Adding and Subtracting Fractions

You can always add or subtract fractions using common denominators. To find common denominators, you need to first nd the least common multiple of all the denominators involved. This can be sometimes be difficult. There is an easier method for adding or subtracting fractions without finding a common denominator.

Adding Fractions using Cross Multiplication

Cross multiplication refers to the multiplication of the numerator from one fraction and the denominator of another. The following example is worked using cross multiplication.

Example:

Here is how cross multiplication works: You multiply 1 × 7 and 6 × 3 then add these two products together. The new denominator for the sum is the product 6 × 7.

Therefore, .

There are some problems where it might be easier for you to use common denominators, like , however, in general, you will save time using the cross multiplication method. If the least common denominator of the two fractions is not the product of the two denominators, then you are going to have to reduce the fraction when you are finished. Be prepared for that situation by not writing anything down until you finish the entire problem. However, when the two denominators differ by only one, the least common denominator for those two fractions is going to be the product of the two denominators. Using algebraic notation, the cross multiplication method for addition is

Subtracting Fractions using Cross Multiplication

The method is virtually the same with subtracting fractions. The only change is that instead of adding, you now subtract the two products. In this case, the order does matter.

Example:

Use cross multiplication and subtract (3 × 9)-(4 × 2) from the numerator.

Thus, .

Using algebraic notation, the cross multiplication method for subtraction is