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 · 5

15 = 3 · 5

LCD = 2 · 3 · 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.