# Addition and Subtraction of Mixed Numbers

🏆Practice addition and subtraction of mixed numbers

#### To add and subtract mixed numbers, we will proceed in 3 steps.

The first step:

We will convert the mixed numbers into equivalent fractions - fractions with numerator and denominator without whole numbers.

The second step:

Find a common denominator (usually by multiplying the denominators).

The third step:

We will only add or subtract the numerators. The denominator will be written once in the final result.

## Test yourself on addition and subtraction of mixed numbers!

$$5\frac{2}{5}+2\frac{1}{5}=$$

## Addition and Subtraction of Mixed Numbers

In this article, we will learn how to add and subtract mixed numbers easily, quickly, and effortlessly.

The solution to add and subtract mixed numbers consists of 3 steps:

### The first step

Convert the mixed number into an equivalent fraction, a fraction with only a numerator and denominator without whole numbers.

How do you convert a mixed number into an equivalent fraction?

Multiply the whole number by the denominator. To the result, you will add the numerator. The final result will be recorded in the new numerator.

The denominator will remain the same.

#### Let's look at an example

Convert the mixed number $3 \frac {4}{5}$ into an equivalent fraction

Solution:

Find the numerator:

We will multiply the whole number: $3$ by the denominator $5$ and then add the numerator $4$. We will obtain:

$3\times 5+4=19$

We obtained $19$ and therefore this is what is written in the numerator.

The denominator will remain the same as the original: $5$.

Therefore, we will obtain that:

$3 \frac {19}{5}= \frac {4}{5}$

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### The second step

Find a common denominator (usually by multiplying the denominators)

Reminder:

Using the method of multiplying the denominators, we multiply the first fraction by the denominator of the second fraction and the second fraction by the denominator of the first fraction.

Remember to multiply both the numerator and the denominator.

##### For example

Find a common denominator for the fractions: $3 \over 4$ and $2 \over 5$

Solution:

We multiply the fraction $3 \over 4$ by $5$ the denominator of the second fraction and obtain $15 \over 20$

We multiply the fraction $2 \over 5$ by $4$ the denominator of the first fraction and obtain: $8 \over 20$

The common denominator is $20$.

### The third step

Sum or subtract numerators only. The denominator will remain the same and will be written once in the final result.

#### For example

$\frac {3}{13}+\frac {9}{13}=\frac {12}{13}$

Solution:

When the denominator is identical, we will only add the numerators and obtain: $\frac {12}{13}$

Do you know what the answer is?

## Exercises on Addition and Subtraction of Mixed Numbers

Now, after having learned all the steps for the solution, we will practice exercises on adding and subtracting mixed numbers:

### Exercise 1 (addition and subtraction of mixed numbers)

$2 \frac {3}{4}+1 \frac {2}{6}=$

Solution:

## Step 1

Let's convert the two mixed numbers in the exercise into equivalent fractions:

$2 \frac {3}{4}= \frac {2 \times 4+3}{4}=\frac {11}{4}$

$1 \frac {2}{6}= \frac {6 \times 1+2}{6}=\frac {8}{6}$

Let's write the exercise again:

$\frac{11}{4}+\frac{8}{6}=$

#### Step 2

We find a common denominator by multiplying the denominators and we obtain:
$\frac {66}{24}+\frac {32}{24}=$

#### Step 3

We will only add the numerators and obtain:

$\frac {66}{24}+\frac {32}{24}= ​​\frac {98}{24}$

### Another exercise on adding and subtracting mixed numbers

$4 \frac {1}{5}-2 \frac {4}{5}=$

Solution:

#### Step 1

Convert the two numbers into equivalent fractions:

$4 \frac {3}{6}= \frac {4 \times 6+3}{6}=\frac {27}{6}$

$2 \frac {1}{5}= \frac {2 \times 5+1}{5}=\frac {11}{5}$

Let's write the exercise again:

$\frac{27}{6}-\frac{11}{5}=$

#### Step 2

We find a common denominator by multiplying the denominators and we get:

$\frac{135}{30}-\frac{66}{30}=$

#### Step 3

We will only subtract the numerators and obtain:

$\frac {135}{30}-\frac {66}{30}=\frac {69}{30}$

## Examples and exercises with solutions for addition and subtraction of mixed numbers

### Exercise #1

$\frac{6}{7}x+\frac{8}{7}x+3\frac{2}{3}x=$

### Step-by-Step Solution

Let's solve the exercise from left to right.

We will combine the left expression in the following way:

$\frac{6+8}{7}x=\frac{14}{7}x=2x$

Now we get:

$2x+3\frac{2}{3}x=5\frac{2}{3}x$

$5\frac{2}{3}x$

### Exercise #2

$5\frac{2}{5}+2\frac{1}{5}=$

### Video Solution

$7\frac{3}{5}$

### Exercise #3

$6\frac{2}{6}+1\frac{2}{6}=$

### Video Solution

$7\frac{4}{6}$

### Exercise #4

$2\frac{1}{3}-1\frac{2}{3}=$

### Video Solution

$\frac{2}{3}$

### Exercise #5

$10\frac{1}{2}-\frac{1}{2}=$

### Video Solution

$10$