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.

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\( 5\frac{2}{5}+2\frac{1}{5}= \)

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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 3453 \frac {4}{5} into an equivalent fraction

Solution:

Find the numerator:

We will multiply the whole number: 33 by the denominator 55 and then add the numerator 44. We will obtain:

3×5+4=193\times 5+4=19

We obtained 1919 and therefore this is what is written in the numerator.

The denominator will remain the same as the original: 55.

Therefore, we will obtain that:

3195=453 \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: 343 \over 4 and 252 \over 5

Solution:

We multiply the fraction 343 \over 4 by 55 the denominator of the second fraction and obtain 152015 \over 20

We multiply the fraction 252 \over 5 by 44 the denominator of the first fraction and obtain: 8208 \over 20

The common denominator is 2020.


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

313+913=1213\frac {3}{13}+\frac {9}{13}=\frac {12}{13}

Solution:

When the denominator is identical, we will only add the numerators and obtain: 1213\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)

234+126=2 \frac {3}{4}+1 \frac {2}{6}=

Solution:

Check your understanding

Step 1

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

234=2×4+34=1142 \frac {3}{4}= \frac {2 \times 4+3}{4}=\frac {11}{4}

126=6×1+26=861 \frac {2}{6}= \frac {6 \times 1+2}{6}=\frac {8}{6}

Let's write the exercise again:

3b - Convert the two numbers into equivalent fractions

114+86= \frac{11}{4}+\frac{8}{6}=

Step 2

We find a common denominator by multiplying the denominators and we obtain:
6624+3224=\frac {66}{24}+\frac {32}{24}=

Step 3

We will only add the numerators and obtain:

6624+3224=​​9824\frac {66}{24}+\frac {32}{24}= ​​\frac {98}{24}


Another exercise on adding and subtracting mixed numbers

415245=4 \frac {1}{5}-2 \frac {4}{5}=

Solution:

Step 1

Convert the two numbers into equivalent fractions:

436=4×6+36=2764 \frac {3}{6}= \frac {4 \times 6+3}{6}=\frac {27}{6}

215=2×5+15=1152 \frac {1}{5}= \frac {2 \times 5+1}{5}=\frac {11}{5}

Let's write the exercise again:

3a - Convert the two numbers into equivalent fractions

276115= \frac{27}{6}-\frac{11}{5}=

Step 2

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

135306630=\frac{135}{30}-\frac{66}{30}=

Step 3

We will only subtract the numerators and obtain:

135306630=6930\frac {135}{30}-\frac {66}{30}=\frac {69}{30}


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

Exercise #1

213123= 2\frac{1}{3}-1\frac{2}{3}=

Video Solution

Step-by-Step Solution

To solve the problem 2131232\frac{1}{3} - 1\frac{2}{3}, we'll perform the following steps:

  • Step 1: Subtract the integer parts: 21=12 - 1 = 1.
  • Step 2: Subtract the fractional parts: 1323\frac{1}{3} - \frac{2}{3}.

To calculate 1323\frac{1}{3} - \frac{2}{3}:

Since the fractions have a common denominator, subtract only the numerators:
12=11 - 2 = -1.
Therefore, 1323=13\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}.

Now combine the results:

The subtraction results in 1131 - \frac{1}{3}.

To simplify, note 1=331 = \frac{3}{3}.

Thus, 113=3313=231 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}.

Therefore, the solution to 2131232\frac{1}{3} - 1\frac{2}{3} is 23\frac{2}{3}.

Answer

23 \frac{2}{3}

Exercise #2

525+215= 5\frac{2}{5}+2\frac{1}{5}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Add the whole number parts.
  • Step 2: Add the fractional parts.
  • Step 3: Combine results and simplify if necessary.

Now, let's work through each step:
Step 1: The mixed numbers are 5255\frac{2}{5} and 2152\frac{1}{5}. First, add the whole number parts: 5+2=75 + 2 = 7.
Step 2: Next, add the fractional parts: 25+15=35\frac{2}{5} + \frac{1}{5} = \frac{3}{5}. Since the denominators are the same, just add the numerators.
Step 3: Combine these sums to form the mixed number: 7+35=7357 + \frac{3}{5} = 7\frac{3}{5}.

Therefore, the solution to the problem is 735 7\frac{3}{5} .

Answer

735 7\frac{3}{5}

Exercise #3

101212= 10\frac{1}{2}-\frac{1}{2}=

Video Solution

Step-by-Step Solution

Let's solve the problem step-by-step:

  • Step 1: Identify the parts of the mixed number 1012 10\frac{1}{2} . It consists of the whole number 10 10 and the fraction 12 \frac{1}{2} .

  • Step 2: We'll subtract 12 \frac{1}{2} (the fraction we are given to subtract) from the fraction part of the mixed number:

1212=0 \frac{1}{2} - \frac{1}{2} = 0

Step 3: After performing the subtraction, the fractional part becomes 0 0 .

Step 4: This leaves us with the whole part of the mixed number on its own, which is 10 10 .

Therefore, the solution to the problem is 10 10 .

Answer

10 10

Exercise #4

626+126= 6\frac{2}{6}+1\frac{2}{6}=

Video Solution

Step-by-Step Solution

To solve this problem, we will add the mixed numbers 626 6\frac{2}{6} and 126 1\frac{2}{6} by following these steps:

  • Step 1: Add the integer parts: 6+1=7 6 + 1 = 7 .
  • Step 2: Add the fractional parts: 26+26=46\frac{2}{6} + \frac{2}{6} = \frac{4}{6}.
  • Step 3: Combine the results to express the sum: 7+46 7 + \frac{4}{6} .

Now, let's work through each step:
Step 1: Adding the whole numbers, we get 7 7 .
Step 2: Since both fractions have a common denominator of 6, we add the numerators: 2+2=4 2 + 2 = 4 , thus giving us the fraction 46\frac{4}{6}.
Step 3: The combined sum of the whole number and the fraction is 746 7\frac{4}{6} .

Hence, the solution to the problem is 746 7\frac{4}{6} .

Answer

746 7\frac{4}{6}

Exercise #5

225+225= 2\frac{2}{5}+2\frac{2}{5}=

Video Solution

Step-by-Step Solution

To solve the problem 225+225 2\frac{2}{5} + 2\frac{2}{5} , follow these steps:

  • Step 1: Add the whole numbers together. We have 2+2=42 + 2 = 4.
  • Step 2: Add the fractional parts together. Since both fractions have the same denominator, simply add the numerators: 25+25=45\frac{2}{5} + \frac{2}{5} = \frac{4}{5}.
  • Step 3: Combine the results from Step 1 and Step 2. The sum of the whole numbers and fraction parts is 4+45=4454 + \frac{4}{5} = 4\frac{4}{5}.

Thus, the sum of 225 2\frac{2}{5} and 225 2\frac{2}{5} is 445\mathbf{4\frac{4}{5}}.

The answer corresponds to choice 4.

Answer

445 4\frac{4}{5}

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