Summarize:

If the values for all the denominators in the equation are the same, only add or subtract the numerators. Rewrite the equation so the numerators are added or subtracted in parentheses over the denominator. Solve for the numerator and simplify the fraction if you’re able to.  For example, if you wanted to solve 3/5 + 1/5, rewrite the equation as (3+1)/5 = 4/5. If you want to solve 5/6 - 2/6, write it as (5-2)/6 = 3/6. Both the numerator and denominator are divisible by 3, so you can simplify the fraction to 1/2. If you have mixed numbers, remember to change them to improper fractions first. For example, if you want to solve 2 ⅓ + 1 ⅓, change the mixed numbers so the problem reads 7/3 + 4/3. Rewrite the equation like (7 + 4)/3 = 11/3. Then convert it back to a mixed number, which would be 3 ⅔. Many times, you’ll encounter problems where the denominators are different. In order to solve the problem, the denominators need to be the same or else you’ll do your math incorrectly. List the multiples of each denominator until you find one that the numbers have in common. If you still can’t find a common multiple, then multiply the denominators together to find a common multiple.  For example, if you want to solve 1/6 + 2/4, list the multiples of 6 and 4. Multiples of 6: 0, 6, 12, 18… Multiples of 4: 0, 4, 8, 12, 16… The least common multiple of 6 and 4 is 12. Multiply the numerator and denominator of the first fraction in the equation by the multiple needed so the denominator equals the common multiple. Then do the same for the second fraction in the equation with the factor that makes its denominator is the common multiple.  In the example 1/6 + 2/4, multiply the numerator and denominator of 1/6 by 2 to get 2/12. Then multiply both numbers of 2/4 by 3 to equal 6/12. Rewrite the equation as 2/12 + 6/12. Once you have the denominators at the same value, add the numerators together as you normally would to get your result. If you can simplify the fraction, then reduce it to its lowest terms.  For example, rewrite 2/12 +6/12 as (2+6)/12 = 8/12. Simplify your answer by dividing the numerator and denominator by 4 to get a final answer of ⅔.
Add or subtract just the numerators if the denominators are the same. Find a common multiple for the denominators if they’re different. Make equivalent fractions so the denominators are the same. Solve the equation as you normally would.