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How to Add Fractions
The numerator of a fraction tells us the number of parts of the whole that we have. It is written above the line in a fraction. The denominator of a fraction tells us the total number of equal parts that something has been divided into. It is written below the line in a fraction.
In order to add fractions together, the fractions need to have the same number below the line. We call this a common denominator.
We can add fractions with a common denominator easily because the whole is divided into parts of the same size. For example:
In the above equation, we are adding two quarters to one quarter. Our answer is going to tell us how many quarters we have now. The denominator stays the same since both fractions are shown in quarters and we add 2 plus 1 to find out the numerator. This gives us an answer of 3/4 (three quarters).
As you can see below, the same process applies when adding any improper fractions. Note that many questions will require you to convert an improper fraction answer to a mixed number.
If the fractions have different denominators, it is harder to add them because the parts are not the same size. As you can see in the picture below, 1/3 and 1/4 can be added together, however, the new amount is neither in thirds or quarters. We need to find a common unit for the amounts we're working with.
We can do this by finding the Lowest Common Multiple (LCM) of our denominators. This number will need to be a multiple of both 3 and 4.
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 4: 4, 8, 12, 16, 20
LCM of 3 & 4: 12
Now we multiply each fraction by a fraction equivalent to 1 to get that LCM as the denominator for each fraction. In this case we multiply by 4/4 and 3/3:
4/12 is equivalent to 1/3 and 3/12 is equivalent to 1/4. The difference now is that both of our fractions have the same denominator. With common denominators, we can add the numerators to find out how many parts we have:
4/12 + 3/12 gives us 7/12, which is our answer!
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