Find the lowest common denominator if the problem involves two fractions with different denominators. The lowest common multiple is the smallest whole number that is divisible by each multiple. For example, the common denominator of 1/2 and 1/4 would be 4 because 4 divided by 4 is 1 and 4 divided by 2 is 2.
Write out a list of multiples of each denominator to find the lowest common denominator. This is not the only way to find the lowest common denominator, but is perhaps the easiest. For instance, if the problem involves adding or subtracting three fractions with different denominations, write out the multiples in three separate rows. Now look for the lowest number each row has in common.
Factor each of the denominators into prime numbers. For example, if we have 1/4 plus 1/6, the prime factorization would be 2 x2 and 2 x3. Now take the largest number of each factorization. In the example, the two largest numbers for each fraction are 2 and 3, respectively. Now multiply the two largest prime numbers to get the lowest common denominator.
Rewrite an equation into a fraction with the same denominators. Once you have found the least common denominator, you can replace each denominator with that number. Start by dividing the lowest common denominator by the denominator of the original fraction, then multiply by the numerator to get the new numerator of each fraction. The equation looks like: (LCD/Denominator) x Numerator. Keep the lowest common denominator as the denominator of each fraction. Now we can simply add the numerators while keeping the lowest common denominator constant.
Reduce the fraction to a mixed number if the answer to the equation is an improper fraction. An improper fraction is a fraction that has a larger numerator than the denominator. Start by reducing the fraction if it can be reduced. For example, 8/6 can be reduced to 4/3. Now we can rewrite the fraction as a whole number by subtracting the denominator by the numerator and using the remainder as the whole number. In this example, we could rewrite 4/3 as 1 and 1/3.