# How to convert improper fraction into a mixed number

Here we will learn how to:

- convert improper fraction into a mixed number.
- We will give a definition of an improper fraction and of a mixed number.
- An example of how to do each one is also shown.
- And as always, followed by some questions and answers.

**What is an improper fraction?**

An improper fraction is when the numerator (top number) is bigger than the denominator (bottom number). For example the fraction ^{9}⁄_{4} has a numerator that is larger than its denominator.

This is called an improper fraction or some times we say top-heavy fraction.

**What is a mixed number?**

A number that is made up of a whole number and a fraction is basically called a mixed number. For example the fraction 1^{3}⁄_{4} is made up of a number 1 and a fraction ^{3}⁄_{4}.

*How can we remember which is which?*

Sometimes, we forget the difference between a mixed number and an improper fraction. So, how can we remember which is which? For a start, A top heavy fraction does not quite, look right hence the term 'improper'.

A mixed number as the word 'mixed' suggests has a whole number and a fraction in it. Hence the term 'mixed'.

This is how some people differentiate the two terms. I hope this helps.

**Example 1**

Change this improper fraction ^{14}⁄_{5} into a mixed number.

Another way to look at this question, would be if we had 14 sweets and we wanted to group them into fives. How many whole groups of five would we have and how many would we have left over?

From the pictures, we have 2 groups of five. So, we have 2 whole numbers. The remainder is 4 (remainder means left over). The remainder that is left over goes on top of the fraction.

Lets do the maths for this.

so then ^{14}⁄_{5}=2^{4}⁄_{5}

Try these questions (answers are at the bottom of the page).

1. Change these to mixed numbes.

a. ^{5}⁄_{4}

b. ^{5}⁄_{2}

c. ^{9}⁄_{5}

d.^{15}⁄_{4}

e. ^{19}⁄_{6}

**Example 2**

Change this mixed number 2^{3}⁄_{4} into an improper fraction.

This is what 2^{3}⁄_{4} looks like

There are 4 quarters in 1 whole square. So, 2 is made up of eight quarters.

This means that 2 ^{3}⁄_{4} is made up of 11 quarters altogether.

We can do this also by counting up the squares in the picture,

A more mathematical method would be to multiply 2 and 4 to give 8. then add eight to the numerator 3 to give 11.

so 2^{3}⁄_{4} = ^{11}⁄_{4}

2. Change these to improper fractions.

a. 2^{1}⁄_{3}

b. 1^{5}⁄_{6}

c. 3^{1}⁄_{4}

d. 4^{2}⁄_{3}

e. 5^{1}⁄_{3}

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**Answers**

1.

a. 1^{1}⁄_{4}

b. 2^{1}⁄_{2}

c. 1^{4}⁄_{5}

d. 3^{3}⁄_{4}

e. 3^{1}⁄_{6}

2.

a. ^{7}⁄_{3}

b. ^{11}⁄_{6}

c. ^{13}⁄_{4}

d. ^{14}⁄_{3}

e. ^{16}⁄_{3}

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