How Do You Find the Sum or Difference of Fractions?

The Washington Post/Getty Images/The Washington Post/Getty Images

To find the sum or difference of fractions, first find the lowest common denominator (LCD) of each fractions. Once you find the LCD, add or subtract the numerators to discover your answer.

  1. Find the LCD

    When the fractions have the same denominator, or bottom number, continue on to solve the problem. When the fractions have different denominators, convert them to equivalent fractions using the LCD rule. To find the LCD, calculate the least common multiple of all of the denominators. For example, you are given two-thirds and four-sixths. The least common multiple is six. Convert two-thirds to an equivalent fraction by multiplying the numerator and the denominator by two. The equivalent fraction is four-sixths.

  2. Find the sum

    Perform addition to find the sum of two or more fractions. When the denominators are the same, add the numerators, or top numbers, to calculate the answer. The denominator doesn’t change. For example, two-thirds plus four-thirds equals six-thirds.

  3. Find the difference

    Subtract the smaller fraction from the larger fraction to calculate the difference. When the denominators are the same, subtract the smallest numerator from the largest. Write the answer over the original denominator for the correct answer. For example, five-eighths minus three-eighths equals two-eighths.