1. The problem asks: Why do you need common denominators when you add and subtract fractions? 2. When adding or subtracting fractions, the denominators (bottom numbers) must be the same because fractions represent parts of a whole divided into equal pieces. 3. If denominators are different, the fractions represent parts of wholes divided into different numbers of pieces, so you cannot directly add or subtract them. 4. To add or subtract fractions, you find a common denominator, usually the least common multiple (LCM) of the denominators. 5. Then, convert each fraction to an equivalent fraction with the common denominator by multiplying numerator and denominator by the same number. 6. After that, you can add or subtract the numerators while keeping the denominator the same. 7. For example, to add $\frac{2}{5}$ and $\frac{1}{6}$, find the LCM of 5 and 6, which is 30. 8. Convert $\frac{2}{5}$ to $\frac{2 \times 6}{5 \times 6} = \frac{12}{30}$ and $\frac{1}{6}$ to $\frac{1 \times 5}{6 \times 5} = \frac{5}{30}$. 9. Now add: $\frac{12}{30} + \frac{5}{30} = \frac{12 + 5}{30} = \frac{17}{30}$. 10. This shows why common denominators are necessary: to combine fractions correctly by ensuring they refer to the same sized parts.