# Unlike fractions

Unlike fractions are fractions that have different denominators. The two fractions below are unlike fractions.

All unlike fractions can be converted into like fractions, which is important because it is a necessary step towards being able to add or subtract fractions. Unlike fractions cannot be directly added or subtracted because they represent different wholes, as in the figure below.

1/2 has 2 parts total while 1/3 has 3 parts total. Adding the numerators and writing it over the denominator of either 1/2 or 1/3 would result in an incorrect solution. We need to instead convert 1/2 and 1/3 to equivalent fractions with the same denominator, such as 3/6 and 2/6, in order to be able to add them:

## Converting unlike fractions to like fractions

To convert unlike fractions to like ones, find a common multiple between the denominators of all the fractions. It does not necessarily have to be the least common multiple (LCM), but using the LCM ensures that the result of any addition or subtraction will already be in simplest form.

The most straightforward way to find a common multiple between the denominators of a set of fractions is to multiply all the denominators. The product will be a common multiple, albeit often it will not be the least common multiple. Then, determine what the denominators of each respective fraction need to be multiplied by to convert the denominator into a common multiple. Multiply each respective numerator by the same number to complete converting them into an equivalent fraction.

Example

Find the sum of 1/3, 5/6, and 7/24.

3 × 6 × 24 = 432

432 is a common multiple of 3, 6, and 24. Next, convert each fraction to an equivalent fraction with a denominator of 432:

Sum the fractions:

Notice that the solution in simplified form has the same denominator as of one of the original fractions. This is because 24 is the least common multiple of 3, 6, and 24. We could have therefore used the denominator 24 and instead added:

This demonstrates the benefit of using the least common multiple of the denominators when adding or subtracting fractions. The process can be slightly more involved, but can be more efficient in certain cases. Refer to the least common multiple page for details on how to find the LCM of a given set of numbers.