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 
is a simple arithmetic task. 
  
I hope this helps!
  
-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/