Fractions and Decimals

A fraction is written as m/n, the m is the numerator and n is the denominator.
Examples of fractions are \frac { 2 }{ 3 } ,\frac { 4 }{ 7 } ,\frac { 11 }{ 12 } ,\frac { -3 }{ 4 } and so on.


When the numerator is smaller than the denominator, we say that the fraction is proper and when the numerator is bigger than the denominator, we say that the fraction is improper.
Some proper fractions are: \frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 11 }{ 13 } ,\frac { 3 }{ 4 } ,\frac { 1 }{ 5 } ,\frac { 100 }{ 101 }
Some improper fractions are \frac { 4 }{ 3 } ,\frac { 7 }{ 3 } ,\frac { 14 }{ 13 } ,\frac { 8 }{ 5 } ,\frac { 12 }{ 7 } ,\frac { 1000 }{ 999 }


When a fraction is improper, we can convert it into a mixed fraction form (or mixed numbers).
\frac { 5 }{ 3 } can also be written as 1\frac { 2 }{ 3 }
\frac { 12 }{ 5 } can also be written as 2\frac { 2 }{ 5 }
\frac { 18 }{ 5 } as 3\frac { 3 }{ 5 }
We use fractions to represent a part of a whole

A rectangle divided into 4 equal parts.


One part of the whole is \frac { 1 }{ 4 }


A rectangle divided into 8 equal parts

.
If we choose 3 parts out of 8 equal parts, then it is represented by \frac { 3 }{ 8 }
A fraction will have the same value if we multiply the numerator and the denominator by the same number.


Hence \frac { 3 }{ 5 } =\frac { 6 }{ 10 } =\frac { 9 }{ 15 } =\frac { 12 }{ 20 }

But among \frac { 3 }{ 5 } ,\frac { 6 }{ 10 } ,\frac { 9 }{ 15 } and \frac { 12 }{ 20 } ,\frac { 3 }{ 5 } is the most simplified one. We usually give functions in its simplest form.
\frac { 3 }{ 5 } ,\frac { 6 }{ 10 } ,\frac { 9 }{ 15 } ,\frac { 12 }{ 20 } are called equivalent fractions.