To add mixed fractions, the fractions need to be converted to improper fractions with the same denominators. Once added, the sum needs to be converted back to a mixed fraction.
- Convert the mixed fractions into improper fractions
An improper fraction is one where the numerator, or upper number, is larger than the denominator, or lower number. To convert a mixed fraction to an improper fraction, multiply the denominator by the whole number. Then add the numerator. This value becomes the new numerator, with the denominator remaining the same. Do this to all the mixed fractions being added together.
- Convert all improper fractions so that the denominators are equal
In order to add fractions together, the denominators need to be the same. Do this by finding a common multiple of both denominators. Then multiply the denominators and their respective numerators by whatever is needed to achieve that common multiple. As an example, if you have three-halves and five-fourths, a common multiple of the denominators is four. In order to convert three-halves to fourths, multiply both the numerator and denominator by two. This gives you six-fourths. This can now be added to five-fourths.
- Add the improper fractions together
Simply add the numerators together. The denominators stay the same. In the previous example, six-fourths plus five-fourths becomes eleven-fourths.
- Convert the improper fraction to a mixed fraction
Divide the numerator by the denominator. The whole number is part of the final mixed fraction, and the remainder becomes the numerator. The denominator doesn't change. In the previous example, 11 divided by four is two with a remainder of three. So the final answer is 2 3/4.