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, lets use their least
common denominator to find equivalent fractions.
10 = 2 Â· 5
15 = 3 Â· 5
LCD = 2 Â· 3 Â· 5 = 30
Lets rewrite the fractions vertically as equivalent
fractions with the denominator 30.
Now we add the equivalent like fractions.
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
- write the answer in simplest form.
First, we find the LCD, which is 48. After finding equivalent
fractions, we add the numerators, keeping the same denominator.
Because 3 is a factor of 12, the LCD is 12. Again, lets
set up the problem vertically.
and then subtract
from this sum. The LCD of
Next, we subtract
. Their LCD is 10.
Do you see another way of solving this problem, using the LCD
of all three fractions?
Find the perimeter of the figure.
Recall that the perimeter of a figure is the sum of the
lengths of its sides.
The perimeter of the figure is