Adding and subtracting fractions

Description

To add or subtract fractions, the denominators must be the same. If they are not, find the lowest common denominator (LCD) first.

Same denominators: $$\frac{3}{7} + \frac{2}{7} = \frac{5}{7}$$

Different denominators — find LCD: $$\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$$

Method:

1. Find the LCM of the denominators
2. Convert each fraction to an equivalent fraction with that denominator
3. Add or subtract the numerators
4. Simplify the result

Mixed numbers: convert to improper fractions first, or work with integer and fractional parts separately. $$2\frac{1}{3} + 1\frac{3}{4} = \frac{7}{3} + \frac{7}{4} = \frac{28}{12} + \frac{21}{12} = \frac{49}{12} = 4\frac{1}{12}$$

Common error: adding both numerators and both denominators (e.g. $\frac{1}{3} + \frac{1}{4} = \frac{2}{7}$ — this is wrong).

Links

Equivalent fractions Lowest Common Multiple Simplifying fractions