# What is Fraction

Are you really interested in fractions?
Ok, it's nothing difficult here.

Look, fraction is only a number got by the special way. You can always make your own fraction when you divide any two numbers.

##### Example:

2 ÷ 5 = 2 ⁄ 5     12 ÷ 1 = 12 ⁄ 1     7 ÷ 3 = 7 ⁄ 3     54 ÷ 54 = 54 ⁄ 54 = 1

So, every fraction looks like a ⁄ b, where a, b are numbers and "⁄" is fraction line (fraction slash) and it means a ÷ b = a ⁄ b; b ≠ 0

### It's interesting!

Every whole number you may write as a fraction (17 ÷ 1 = 17 ⁄ 1), but not every fraction is the whole number (7 ÷ 8 = 7 ⁄ 8).
Moreover, you have to see the difference between a fraction and fractional number (or rational number). They are not the same things. It means that every fractional (or rational) number is a fraction, too. But not every fraction is a fractional number.

##### Example:

4 ⁄ 7 – fraction and fractional number at the same time.

√3 ⁄ 5 – fraction and not fractional number.

So, if you have a fraction a ⁄ b it will be fractional number (or rational number) then and only then, when a, b are whole numbers (a ∈ Z, b ∈ Z, b ≠ 0) and this time you can write a ⁄ b ∈ Q.

##### Example:

8 ⁄ 9 ∈ Q, 21 ⁄ 5 ∈ Q, 7 ⁄ 7 ∈ Q -- all they are fractions and fractional numbers, too.

√5 ⁄ 2 ∉ Q, 11 ⁄ √2 ∉ Q, √7 ⁄ √3 ∉ Q -- all they are only fractions and not fractional numbers.

### There are different fractions:

Proper fraction, improper fraction, decimal fraction, vulgar fraction.

You may read about them to know more about fractions and you'll see "The devil is not so black as he is painted".

#### Note

- fraction slash

= - is equal to; equals

- is not equal to; does not equal

÷ - divided by

- belongs to; a member of; an element of

- does not belong to; is not a member of; is not an element of

Q - all rational numbers

- square root