Subtracting mixed numbers
Free lesson plan from HomeschoolMath.net

See if you can figure out the following subtraction problems with mixed numbers.  
Write a subtraction sentence for each.

Shade 2 3 4 .  Cross out 1 1 4 2 3 4 - 1 1 4 =

Shade 2 1 8 .  Cross out 5 8 2 1 8 - 5 8 =

Write below your explanation of how to subtract mixed numbers.  Discuss it with
your teacher before proceeding.  Then check the explanations in the end of the lesson.

To subtract mixed numbers, ________________________________

______________________________________________________

______________________________________________________.

Subtracting mixed numbers

The natural approach is to subtract whole parts and fractional parts separately. 
It works sometimes.
   

Cross out 1 1 4        2  3 4 -   1  1 4     2 3 4 - 1 1 4 = 1 2 4

But many times that doesn't work.  Often the fractional part is "too small" to take away
a bigger piece.  In that situation we can "rename" one whole into a fraction and then
subtract.  Or, you can subtract in parts: divide what you want to subtract into two parts
so that you first take away what can be taken from the fractional part, then the rest from
the whole part.

In the example below, one whole is renamed into 8/8.  It is like borrowing one whole
or 8/8.  Since there are already 1/8, the fractional part becomes 9/8.
 

Cross out  5 8   - rename        1  9 8 2  1 8 -   1  1 4     2 1 8 - 5 8 = 1 9 8 - 5 8 = 1 4 8

Below the 5/8 is subtracted in two parts: first 1/8, then 4/8.

Cross out  5 8 . 2 1 8 - 5 8 = 2 1 8 - 1 8 - 4 8 = 2 - 4 8 = 1 4 8

Of course if the fractional parts are unlike, we need to find a common denominator
first, and then rename or subtract in parts.

Cross out 1 2 3                 1 9 6 2  1 2   2  3 6 -   1  2 3 -   1  4 6     = 2 1 2 - 1 2 3 = 2 3 6 - 1 4 6 =  1 9 6 - 1 4 6 = 5 6