EDGE Math 8

Addition and Subtraction of Rational Expressions with the Same Denominator

In the previous grade levels, you have learned how to add or subtract unlike fractions. Below is an example that gives a review of the process.

Add the following: $\frac{7}{12} + \frac{5}{18} .$

Step 1:

Find the least common denominator (LCD) of the two fractions.
The prime factorizations of the denominators 12 and 18 are shown below.

12 = 2 \times 2 \times 3

18 = 2 \times 3 \times 3

Based on the prime factorizations, you can get first the greatest common factor (GCF). The GCF of 12 and 18 is $2 \times 3,$ or 6. The LCD or the least common multiple (LCM) of 12 and 18 is the product of the GCF and the remaining uncommon prime factors. Hence, the LCD is equal to $6 \times 2 \times 3,$ or 36.

Step 2:

Rewrite each fraction to its equivalent fraction using the LCD.

\frac{7}{12} = \frac{?}{36} = \frac{7 \times 3}{12 \times 3} = \frac{21}{36}

\frac{5}{18} = \frac{?}{36} = \frac{5 \times 2}{18 \times 2} = \frac{10}{36}

Step 3:

Add the resulting like fractions. Simplify the sum, if possible.

\frac{21}{36} + \frac{10}{36} = \frac{31}{36}

The sum is already in simplest form. Hence, $\frac{7}{12} + \frac{5}{18} = \frac{31}{36} .$