Adding mixed numbers 

Adding mixed numbers is the goal of this lesson. We will get you through this with some carefully chosen examples to help you master the topic. A mixed number is any number that has the following format:

4 2 3

Anything that is a combination of a whole number and a proper fraction is a mixed number.

In our example, the whole number is 4.

The fractional part is the fraction you see below.

2 3

When adding mixed numbers, it is not necessary to convert a mixed number into an improper fraction before doing the addition.

In case you want to do it that way anyway, we will show you how to convert a mixed number into an improper fraction.

Follow the guidelines shown below to convert a mixed number into an improper fraction.

Step 1. Multiply the whole number by the denominator of the fraction.

Step 2. Add the result of step 1 to the numerator of the fraction.

Step 3. Your numerator is the answer of step 2. Your denominator stays the same

Let us see how this is done with the following mixed number.

1 5 6

Step 1. Multiply the whole number by the denominator of the fraction.

1 × 6 = 6

Step 2. Add the result of step 1 to the numerator of the fraction.

6 + 5 = 11

Step 3. Your numerator is the answer of step 2. Your denominator stays the same

Therefore, here is the improper fraction.

11 6

Adding mixed numbers by converting the mixed numbers into improper fractions

Example #1:

5 1 2 + 4 7 2

Convert each mixed number by following the steps outlined above. Here is how to convert into improper fractions and adding the fractions afterward.

(5 × 2 + 1) 2 + (4 × 2 + 7) 2


= 11 2 + 15 2


= 11 + 15 2


= 26 2 = 13

Since both fractions have the same denominator we can just do this by adding the numerators together. The denominator stays the same. We don't add denominators when adding fractions!

You could have arrived to the answer by not converting the mixed numbers into fractions first. When adding mixed numbers, you can just add the whole numbers separately and add the fractions separately.

5 1 2 + 4 7 2

Looking at example #1 again, just add 5 and 4. We get 9.

Just add the fractional parts. 

1 2 + 7 2


= 1 + 7 2 = 8 2 = 4

And 9 + 4 = 13. As you can see, it took less time in this case. When adding mixed numbers, I recommend doing this way.

Example #2:

6 2 3 + 8 5 9

Add the whole numbers. 6 + 8 = 14

Add the fractional parts. However, before you do so, make sure both fractions have the same denominator.

2 3 + 5 9


= 2 3 × 3 3 + 5 9


= 6 9 + 5 9


= 6+5 9 = 11 9

Writing the whole number next to the fractional part, the answer is the mixed fraction you see below.

14 11 9

Did you make the following observation?

11 9 = 1 + 2 9
14 11 9 = 14 + 1 + 2 9
= 15 2 9

Quiz about adding mixed numbers

Adding fractions