Addition and Subtraction
In order to add or subtract fractions they must have the same denominators (Same bottom number)!
Adding fractions with the same denominators
Easy! Add the top, Keep the bottom.
Adding Fractions with different denominators
A little more work…
First you have to get the common denominators!
You have two options:
Option 1: You can multiply the denominators together to get a common denominator.
Common Denominator = 32
Or
Option 2: You can multiply one or both denominators by a number, in order to make both the same.
Common Denominator = 8
In order to keep the fractions equivalent to their original value, you must multiply the numerator of the fraction by the number you multiplied the denominator by.
Whenever you multiply the top and bottom of a fraction by the same number- you are really multiplying it by 1, which doesn’t change its value!
Here is what you would have for each of the previous options:
Option 1:
You would now reduce the answer by dividing the top and bottom by a common factor, in this case by 4.
The final reduced answer would be: 
Option 2:
In this case no reducing is necessary. Notice we ended up with the same answer each time.
Adding and Subtracting Fractions as mixed numbers
Yes, you can add fractions as mixed numbers, but in order to simplify the process you can always change to the improper form and add.(See the getting started page for help changing forms)
Let’s Review
Before you add or subtract fractions you need to have the same denominators- same bottoms!
Very Important!
Remember once the bottoms are the same:
- Add/Subtract the top
- Keep the bottom.
Try these examples:
(Rollover the red rectangle to check your answers.)
For extra practice problems click here!
Or see the Resources Page for additional websites.
Adding and subtracting fractions are a basic skill that we often use in “real life”. In cooking we often want to adjust a recipe to fit the number of people we are cooking for. This can easily be done by doubling a recipe. A recipe often consists of many fractions: a ½ cup of one item a 1/3 of another. By adding 1/3 + 1/3 you have just “doubled” that portion of the recipe.
