Subtracting Mixed Numbers

Date: 01/23/98 at 14:24:02
From: Sean Ferguson
Subject: Subtracting mixed numbers

I don't really get subtracting mixed numbers.

Date: 01/27/98 at 16:35:49
From: Doctor Loni
Subject: Re: Subtracting mixed numbers

Subtracting mixed numbers can be tough to understand at first, but 
once you understand how to set them up, they get easier.  Let's try a 
couple of examples:

    2 2/3  -  1 1/6

Write it down like this:

    2  2/3

  - 1  1/6
  ---------

Just as in any other subtraction problem, start at the far right of 
the problem. You would begin with 2/3 - 1/6. You would do this just as 
you would any other subtraction of fractions. First you find a common 
denominator (a number, preferably the smallest one, that both 
denominators will divide into evenly)  In this case the common 
denominator is 6. 

First you change 2/3 into sixths.   

    2/3 = ?/6

Ask yourself, "how many times does 3 go into 6?" The answer is 2. Now 
take 2 times the numerator of the original fraction (in this case 2)  
You will get 4. So:

    2/3 = 4/6     

4/6 and 2/3 are equivalent fractions, which means they are equal

1/6 is already in sixths so there is no need to change it. Now your 
problem looks like this:

    2 4/6

  - 1 1/6
 --------

Again starting at the right 

   4/6 - 1/6 =  3/6

    2  4/6
 
  - 1  1/6
  --------
    1  3/6

Now move to the next number to the left and subtract 1 from 2. The 
answer to your problem so far is   

  1 3/6       

However, the fraction, 3/6, is not in lowest terms.

If you divide both the top and bottom of 3/6 by 3 you get 1/2. So the 
answer to this problem is: 

   1 1/2

Let's try one where you will have to borrow.

    5  1/3

  - 3  1/2
-----------

Starting at the right you have 1/3 - 1/2. You need to find the common 
denominator.

In this case the least common denominator is 6.

  1/3  =  2/6          1/2 = 3/6

Now you have:

    5  2/6

 -  3  3/6
-----------

Here we have a problem. We can't take 3/6 away from 2/3 because 3/6 is 
a bigger number. So just like any other subtraction problem, we have 
to borrow from the next column over. We cross off the 5 and write 4 
because we are borrowing 1.
  
Here comes the tricky part. We have actually borrowed 1. However, our 
fractions are written as parts of a whole (in this case sixths). So 1 
expressed in sixths is  6/6 (remember 6/6 = 1; we are just writing it 
differently). When we borrow, we add what we borrowed to the next 
column over - just as in regular subtraction:

    4  2/6 + 6/6

 -  3  3/6
----------------       

Remember it's now 4 instead of 5 because we borrowed 1.  

   2/6 + 6/6 = 8/6, so
          
    4  8/6

 -  3  3/6
 ----------

Now we can do the subtraction.  8/6 - 3/6 = 5/6 and 4 - 3 = 1 so:

    4  8/6

  - 3  3/6
 ---------
    1  5/6

If you are still having trouble or are confused about common 
denominators, let me know!

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