# Adding and Subtracting Unlike Fractions
Adding (or subtracting) unlike fractions is more complicated
than adding (or subtracting) like fractions. An extra step is
required: changing the unlike fractions to equivalent like
fractions. For instance, suppose that we want to add
. Even though we can use any common
denominator for these fractions, let’s use their least
common denominator to find equivalent fractions.
10 = 2 Â· 5
15 = 3 Â· 5
LCD = 2 Â· 3 Â· 5 = 30
Let’s rewrite the fractions vertically as equivalent
fractions with the denominator 30.
Now we add the equivalent like fractions.
So
.
We can also add and subtract unlike fractions horizontally.
**To Add (or Subtract) Unlike Fractions **
- rewrite the fractions as equivalent fractions with a
common denominator, usually the LCD;
- add (or subtract) the numerators, keeping the same
denominator; and
- write the answer in simplest form.
**EXAMPLE 1 **
Add:
**Solution **
First, we find the LCD, which is 48. After finding equivalent
fractions, we add the numerators, keeping the same denominator.
**EXAMPLE 2 **
Subtract
.
**Solution**
Because 3 is a factor of 12, the LCD is 12. Again, let’s
set up the problem vertically.
**EXAMPLE 3 **
Combine:
.
**Solution **
We add
and then subtract
from this sum. The LCD of
is 6.
Next, we subtract
. Their LCD is 10.
So
Do you see another way of solving this problem, using the LCD
of all three fractions?
**EXAMPLE 4 **
Find the perimeter of the figure.
**Solution **
Recall that the perimeter of a figure is the sum of the
lengths of its sides.
The perimeter of the figure is
feet. |