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Adding Mixed Numbers and Improper Fractions

Just like whole numbers, fractions can also be added. The difference is that when counting improper fractions and mixed numbers, we are now counting the number wholes and parts.


Let’s work through an example to demonstrate how we add mixed numbers and improper fractions.

The example is: add the fractions

adding mixed numbers and improper fractions

 

 

 

 

 

Step 1: Convert all mixed numbers into improper fraction.

adding mixed numbers and improper fractions

 

 

 

 

adding mixed numbers and improper fractions

 

 

 

 

Step 2: Do you have a common denominator? If not, find a common denominator.


List the multiples of 4:

adding mixed numbers and improper fractions

 

 

 

 

List the multiples of 7:

adding mixed numbers and improper fractions

 

 

 

 

The Lowest Common Multiple (LCM) between 4 and 7 is 28.

Step 3: Create equivalent fractions.


We need to find the number when multiplied to the top and bottom of 11/4 we get the LCM of 28 as the new denominator.

adding mixed numbers and improper fractions

 

 

 

 

 

 

4 x 7 = 28, so we need to multiply the numerator and the denominator by 7.

adding mixed numbers and improper fractions

 

 

 

 

 

 

 

Now, we need to find the number when multiplied to the top and bottom of 8/7 we get the LCM of 28 as the new denominator.

adding mixed numbers and improper fractions

 

 

 

 

 

7 x 4 = 28, so we need to multiply the numerator and the denominator by 4.

adding mixed numbers and improper fractions

 

 

 

 

 

 

Step 4: Add the numerators and keep the denominator the same.

adding mixed numbers and improper fractions

 

 

 

 

 

 

Step 5: Reduce the fraction to a mixed number.

adding mixed numbers and improper fractions

 

 

 

 

 

 

 

For practice, we offer free fractions worksheets on adding and subtracting mixed numbers and fractions in our grade 4 fractions section, our grade 5 fractions section and our grade 6 fractions section.