Adding Fractions with Unlike Denominators

Finding a Common Denominator

To add fractions with different denominators, first find a common denominator — a number both denominators divide into evenly.

$\frac{1}{3} + \frac{1}{4}$

The least common denominator (LCD) of 3 and 4 is 12.

Steps

1. Find the LCD
2. Write equivalent fractions with the LCD
3. Add the numerators
4. Simplify if needed

$\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$

More Examples

$\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}$

$\frac{3}{4} + \frac{5}{6} = \frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12}$

Adding Mixed Numbers

$2\frac{1}{3} + 1\frac{3}{4}$

1. Convert fractions to common denominator: $\frac{1}{3} = \frac{4}{12}$, $\frac{3}{4} = \frac{9}{12}$
2. Add whole numbers: $2 + 1 = 3$
3. Add fractions: $\frac{4}{12} + \frac{9}{12} = \frac{13}{12} = 1\frac{1}{12}$
4. Combine: $3 + 1\frac{1}{12} = 4\frac{1}{12}$

Subtracting with Unlike Denominators

Same process — find LCD, convert, then subtract numerators:

$\frac{5}{6} - \frac{1}{4} = \frac{10}{12} - \frac{3}{12} = \frac{7}{12}$

Finding LCD: List multiples of each denominator until you find a match. For 3: 3, 6, 9, 12... For 4: 4, 8, 12... LCD = 12!