it's right

I hope that helps. If the this and the archives don't give you what
you need, please write back with a specific problem to show where you
need help.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Division

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