1. The problem is to understand what happens when the denominators in fractions are not the same. 2. When adding or subtracting fractions, the denominators must be the same to combine them directly. 3. If denominators differ, find the least common denominator (LCD), which is the least common multiple of the denominators. 4. Convert each fraction to an equivalent fraction with the LCD as the new denominator by multiplying numerator and denominator by the necessary factor. 5. For example, to add $\frac{a}{b}$ and $\frac{c}{d}$ where $b \neq d$, find LCD $= \text{lcm}(b,d)$. 6. Then rewrite fractions as $\frac{a \times \frac{\text{LCD}}{b}}{\text{LCD}}$ and $\frac{c \times \frac{\text{LCD}}{d}}{\text{LCD}}$. 7. Now add numerators: $$\frac{a \times \frac{\text{LCD}}{b} + c \times \frac{\text{LCD}}{d}}{\text{LCD}}$$. 8. This process ensures denominators are the same, allowing addition or subtraction. 9. Always simplify the resulting fraction if possible by dividing numerator and denominator by their greatest common divisor (GCD).