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, $$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$ .

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

A mixed number is a whole number combined with a fraction. For example, $$2 \frac{1}{3}$$ is a mixed number, where 2 is the whole number and $$\frac{1}{3}$$ is the fraction.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, $$2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$$ .

The first step is to find a common denominator. This is a number that both denominators can divide into evenly.

The least common multiple (LCM) of 4 and 6 is 12. So, the common denominator is 12.

Convert both fractions to have the common denominator of 12: $$\frac{1}{4} = \frac{3}{12}$$ and $$\frac{1}{6} = \frac{2}{12}$$ . Then add: $$\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$$ .

First, convert $$\frac{1}{3}$$ to have a common denominator with $$\frac{5}{9}$$ . The common denominator is 9: $$\frac{1}{3} = \frac{3}{9}$$ . Then subtract: $$\frac{5}{9} - \frac{3}{9} = \frac{2}{9}$$ .

Convert mixed numbers to improper fractions: $$3 \frac{1}{2} = \frac{7}{2}$$ and $$2 \frac{1}{2} = \frac{5}{2}$$ . Then add: $$\frac{7}{2} + \frac{5}{2} = \frac{12}{2} = 6$$ .