The operations with fractions that require common denominators are:
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Addition of Fractions: When adding two or more fractions, you need to have a common denominator to combine the numerators effectively. For example, to add \( \frac{1}{4} + \frac{1}{6} \), you first find a common denominator (in this case, 12), and convert each fraction to an equivalent form before adding.
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Subtraction of Fractions: Similar to addition, when subtracting fractions, a common denominator is necessary. For instance, \( \frac{3}{5} - \frac{1}{3} \) would require a common denominator to perform the subtraction.
In summary, both addition and subtraction of fractions require common denominators to be carried out correctly.