# Proper and improper fractions. Mixed numbers

A concise but great lesson about improper fractions, proper fractions, and mixed numbers.

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,   2 +
1 / 3
is a mixed number.

The + sign is usually omitted so as to write   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.

The above is a shortcut!

 To get  7 / 3 ,you will normally add 2 / 1 and   1 / 3

Using the shortcut however takes less time!

Notice that the denominator for 2 is 1 since 2 =
2 / 1

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,   2 +
1 / 3
is a mixed number.

The + sign is usually omitted so as to write   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.

The above is a shortcut!

 To get  7 / 3 ,you will normally add 2 / 1 and   1 / 3

Using the shortcut however takes less time!

Notice that the denominator for 2 is 1 since 2 =
2 / 1

Converting to a mixed number

You can also convert an improper fraction to a mixed number

Say you want to convert
13 / 5
to a mixed number

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

The mixed number is 2
3 / 5

Another example will make this crystal clear may be

Convert
25 / 6
to 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

The mixed number is 4
1 / 6

## Proper fractions, improper fractions, and mixed number quiz.

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