A concise but great lesson about the different types of fractions such as improper fractions, proper fractions, and mixed numbers.

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2

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2

What type of fraction is this?

Convert this improper fraction to a mixed number:

**Improper fractions:**

Fractions with a numerator that is bigger than the denominator.

For instance, the following fractions are improper.

9
2
,
7
4
, and
8
3

**Proper fraction:**

A fraction with a numerator that is smaller than the denominator.

For instance, the following are all proper fractions.

2
3
,
1
4
, and
6
8

**Mixed number:**

A number written as the sum of a whole number and a proper fraction. For instance the following is a mixed number.

2 +
1
3

The + sign is usually omitted and we prefer to write it as you see below.

2
1
3

Mixed numbers can be converted to improper fractions and vice versa. In our example above,

2
1
3
=
7
3

To get 7/3, multiply 2 by 3 and then add 1. Keep the same denominator. This is a shortcut! To get 7/3, you will normally add 2/1 and 1/3.

Using the shortcut takes less time. Notice that the denominator for 2 is 1 since 2 = 2/1

You can also convert an improper fraction to a mixed number. Say you want to convert the fraction below to a mixed number.

13
5

Ask yourself, " How many 5 can go into 13? " The answer is 2.

2 is your whole number piece of the mixed number.

What is the remainder of this division? 5 × 2 = 10 and 13 - 10 = 3.

3 is the numerator of the fraction piece.

The denominator remains the same, so it will be 5. Therefore the mixed number is:

2
3
5

Another example will make this crystal clear may be. Convert the 25/6 into a mixed number.

Ask yourself, " How many 6 can go into 25? " The answer is 4.

4 is your whole number piece of the mixed number.

What is the remainder of this division? 6 × 4 = 24 and 25 - 24 = 1.

1 is the numerator of the fraction piece.

The denominator remains the same, so it will be 6.

Therefore 25/6 converted into a mixed number is:

4
1
6

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If you don't know fractions very well, you will probably struggle to do well on most math tests. Build a strong foundation in math today before it is too late!

Buy my fractions ebook now. It offers a thorough coverage of fractions!