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 the fractions easily.

To find a common denominator for $$\frac{1}{3}$$ and $$\frac{1}{5}$$ , you can multiply the denominators together. The common denominator is 15.

The first step is to find the common denominator, which is 15. Then, convert each fraction to an equivalent fraction with the common denominator.

$$\frac{1}{3} = \frac{5}{15}$$ (Multiply both the numerator and denominator by 5).

$$\frac{1}{5} = \frac{3}{15}$$ (Multiply both the numerator and denominator by 3).

The next step is to add the numerators while keeping the common denominator. So, $$\frac{5}{15} + \frac{3}{15} = \frac{8}{15}$$ .

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

Simplifying fractions makes them easier to understand and work with. It helps to express the fraction in its simplest form.