Math: Adding and Subtracting Fractions
With Like Denominators
Fractions with Like Denominators
Adding and subtracting fractions by hand is a very easy process. If the denominators (bottom numbers) of the fractions are the same, then you simply add the numerators (top numbers). This applies to both addition and subtraction, as shown in examples (a) and (b) above.
With Unlike Denominators
Fractions with Unlike Denominators
If you want to add and subtract fractions with different denominators, you will need to follow these steps. Your goal is to make the denominators the same, and the process is commonly referred to as finding the “least common denominator.” In the example above, we see that the denominators are 3 and 6. The easiest way to make them the same is to multiply 3 by 2 so that we end up with 6 as the denominator of the first fraction (thus matching the denominator of the second fraction). However, we also need to multiply the numerator of that fraction by the same number (so that the value of the fraction does not change). In this case, we get 2 multiplied by 2, which becomes 4. We can now simply add our fractions with the denominator of 6, as shown in example #1.
Least Common Denominator - Example 2
In this next example, we will need to multiply both fractions by numbers that will make their denominators the same. The least common denominator divisible by both 8 and 6 is 24. So, we simply multiply each fraction by the number that will make the denominator equal to 24. Remember to multiply BOTH the top and bottom of each fraction (numerator and denominator) by the same number. Follow the steps in example #2. We end up with 34/24 as our solution, which can be reduced (by dividing both numbers by 2) to 17/12.
Least Common Denominator - Subtraction
Our final example shows the same process with subtraction. Once again, we’ll need to multiply both fractions by numbers that will make their denominators the same. In this case, our least common denominator is 36, so we multiply both sides by numbers that will make the denominators equal to 36. Example #3 shows the steps.
Video Example - Subtracting Unlike Fractions
For another example of how to subtract (and add) fractions with unlike denominators, check out the step-by-step video below (by Khan Academy):