Adding Mixed Numbers and Fractions
Although reducing an improper fraction is a useful skill, you are going to see improper fractions more often when you need to add and subtract fractions with mixed numbers. For this example, we are going to add two mixed numbers together and then reduce an improper fraction to get our final answer. This example may help you understand the concept of what an improper fraction is and how it applies to real problems in mathematics.
For our example, we are going to use the problem 3 2/3 + 5 2/3. This is an easier problem to work with because the denominators are the same, which eliminates the need to reduce the fraction to lowest terms. First, add the numerators on both fractions together and place the number over the current denominator. 2/3 + 2/4 = 4/3. We now have an improper fraction.
Convert the improper fraction to a mixed number by dividing 3 by 4. 3 goes into 4 one time. Write down the 1, which is the number part of the new mixed fraction.
Take 4, which is the numerator and subtract 3, since 3 went into 4 once. We have 1 left. Place the 1 over the denominator, which is 3 to get 1/3. Our total is 1 1/3.
Complete the problem by adding the three whole numbers together; the 3 from 3 2/3, 5 from 5 2/3, and the 1 from 4/3 to get a final answer of 9 1/3.
For more information on fractions, read these basic fraction rules.