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.

Adding fractions with unlike denominators means you need to find a common denominator before you can combine the fractions. This ensures that the fractions are expressed in terms of the same whole.

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 easily.

The least common multiple (LCM) of 3 and 5 is 15. So, the common denominator for $$\frac{1}{3}$$ and $$\frac{1}{5}$$ is 15.

To convert $$\frac{1}{3}$$ to a fraction with a denominator of 15, multiply the numerator and denominator by 5: $$\frac{1 \times 5}{3 \times 5} = \frac{5}{15}$$ .

To convert $$\frac{1}{5}$$ to a fraction with a denominator of 15, multiply the numerator and denominator by 3: $$\frac{1 \times 3}{5 \times 3} = \frac{3}{15}$$ .

The first step is to convert both fractions to have a common denominator. In this case, convert them to have a denominator of 15.

$$\frac{5}{15} + \frac{3}{15} = \frac{5 + 3}{15} = \frac{8}{15}$$ .

The formula for adding fractions is: $$\frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + b \cdot c}{b \cdot d}$$ , where $$a$$ and $$c$$ are the numerators and $$b$$ and $$d$$ are the denominators.

First, find a common denominator (15). Convert $$\frac{2}{3}$$ to $$\frac{10}{15}$$ and $$\frac{1}{5}$$ to $$\frac{3}{15}$$ . Then, add: $$\frac{10}{15} + \frac{3}{15} = \frac{13}{15}$$ .