Adding and subtracting fractions is easy when the denominators are the same. (The denominator is the bottom number in the fraction; the top number is called the numerator.) When fractions have different denominators, there are a few steps you have to follow to find a common denominator so the fractions can be added to or subtracted from each other.
How to Find the Least Common Denominator of Two Fractions
Pick the larger denominator of the two fractions you are adding or subtracting. In the problem 1/3 + 1/2, 3 is the larger denominator of the two fractions.
List the multiples of the larger denominator. A multiple is a number that another number divides into evenly. In our example, multiples of 3 are 3, 6, 9, 12, 15 and so on.
Find multiples for the smaller denominator. The multiples of 2 are 2, 4, 6, 8, 10 and so on.
Choose the smallest multiple that is common to both denominators. Six is a common multiple of both 3 and 2. This is the least common denominator.
How to Add and Subtract Fractions With Different Denominators
Find the least common denominator for both fractions. (See Section 1.) In the example 1/3 + 1/2, 6 is the least common denominator of both fractions.
Rename both fractions using the least common denominator. In the example 1/3 + 1/2, you would write both denominators as a 6.
Change the numerators to make equal fractions. Multiply the top number by the number you multiplied by the denominator to get the least common denominator. In the example, 1/3 + 1/2 becomes 2/6 + 3/6. The fraction 1/3 is multiplied by 2 because 3 x 2 = 6. The fraction 1/2 is multiplied by 3 because 2 x 3 = 6.
Finish the problem by either adding or subtracting. In the example of 2/6 + 3/6, the answer is 5/6.