Which of these operations cannot be performed directly on fractions without a common denominator?

The operation that cannot be performed directly on fractions without a common denominator is addition. When adding fractions, it is essential to have a common denominator so that the slices of the whole being represented can be combined accurately. Without a common denominator, the fractions may represent different-sized parts of a whole, making it impossible to simply combine them.

For example, if you were to add 1/4 and 1/3, you cannot simply add the numerators and the denominators directly. Instead, you need to find a common denominator, which in this case would be 12, and then convert each fraction accordingly before performing the addition.

In contrast, multiplication and division can be performed directly on fractions without the need for a common denominator. When multiplying fractions, you simply multiply the numerators and the denominators together. For division, you multiply by the reciprocal of the second fraction, also without needing a common denominator.