


FractionsAdditionThink for a moment about a pie divided into 6 equal pieces. Each piece is 1/6. To add up how much pie we have we can simply add the number of pieces. += To add two fractional numbers with the same denominator, we simply add the numerators and keep the same denominator:.
The result is called the sum of the two fractions. ExampleClick on the question mark to see the addition stepbystep:
ExercisePractice adding fractions with the same denominators:
If the pieces of the pie are of different sizes, we have to cut our pie into smaller equal sized pieces so we can add them up. Consider having one piece that is 1/4 and another that is 2/3. We can divide each piece into 1/12 sized pieces. Then they are easy to add up. + = To add two fractional numbers with different denominators:
We illustrate how to add two fractional numbers using two different methods. Method 1: Use the product of the two denominators as a common denominator. ExampleClick on the question mark to see the addition stepbystep: This is usually presented as In general,
ExercisePractice adding fractions with different denominators. No need to reduce your answer at this stage. Method 2: Use the LCM of the denominators as a common denominator. This method is preferred to Method 1 as, in general, the final solution is further reduced than the solution using Method 1. ExampleBy using method 1 we can do the following: However, the result can be reduced as 2 divides evenly into both the numerator and the denominator: Note that the reduced denominator 12 is the LCM of 4 and 6 (the denominators of the two original fractions added). To solve the above problem using Method 2: First note that 12 is the LCM of 4 and 6. Also, . Click on the question marks to see the rest of the solution stepbystep:
ExampleHere is another example. In the sum , the LCM(8,6)=24, and . Click on the question mark to see this example stepbystep: ExerciseNow try practicing addition with fractions using this second method: Addition of signed fractionsSo far we have dealt only with positive fractions. Now you can extend the method to positive and negative fractions. Carry the sign with the numerator. The method is just the same, except now you may need to add negative or positive numerators. ExamplesIf you have difficulty adding positive and negative numbers, try working through adding integers first. ExerciseTry some of these exercises. If you are not sure, just get an exercise and immediately check the answer to see another completed example. << Division  Fractions Index  Subtract Fractions >>
