\( \frac{1}{4}, \frac{2}{3} \) common denominator:

To find a common denominator for the fractions \( \frac{1}{4} \) and \( \frac{2}{3} \), we need to determine the least common multiple (LCM) of the denominators 4 and 3. 1. **Identify the denominators**: The denominators are 4 and 3. 2. **Find the LCM**: - The multiples of 4 are: 4, 8, 12, 16, 20, ... - The multiples of 3 are: 3, 6, 9, 12, 15, ... - The smallest common multiple is 12. Thus, the least common denominator (LCD) is 12. Now, we can convert each fraction to have this common denominator: - For \( \frac{1}{4} \): \[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \] - For \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \] Therefore, the fractions with a common denominator of 12 are \( \frac{3}{12} \) and \( \frac{8}{12} \).