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 $$\frac{3}{4}$$ , 3 is the numerator and 4 is the denominator.

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

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.

The least common denominator (LCD) is the smallest multiple that two or more denominators share. For example, the LCD of 4 and 6 is 12.

To convert $$\frac{1}{4}$$ to a fraction with a denominator of 16, multiply both the numerator and denominator by 4: $$\frac{1 \times 4}{4 \times 4} = \frac{4}{16}$$ .

First, convert $$\frac{1}{4}$$ to $$\frac{4}{16}$$ . Then, add: $$\frac{7}{16} + \frac{4}{16} = \frac{11}{16}$$ .

To find the sum of two fractions, ensure they have the same denominator, add the numerators, and keep the denominator the same. Simplify if necessary.

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

First, find the LCD, which is 15. Convert the fractions: $$\frac{1}{3} = \frac{5}{15}$$ and $$\frac{2}{5} = \frac{6}{15}$$ . Then, add: $$\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$$ .

Find the LCD, which is 8. Convert $$\frac{1}{2}$$ to $$\frac{4}{8}$$ . Then, add: $$\frac{4}{8} + \frac{3}{8} = \frac{7}{8}$$ .