Fractions are representations of parts of a larger whole. They are divided into two parts, the denominator and the numerator. The denominator sits on the bottom and represents how many pieces there are in total. For example, a whole pizza may be cut into eight pieces, so a fraction of that pizza would have eight as the denominator. The numerator, which sits on top, represents how many pieces you are dealing with. For example, if you want to represent how many pieces of pizza you eat with a fraction, you would place that number on top of the total number of pieces there were to begin with. If you ate two pieces out of eight, the fraction will look like this: 2/8.
Denominators must match before fractions can be added. To make different denominators match, find the smallest number that can be evenly divided by the two different denominators. This will be your new, matching denominator. You will need to multiply the respective mismatched denominators to get each to this new number. Afterward, multiply the numerators by the same respective numbers to keep the fractions symmetrical. You can now add the new numerators together and simply move the new denominator to the bottom of your answer.
Sometimes, after you add two fractions together, the numerator will be larger than the denominator. This is called an improper fraction, and occurs when the number of the parts you are dealing with is greater than the number of parts in a whole. For example, if you add five out of eight pieces of one pizza to six pieces of another, you will have more than just one whole pizza. You will need to turn this improper fraction into what is called a mixed number, a whole number beside a fraction. Accomplish this by dividing the numerator by the denominator — fractions are, after all, division problems. The remainder is the numerator of the new fraction in the mixed number, and the denominator stays the same.
After you have added two fractions together, you may need to simplify the sum, or make the numbers in the fraction as small and simple as possible. You accomplish this by finding the greatest common factor of the numerator and denominator. The greatest common factor is the largest number by which both the numerator and denominator can be evenly divided. For instance, if your fraction is 4/12, the largest number both 4 and 12 can be divided by is 4. Complete the division process with both the numerator and denominator, and your fraction is simplified. The fraction 4/12, for example, can be simplified to 1/3 because 4 divided by 4 is 1, and 12 divided by 4 is 3.