Mixed Numbers

Mixed Numbers and Fractions Greater than 1 Equivalent Fractions Addition and Subtraction of Mixed Numbers Multiplication of Integers by a Fraction and a Mixed number All Operations in Mixed Fractions Multiplication and Division of Mixed Numbers Dividing Whole Numbers by Fractions and Mixed Numbers Mixed Fractions - Examples, Exercises and Solutions

Mixed Numbers

In this article, we will teach you the basics of everything you need to know about mixed numbers.
If you wish to delve deeper into a specific topic, you can access the corresponding extensive article.

Mixed Number and Fraction Greater Than 1

A fraction that is greater than 1 is a fraction whose numerator is larger than its denominator, this type of fractions can be converted into mixed numbers.

It is important that we remember similar topics:

How do you convert a mixed number to a fraction?

Multiply the whole number by the denominator.
To the obtained product, add the numerator. The final result will be the new numerator.
Nothing is changed in the denominator.

How do you convert an integer to a fraction?

The whole number is written in the numerator and the 1 in the denominator.

You can continue reading in these articles:

Detailed explanation

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Test yourself on mixed fractions!

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

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Mixed Numbers

Addition and Subtraction of Mixed Numbers

To add and subtract mixed numbers, we will act as follows:

First step

We will convert mixed numbers into fractions - fractions with numerator and denominator that do not have whole numbers.

Second step

We will find a common denominator (usually by multiplying the denominators).

Third step

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

Multiplication of an Integer by a Fraction and by a Mixed Number

We will solve the multiplication of an integer by a fraction and by a mixed number in the following way:

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Question 1

$2\times\frac{5}{7}=$

Question 2

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

Question 3

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

First step

We will convert the whole numbers and mixed numbers to fractions and rewrite the exercise.

Second step

We will multiply the numerators and the denominators separately.
The product of the numerators will be written in the new numerator.
The product of the denominators will be written in the new denominator.

Do you know what the answer is?

Question 1

$1:\frac{1}{4}=$

Question 2

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

Question 3

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

Multiplication and Division of Mixed Numbers

In multiplications

First step

We will convert mixed numbers to fractions and rewrite the exercise.

Second step

We will multiply the numerators and the denominators separately.
The product of the numerators will be written in the new numerator.
The product of the denominators will be written in the new denominator.
• The commutative property works - We can change the order of the fractions within the exercise without altering the result.

In divisions

First step

We will convert mixed numbers to fractions and rewrite the exercise.

Second step

We will convert the division into multiplication and swap between the numerator and the denominator in the second fraction.

Third step

We will solve by multiplying numerator by numerator and denominator by denominator.

Check your understanding

Question 1

Solve:

$7\times\frac{3}{8}=$

Question 2

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

Question 3

$3\times\frac{6}{7}=$

Division of an Integer by a Fraction and by a Mixed Number

First step

In case there is any mixed number - we will convert it into a fraction
• In case there is any whole number - we will convert it into a fraction

Second step

We will convert the division into multiplication and swap between the numerator and the denominator in the second fraction.

Third step

We will solve by multiplying numerator by numerator and denominator by denominator.

Examples and exercises with solutions of mixed fractions

Exercise #1

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

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:

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

Now we will get the exercise:

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

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

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

Now the exercise we get is:

$4+4\frac{1}{2}=8\frac{1}{2}$

Answer

$8\frac{1}{2}$

Exercise #2

$7\frac{5}{6}+6\frac{2}{3}+\frac{1}{3}=$

Video Solution

Step-by-Step Solution

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

$6\frac{2}{3}+\frac{1}{3}=7$

Now we get:

$7\frac{5}{6}+7=14\frac{5}{6}$

Answer

$14\frac{5}{6}$

Exercise #3

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

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:

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

We should obtain the following exercise:

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

Answer

$3\frac{3}{4}$

Exercise #4

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

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:

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

Now we get:

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

Answer

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

Exercise #5

$1:\frac{1}{4}=$

Video Solution

Answer

$4$

Do you think you will be able to solve it?

Question 1

$7\times\frac{2}{5}=$

Question 2

$2:\frac{2}{3}=$

Question 3

$3:\frac{3}{4}=$

Start practice

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