Which of the following is a necessary condition for adding or subtracting mixed fractions?

When adding or subtracting mixed fractions, the primary requirement is that the denominators must be the same. This is because fractions represent parts of a whole, and consistent denominators ensure that the parts being added or subtracted are comparable. When the denominators are identical, it is straightforward to combine the numerators while keeping the common denominator intact.

For example, when adding ( \frac{2}{3} ) and ( \frac{1}{3} ), both fractions share the denominator of 3. Thus, they can be easily added to yield ( \frac{3}{3} ).

Having different denominators complicates the process, necessitating a conversion to a common denominator before performing any operations, which is not a necessary condition. The requirement that fractions be in lowest terms (as stated in one of the options) is not essential for addition or subtraction; fractions can be simplified after performing the operation. Lastly, the numerators do not need to be the same, as different numerators can still be combined as long as the denominators align. Thus, the necessity for equal denominators is crucial for effective addition or subtraction of mixed fractions.