Adding Fractions That Have Variables

Date: 03/24/2002 at 13:39:33
From: Sal Anicito
Subject: Adding fractions with variables
                        
   9a        2
  ----  +  ----     
   10        5 

I have the answer in the back of the book but I don't know how to 
solve it. The answer is showing:

               9a + 4
              --------
                 10

Date: 03/24/2002 at 13:45:11
From: Doctor Ian
Subject: Re: Adding fractions with variables

Hi Sal, 

Let's back up a step. Would you be able to handle this without the 
variable?  That is, how would you add

   9   2
  -- + - = ?
  10   5


Don't just tell me the answer. Show me the steps that you would 
follow. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 03/24/2002 at 23:18:26
From: Sal Anicito
Subject: Adding fractions with variables

I would first find the LCD, which would be 10. Then say 5 into 10 is 
2 and 2 x 2 = 4, which would give me 4/10. Then 10 into 10 is 1 and 
1 x 9 is 9, which would give me 9/10. Then add 9 + 4, which is 13, so 
I would get 13/10 for an answer. Is that right?

Date: 03/25/2002 at 07:09:14
From: Doctor Ian
Subject: Re: Adding fractions with variables

Hi Sal,

That's exactly right. 

  9   2    9   2   2    9    4   13
 -- + - = -- + - * - = -- + -- = -- 
 10   5   10   5   2   10   10   10

The thing is, it works the same way even if you have a variable in 
there:

  9a   2    9a   2   2    9a    4   9a + 4
 --- + - = --- + - * - = --- + -- = ------
  10   5    10   5   2    10   10      10


The only difference is that you don't know what the value of a happens 
to be. To see why this works, choose a value for a, but don't do the 
multiplication yet:

  9*2    2    9*2    2   2    9*2     4   9*2 + 4
 ----- + - = ----- + - * - = ----- + -- = --------
  10     5      10   5   2     10    10      10

A variable is just a number whose value you don't yet know; and a 
variable expression (like '9a') is just an operation that you're 
putting off until later.  

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/