Question

Can you add or subtract fractions with unlike denominators

Answer 1

Yes, you can add or subtract fractions with unlike denominators by following these steps:

1. **Find a Common Denominator**: Identify the least common multiple (LCM) of the denominators.

2. **Rewrite Each Fraction**: Convert each fraction to an equivalent fraction with the common denominator. To do this, multiply the numerator and denominator of each fraction by the appropriate value so that the denominator becomes the common denominator.

3. **Add or Subtract the Numerators**: Once the fractions have the same denominator, you can add or subtract the numerators while keeping the common denominator.

4. **Simplify if Necessary**: If the resulting fraction can be simplified, reduce it to its lowest terms.

### Example:

**Adding**: \( \frac{1}{3} + \frac{1}{4} \)

1. **Common Denominator**: The LCM of 3 and 4 is 12.
2. **Rewrite Each Fraction**:
- \( \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \)
- \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
3. **Add the Numerators**:
- \( \frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12} \)

**Subtracting**: \( \frac{2}{5} - \frac{1}{10} \)

1. **Common Denominator**: The LCM of 5 and 10 is 10.
2. **Rewrite Each Fraction**:
- \( \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \)
- \( \frac{1}{10} \) stays the same: \( \frac{1}{10} = \frac{1}{10} \)
3. **Subtract the Numerators**:
- \( \frac{4}{10} - \frac{1}{10} = \frac{4 - 1}{10} = \frac{3}{10} \)

This method works for any set of fractions with unlike denominators.