How Do You Add Fractions?
The answer to that question depends on whether you are adding fractions with like denominators or adding fractions with unlike denominators.
Adding Fractions with Like Denominators
Adding fractions with like denominators is easy. All you do is add the numerators together and keep the denominator the same, like this:
| Adding with Like Denominators | ||||||
| 1 | + | 2 | = | 3 | ||
| 5 | 5 | 5 | ||||
Adding Fractions with Unlike Denominators
Adding fractions with unlike denominators requires a little more work (unless you use the calculator on this page), because in order to add the fractions you must first turn their unlike denominators into like denominators. You do that by finding the lowest common multiple (LCM) of the denominators.
To illustrate how you use LCM to turn unlike denominators into like denominators, let's suppose you want to add the fraction 1/3 to the fraction 2/5.
The first step is to find the lowest number that both 3 and 5 will divide into evenly (the LCM). According to my calculations, the LCM of the two denominators (3 & 5) is 15.
Once we have found the LCM for the two denominators, the next step is to multiply the top and bottom of each fraction by the number of times each fraction's denominator goes into the LCM.
Since 3 goes into 15 a total of 5 times, you would multiply the top and bottom of 1/3 by 5, which results in 5/15.
Next, since 5 goes into 15 a total of 3 times, you would multiply the top and bottom of 2/5 by 3, which results in 6/15.
Finally, since both denominators are now the same, you simply add the numerators (5 + 6) while keeping the denominator (15) the same -- giving you a result of 11/15. Here is how our example of adding fractions with unlike denominators might appear on paper:
| Adding with Unlike Denominators | ||||||||||
| 1x 5 | + | 2x 3 | = | 5 | + | 6 | = | 11 | ||
| 3x 5 | 5x 3 | 15 | 15 | 15 | ||||||
What About the Steps to Subtract Fractions?
The steps to subtract fractions are the same as the steps to add fractions.
If you are subtracting fractions with like denominators, you simply subtract the second numerator from the first numerator and keep the denominator the same.
| Subtracting with Like Denominators | ||||||
| 2 | - | 1 | = | 1 | ||
| 5 | 5 | 5 | ||||
If you are subtracting fractions with unlike denominators, you go through the same process as when adding fractions with unlike denominators.
| Subtracting with Unlike Denominators | ||||||||||
| 2x 5 | - | 1x 3 | = | 10 | - | 3 | = | 7 | ||
| 3x 5 | 5x 3 | 15 | 15 | 15 | ||||||
So for like denominators you simply add or subtract the numerators, and for unlike denominators you multiply the top and bottom by the least common multiple of each denominator, and then add or subtract the numerators.
Happy adding and subtracting!