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.
