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 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.


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

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

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

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)


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

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)


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

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

Just add the fractions

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.


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

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

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

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)


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

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)


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

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

Just add the fractions

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


Quiz about adding mixed numbers

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