Operations with Fractions

Addition/Subtraction of Fractions The first rule of addition/subtraction of fractions is that the fractions must have a common denominator. When fractions have the same denominator, simply add (or subtract) the numerators and place the sum (or difference) over the common denominator.


To combine fractions with unlike denominators, it is necessary to convert all fractions to like denominators; therefore, a common denominator must be found. The LCD or least common denominator is the smallest common multiple that the numbers in question have in common.

For example, consider adding the following two fractions whose LCD = 12.


Convert the first fraction to an equivalent fraction with a denominator of 12 by multiplying both the numerator and denominator of the first fraction by three:


Now, convert the second fraction to an equivalent fraction with a denominator of 12 by multiplying both the numerator and denominator of the second fraction by four:


Now proceed as above adding the numerators and placing the sum over the common denominator.

                    is equivalent to        

The process for subtracting fractions is the same as that of adding them (1) find a common denominator, (2) change each fraction to an equivalent fraction with the chosen common denominator, (3) subtract the numerators, (4) place this difference over the common denominator:


Mulitplication/Division of Fractions To multiply fractions, multiply the numerators and multiply the denominators and reduce the fraction.


To divide fractions (1) maintain the first fraction as is, (2) change the operation to multiplication and (3) reciprocate (“flip-over”) the second fraction. Now proceed as above for the multiplication of fractions.  For example:


Improper Fraction to Mixed NumberAn improper fraction is a fraction whose numerator is larger than it's denominator, such as . To change an improper fraction to a mixed number (a number with a whole part and a fraction) divide the denominator into the numerator: .

To change a mixed number to an improper fraction, multiply the whole part and the denominator and then add the numerator. This number will be the new numerator to the improper fraction whose denominator will be that of the fraction in the original whole number: .

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 28-Jan-2013