Addition and Subtraction of Mixed Numbers

๐Ÿ†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:

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

126=6ร—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=โ€‹โ€‹9824\frac {66}{24}+\frac {32}{24}= โ€‹โ€‹\frac {98}{24}


Another exercise on adding and subtracting mixed numbers

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

Solution:

Step 1

Convert the two numbers into equivalent fractions:

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

215=2ร—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

276โˆ’115= \frac{27}{6}-\frac{11}{5}=

Step 2

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

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

Step 3

We will only subtract the numerators and obtain:

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


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

Exercise #1

756+623+13=ย ? 7\frac{5}{6}+6\frac{2}{3}+\frac{1}{3}=\text{ ?}

Video Solution

Step-by-Step Solution

Note that the right-hand side of the addition exercise between the fractions gives a result of a whole number, so we'll start with that:

623+13=7 6\frac{2}{3}+\frac{1}{3}=7

Giving us:

756+7=1456 7\frac{5}{6}+7=14\frac{5}{6}

Answer

1456 14\frac{5}{6}

Exercise #2

67x+87x+323x= \frac{6}{7}x+\frac{8}{7}x+3\frac{2}{3}x=

Video Solution

Step-by-Step Solution

Let's solve the exercise from left to right.

We will combine the left expression in the following way:

6+87x=147x=2x \frac{6+8}{7}x=\frac{14}{7}x=2x

Now we get:

2x+323x=523x 2x+3\frac{2}{3}x=5\frac{2}{3}x

Answer

523x 5\frac{2}{3}x

Exercise #3

13+23+234= \frac{1}{3}+\frac{2}{3}+2\frac{3}{4}=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations in arithmetic, we solve the exercise from left to right.

Let's note that:

13+23=33=1 \frac{1}{3}+\frac{2}{3}=\frac{3}{3}=1

We should obtain the following exercise:

1+234=334 1+2\frac{3}{4}=3\frac{3}{4}

Answer

334 3\frac{3}{4}

Exercise #4

12+312+424= \frac{1}{2}+3\frac{1}{2}+4\frac{2}{4}=

Video Solution

Step-by-Step Solution

According to the order of operations, we will solve the exercise from left to right.

Let's note that in the first addition exercise, we have an addition between two halves that will give us a whole number, so:

12+312=4 \frac{1}{2}+3\frac{1}{2}=4

Now we will get the exercise:

4+424= 4+4\frac{2}{4}=

Let's note that we can simplify the mixed fraction:

24=12 \frac{2}{4}=\frac{1}{2}

Now the exercise we get is:

4+412=812 4+4\frac{1}{2}=8\frac{1}{2}

Answer

812 8\frac{1}{2}

Exercise #5

312โˆ’1316= 3\frac{1}{2}-\frac{\frac{1}{3}}{\frac{1}{6}}=

Video Solution

Step-by-Step Solution

When we have a fraction over a fraction, in this case one-third over one-sixth, we can convert it to a form that might be more familiar to us:

1/3:1/6 1/3 : 1/6

It's important to remember that a fraction is actually another sign of division, so the exercise we have is one-third divided by one-sixth.
When dealing with division of fractions, the easiest method for solving is performing "multiplication by the reciprocal", meaning:

1/3ร—6/1 1/3\times6/1

Multiply numerator by numerator and denominator by denominator and get:

63 \frac{6}{3}

Which when reduced equals

21 \frac{2}{1}

Now let's return to the original exercise, to solve it we need to take the mixed fraction and convert it to an improper fraction,
meaning move the whole numbers back to the numerator.

To do this we'll multiply the whole number by the denominator and add to the numerator

3ร—2=6 3\times2=6

6+1=7 6+1=7

And therefore the fraction is:

72 \frac{7}{2}

Now we want to do the subtraction exercise, but we see that we have another step on the way.
We subtract fractions when both fractions have the same denominator,
so we'll expand the fraction 21 \frac{2}{1} to a denominator of 2, and we'll get:

42 \frac{4}{2}

And now we can perform subtraction -

72โˆ’42=32 \frac{7}{2}-\frac{4}{2}=\frac{3}{2}

We'll convert this back to a mixed fraction and we'll see that the result is

Answer

112 1\frac{1}{2}

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Addition and Subtraction of Mixed Numbers