Addition and Subtraction of Mixed Numbers

πŸ†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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\( 2\frac{1}{3}-1\frac{2}{3}= \)

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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:

3Γ—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=2Γ—4+34=1142 \frac {3}{4}= \frac {2 \times 4+3}{4}=\frac {11}{4}

126=6Γ—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

415βˆ’245=4 \frac {1}{5}-2 \frac {4}{5}=

Solution:

Step 1

Convert the two numbers into equivalent fractions:

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

215=2Γ—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

276βˆ’115= \frac{27}{6}-\frac{11}{5}=

Step 2

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

13530βˆ’6630=\frac{135}{30}-\frac{66}{30}=

Step 3

We will only subtract the numerators and obtain:

13530βˆ’6630=6930\frac {135}{30}-\frac {66}{30}=\frac {69}{30}


Do you think you will be able to solve it?
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