Adding Fractions

Adding Fractions with the Same Denominator (Like Denominators)

There are 3 Simple Steps to add fractions:

1- Make sure the bottom numbers (the denominators) are the same

2- Add the top numbers (the numerators). Put the answer over the same denominator.

3- Simplify the fraction (if needed).


Example 1:  Add the fractions

The denominators are the same, so you can skip step 1. The denominator of the answer will be 7.

Add the numerators for the numerator in the answer. 3 + 2 = 5. The answer is.

This answer is already reduced, so you can skip step 3.

All you have to do is to add the numerators.
And it is always a good idea to make your result "nice" by converting it to a mixed number and simplifying if possible.


Example 2:  Add the fractions and reduce your answer.

Adding Fractions with Different Denominators (Unlike Denominators)

1- Find the Least Common Denominator (LCD) of the fractions
2- Rename the fractions to have the LCD
3- Add the numerators of the fractions
4- Simplify the Fraction (if needed).

Example 1: Add the fractions

The denominators are different, so you must build each fraction to a form where they both have the same denominator.
Since both 5 and 15 will divide evenly into 15, build both fractions to a denominator of 15.

Build the fraction 3 / 5 to an equivalent fraction whose denominator is 15.

Add the numerators to get the numerator in the answer.

This answer is already reduced, so you can skip step 4.


Example 2 : Add the fractions and reduce your answer.

The denominators are different, so you must build each fraction to a form where they both have the same denominator. Rewrite the problem with both denominators factored.

The common denominator will have to have factors 2, 5, and 7. Build each fraction so that each denominators has these three factors.

Simplify the answer.


Adding Mixed Numbers with the same Denominator

How to add two mixed numbers whose fractions have the same denominator:
- Add the numerators of the two fractions - Place that sum over the common denominator.
- If this fraction is improper (numerator larger than or equal to the denominator) then convert it to a mixed number
- Add the integer portions of the two mixed numbers
- If adding the fractional parts created a mixed number then add its integer portion to the sum.

Example 1:  4 2/5 + 7 4/5= ?

Example 2 :  Add the fractions 3 4/7 + 5 6/7= ?

- Add the fractional part of the mixed numbers
- Convert 10/7 to a mixed number
- Add the integer portions of the mixed numbers
- Add the integer from the sum of the fractions