Adding and Subtracting Fractions

A fraction represents a part of a whole and 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.

To add fractions with the same denominator, keep the denominator the same and add the numerators. For example, $$\frac{2}{5} + \frac{1}{5} = \frac{2+1}{5} = \frac{3}{5}$$ .

To subtract fractions with the same denominator, keep the denominator the same and subtract the numerators. For example, $$\frac{5}{9} - \frac{3}{9} = \frac{5-3}{9} = \frac{2}{9}$$ .

A common denominator is a shared multiple of the denominators of two or more fractions. It is used to add or subtract fractions with different denominators.

The least common denominator (LCD) of $$\frac{1}{3}$$ and $$\frac{1}{4}$$ is 12. You can convert the fractions to $$\frac{4}{12}$$ and $$\frac{3}{12}$$ .

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as $$\frac{7}{4}$$ .

To convert an improper fraction to a mixed number, divide the numerator by the denominator. For example, $$\frac{7}{4}$$ becomes 1 $$\frac{3}{4}$$ .

A mixed number is a whole number combined with a proper fraction, such as 1 $$\frac{3}{4}$$ .

To add fractions with different denominators, first find a common denominator, convert the fractions, and then add the numerators. For example, $$\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$$ .

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