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### Algebra using Fractions

```
Date: 5/27/96 at 23:48:13
From: Leslie Besman
Subject: Algebra using Fractions

Dr Math, I need you to answer this question and then show me how you
did it:
5
- X = 9
8

Leslie Besman
Northern Lights College, Dawson Creek, BC.
lbesman@nlc.bc.ca
```

```
Date: 5/30/96 at 14:30:32
From: Doctor Mike
Subject:Re: Algebra using Fractions

Hello Leslie,

First, let me be sure I understand your question.  In words, I think
you mean "If the fraction (5/8) times the unknown X is equal to 9,
then what number does X have to be?"  Is that right?

The value of X is 14.4 in decimal form, which is the same as 72/5 in
the form of a fraction reduced to lowest terms. The expert didn't have
to be an Einstein to get that answer for you.  One of the most
important BUT ALSO MOST SIMPLE algebraic ideas is that if an equation
is true, it is STILL going to be true if you do the same thing to both
sides of the equation.  In this case "the same thing" is to multiply
by (8/5).  Here's what I mean:

8   5       8
- * - * X = - * 9
5   8       5

The (8/5) times (5/8) on the left equals one (1).  You can tell this
just by what you probably call "cancellation", or also because
multiplying those two fractions together gives 40 divided by 40.  So,
the left side is just the unknown X all by itself, and the right side

I hope this helps!

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions

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