Adding Fractions with Unlike Denominators

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction $$\frac{1}{2}$$ , 1 is the part and 2 is the whole.

Unlike denominators are denominators that are not the same. For example, in the fractions $$\frac{1}{3}$$ and $$\frac{1}{4}$$ , the denominators 3 and 4 are unlike.

To add fractions with unlike denominators, first find a common denominator, convert each fraction to an equivalent fraction with that denominator, and then add the numerators.

A common denominator is a number that is a multiple of the denominators of two or more fractions. It allows you to add or subtract fractions.

The first step is to find a common denominator. The least common multiple of 2 and 8 is 8.

To convert $$\frac{1}{2}$$ to a fraction with a denominator of 8, multiply both the numerator and denominator by 4: $$\frac{1 \times 4}{2 \times 4} = \frac{4}{8}$$ .

$$\frac{4}{8} + \frac{3}{8} = \frac{7}{8}$$ .

First, find a common denominator (24). Convert: $$\frac{1}{12} = \frac{2}{24}$$ and $$\frac{5}{8} = \frac{15}{24}$$ . Then add: $$\frac{2}{24} + \frac{15}{24} = \frac{17}{24}$$ .

To find the total fraction of two different fractions, add them together after converting to a common denominator.

First, find a common denominator (15). Convert: $$\frac{1}{3} = \frac{5}{15}$$ and $$\frac{2}{5} = \frac{6}{15}$$ . Then add: $$\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$$ .