How Do You Add 3 Fractions?
The answer to that question depends on whether you are adding fractions with like denominators or adding fractions with unlike denominators.
Adding 3 Fractions with Like Denominators
Adding 3 fractions with like denominators is easy. All you do is add the numerators together and keep the denominator the same, like this:
| 1 | + | 3 | + | 5 | = | 9 | |
| 10 | 10 | 10 | 10 |
Adding 3 Fractions with Unlike Denominators
Adding 3 fractions with unlike denominators requires a little more work (unless you use the calculator on this page), because in order to add the 3 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 fractions 1/2, 2/3, and 3/4.
The first step is to find the lowest number that 2, 3, and 4 will each divide into evenly (the LCM). According to my calculations, the LCM of the three denominators is 12.
Once we have found the LCM for the three 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. Remember, as long as you multiply the top and bottom of a fraction by the same number, the fraction's decimal value does not change, as in 1/2 = 2/4 = 4/8 and so on -- because all of the latter divide out to 0.5.
Since 2 goes into 12 a total of 6 times, you would multiply the top and bottom of 1/2 by 6, which results in 6/12.
Next, since 3 goes into 12 a total of 4 times, you would multiply the top and bottom of 2/3 by 4, which results in 8/12.
Then, since 4 goes into 12 a total of 3 times, you would multiply the top and bottom of 3/4 by 3, which results in 9/12.
Finally, since all three denominators are now the same, you simply add the numerators (6 + 8 + 9) while keeping the denominator (12) the same -- giving you a result of 23/12. But since 23/12 is an improper fraction, you would convert it to the mixed number 1 and 11/12.
Here is how our example of adding 3 fractions with unlike denominators might appear on paper:
| = | 1x 6 | + | 2x 4 | + | 3x 3 |
| 2x 6 | 3x 4 | 4x 3 |
| = | 6 | + | 8 | + | 9 | = | 23 |
| 12 | 12 | 12 | 12 |
| = | 23 |
| 12 |
| = | 1 | 11 |
| 12 |
The steps to subtract 3 fractions with like or different denominators are the same as the steps to add fractions; you just subtract the numerators while keeping the denominators the same.
Happy adding and subtracting!