Adding and Subtracting Fractions

A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number).

To add fractions with the same denominator, keep the denominator the same and add the numerators. For example, $$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$ .

To add fractions with different denominators, find a common denominator, convert the fractions, and then add the numerators. For example, $$\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$ .

A mixed number is a whole number combined with a fraction, such as $$1 \frac{1}{2}$$ .

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator.

$$\frac{5}{6} + \frac{1}{3} = \frac{7}{6} = 1 \frac{1}{6}$$ .

$$\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$$ .

The least common denominator (LCD) is the smallest multiple that two or more denominators share.

To subtract fractions with different denominators, find a common denominator, convert the fractions, and then subtract the numerators.

An equivalent fraction is a fraction that represents the same value as another fraction, such as $$\frac{1}{2}$$ and $$\frac{2}{4}$$ .