To add fractions, you must first make the denominators the same. The denominators are the bottom numbers of the fractions. When you add a negative fraction and a positive fraction, you are essentially subtracting one fraction from the other.
- Create a common denominator
First, you must create a common denominator. You find the lowest number that both denominators divide into evenly by multiplying the numbers together. For instance, if the fractions are 1/4 and -2/3, you multiply 4 and 3 together for the new denominator, 12.
- Multiply the numerators by the same number
Next, you multiply the top numbers (the numerators) by the same number as the denominators. For instance, since you multiplied the 4 in 1/4 by 3 to reach 12, you do the same for the top to reach 3/12. On the other hand, you multiplied the 3 in -2/3 by 4 to reach 12, so you do the same for the top and obtain -8/12.
- Add (or subtract) the top numbers
Now, you essentially add the numerators. Because one of them is negative, you subtract its absolute value from the other. Therefore, you subtract 8 from 3 to get -5, making the answer -5/12.
- Simplify if necessary
You may need to reduce the fraction if it's not the smallest it can be. Because -5/12 is already the smallest, it can be left on the top as both the top and bottom cannot be divided by the same number evenly. However, if you had ended up with something like -6/12, both the top and bottom could be divided by 6, leaving you with -1/2.