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### Multiplication and Division Equations

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Date: 11/29/2001 at 07:03:55
From: Dean
Subject: Solving Multiplication and Division Equations

Dear Dr. Math,

I am having a hard time in math. Solving multiplication and division
equations is driving me nuts. For example: 17x = 85 (X= ?)

If you can help me that will be great.

Thank you,
Dean
```

```
Date: 11/29/2001 at 12:30:17
From: Doctor Peterson
Subject: Re: Solving Multiplication and Division Equations

Hi, Dean.

The equation

17x = 85

can be thought of this way: Someone has chosen a secret number, and
hasn't told you what it is, but wants to give you a clue. So he
multiplies the number by 17, and tells you that he got 85. You want to
find what his number is.

You have to work backward and determine what number he started with.
So, what number, times 17, gives 85?

If you think back to when you first learned about division, you should
recognize that this is exactly what division tells you: what number do
you multiply by this number to get that? For example, when you divide
6 by 2, the answer is 3 because 2 times 3 gives 6. The quotient, 3, is
the number you multiply by 2 to get 6.

So we can work backward by dividing 85 by 17. Use your usual methods
to do that, and you will find the answer.

Another way to look at this is to recognize that division "undoes"
multiplication. That is, if you multiply a number by 17, and then
divide the result by 17, you get back your original number. You have
been told that multiplying x by 17 gives 85; dividing by 17 will give
back the original number.

This is the basic idea behind much of what you will do in algebra:
undo operations to find what number you started with. I hope this
gives you a good start.

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

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