When combining fractions, what must be done to ensure they have a common denominator?

• A. Add the numerators
• B. Multiply the denominators
• C. Find the least common multiple of the denominators
• D. Subtract the fractions

Answer: (C)

To combine fractions, it's essential to have a common denominator so that the fractions can be easily added or subtracted. Finding the least common multiple (LCM) of the denominators is the correct approach for achieving this. The LCM of the denominators provides the smallest number that both denominators can divide into without leaving a remainder, ensuring that the fractions can be expressed in terms of the same base.

Once the least common denominator is identified, each fraction can be adjusted accordingly: the numerator of each fraction is multiplied by whatever factor needed to reach this common denominator. This ensures that the values represented by the fractions remain equivalent while allowing for their combination.

In contrast, simply adding the numerators or multiplying the denominators does not facilitate a meaningful combination of the fractions, as they would still be based on different denominators. Subtracting the fractions without a common denominator would also lead to incorrect results, as it would violate the fundamental principle of fraction operation.