# ASVAB Preparation: How to Add and Subtract Fractions

Adding and subtracting fractions for the ASVAB (or for any other purpose) can be as simple as multiplying and dividing them, or it can be more difficult. As the following information shows, it all depends on whether the fractions have the same denominator.

**Adding and subtracting fractions with like denominators**

To add or subtract two fractions with the same denominator, add (or subtract) the numerators and place that sum (or difference) over the common denominator:

Adding and subtracting fractions are set up similarly.

**Adding and subtracting fractions with different denominators**

You can’t add or subtract fractions with different denominators. You have to convert the fractions so they all have the same denominator, and then you perform addition or subtraction.

Converting fractions so they share the same denominator involves finding a *common denominator.* A common denominator is nothing more than a common multiple of all the denominators.

Find a common denominator for the fractions 3/5 and 1/8.

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, and 40.

The multiples of 8 are 8, 16, 24, 32, and 40.

A common denominator for the fractions 3/5 and 1/8 is 40.

The next step in the addition/subtraction process is to convert the fractions so they share the common denominator. In order to do this, divide the original denominator into the new common denominator and then multiply the result by the original numerator.

Start with 3/5. Divide the original denominator (5) into the new common denominator (40): 40 ÷ 5 = 8. Next multiply the result (8) by the original numerator (3): 8 × 3 = 24. The equivalent fraction is 24/40.

Perform the same operation with the second fraction,1/8 . Divide the original denominator (8) into the new common denominator (40): 40 ÷ 8 = 5. Next multiply this (5) by the original numerator (1): 5 × 1 = 5. The equivalent fraction is 5/40.

Now that the fractions have the same denominator, you can add or subtract them: