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 fraction is
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

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.

Let's us see how this is done with 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

The fraction is
11 / 6

Adding mixed numbers with a couple of good examples is what we show next

Example #1:

 5 1 / 2 +   4 7 / 2

Convert each mixed number by following the steps outlined above

Here is how for 5
1 / 2

Step 1. Multiply the whole number by the denominator of the fraction. (5 × 2 = 10)

Step 2. Add the result of step 1 to the numerator of the fraction (10 + 1 = 11)

The fraction is
11 / 2

Here is how for 4
7 / 2

Step 1. Multiply the whole number by the denominator of the fraction. (4 × 2 = 8)

Step 2. Add the result of step 1 to the numerator of the fraction (8 + 7 = 15)

The fraction is
15 / 2

Now just add the fractions. 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

 11 / 2 +   15 / 2 =   11 + 15 / 2 =   26 / 2

26 / 2
=   13

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 exercise #1 again, just add 5 and 4. We get 9

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

 2 / 3 ×   3 / 3 =   6 / 9

 6 / 9 +   5 / 9 =   6 + 5 / 9 =   11 / 9

Let us put it together. when adding the whole numbers, you got 14

When adding the fractions, you got
11 / 9

You can keep the answer as shown below

14
11 / 9

Notice that 11/9 = 1 + 2/9

As a mixed number, the answer is

15
2 / 9

Otherwise, you can write the answer as a fraction

14 × 9 + 11 = 137

As a fraction, the answer is
137 / 9

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 fraction is a mixed number

In our example, the whole number is 4

The fraction is
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:

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.

Let's us see how this is done with 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

The fraction is
11 / 6

Adding mixed numbers with a couple of good examples is what we show next

Example #1:

 5 1 / 2 +   4 7 / 2

Convert each mixed number by following the steps outlined above

Here is how for 5
1 / 2

Step 1. Multiply the whole number by the denominator of the fraction. (5 × 2 = 10)

Step 2. Add the result of step 1 to the numerator of the fraction (10 + 1 = 11)

The fraction is
11 / 2

Here is how for 4
7 / 2

Step 1. Multiply the whole number by the denominator of the fraction. (4 × 2 = 8)

Step 2. Add the result of step 1 to the numerator of the fraction (8 + 7 = 15)

The fraction is
15 / 2

Now just add the fractions. 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

 11 / 2 +   15 / 2 =   11 + 15 / 2 =   26 / 2

26 / 2
=   13

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 exercise #1 again, just add 5 and 4. We get 9

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

 2 / 3 ×   3 / 3 =   6 / 9

 6 / 9 +   5 / 9 =   6 + 5 / 9 =   11 / 9

Let us put it together. when adding the whole numbers, you got 14

When adding the fractions, you got
11 / 9

You can keep the answer as shown below

14
11 / 9

Notice that 11/9 = 1 + 2/9

As a mixed number, the answer is

15
2 / 9

Otherwise, you can write the answer as a fraction

14 × 9 + 11 = 137

As a fraction, the answer is
137 / 9