Multiplication and Division Equations

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/