Subtracting Mixed Numbers By Counting On

Date: 06/01/98 at 17:48:01
From: james owen
Subject: Subtracting mixed numbers

 ?? + 1 and 3 fourths = 4 and 5 twelfths     
                
I tried inverse operations and it doesn't work.

Date: 06/01/98 at 18:07:41
From: Doctor Pat
Subject: Re: Subtracting mixed numbers

James,

Let's picture the problem in our minds. The question is, how much must 
we add to 1 and 3 fourths to make something 4 and 5 twelfths long.  
Let's add a little at a time until we get there.  

How much would we have to add to make it to 2 units? One fourth.

So now we have a length of 2 units and we still need to make it 
longer. Can you think how much to add to get out to 4? Of course you 
could, and it is 2 more units.

Now we just need to add enough to get from 4 out to 4 and 5 twelfths, 
and that seems easy, too. We need to add five twelfths. 

So in all we need to add 1 fourth + 2 wholes + 5 twelfths. 

Since 1 fourth is the same as 3 twelfths we can rewrite that as:

  3 twelfths + 2 wholes + 5 twelfths = 2 wholes and 8 twelfths

If you know how to simplify fractions you can make that 2 and 
2 thirds.  

This method is called "counting on" and is a good way to think about 
doing fraction problems. Sometimes a picture of a number line will 
help, so I've drawn the kind of picture I would use below:

    |___________|___________|___________|___________|_____
    0           1           2           3           4     4 + 5/12
 
    |___________|_________
    0           1         1 + 3/4

                          |_______________________________| 
                            this is what we need to find 

                          |1/4|
                              |_______2 units________|
                                                     |5/12|

Can you see how we can put the pieces together? I hope this helps you 
figure out how to do mixed number subtraction by adding on. 

Good luck,
         
-Doctor Pat,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/