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Fractions

Addition

Think 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.

+=
1/6 + 2/6 = 3/6 = 1/2.

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.

Example

Click on the question mark to see the addition step-by-step:

More Examples

Exercise

Practice 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.

+ =
1/4 + 2/3 = 3/12 + 8/12 = 11/12

To add two fractional numbers with different denominators:

• Write each fraction using a common denominator
• Add the "new" fractions

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.

Example

Click on the question mark to see the addition step-by-step:

This is usually presented as

In general,

More Examples

Exercise

Practice 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.

Example

By 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 step-by-step:

Example

Here is another example.

In the sum , the LCM(8,6)=24, and .

Click on the question mark to see this example step-by-step:

Exercise

Now try practicing addition with fractions using this second method:

Addition of signed fractions

So 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.

Examples

If you have difficulty adding positive and negative numbers, try working through adding integers first.

Exercise

Try 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 >>