General Mathematics

Fraction

Fraction can be defined as a part of a whole. If an orange is cut into two (2) equal parts, each part of the orange can be described as a fractional part of the whole orange.

It should be noted that "a whole" is represented with "1" in Mathematics or simply put, "a whole" means "1".

In the case of the orange used as example above and for Mathematics purpose, the whole orange can be represented with "1". If half $\left(\frac{1}{2}\right)$ of the orange is cut and we want to know what remains, it will be done like this:

The whole orange = 1
The part cut = $\frac{1}{2}$
The remaining orange = $1-\frac{1}{2}\left(\frac{1}{1}-\frac{1}{2}=\frac{2-1}{2}=\frac{1}{2}\right)$ Note that the LCM of "1" and "2" is "2".

N.B. You will notice that i introduced 1 as a denominator for 1 (which is a whole number) while trying to subtract $\frac{1}{2}$ from 1. That is the usual practice anytime we want to subtract a fraction from 1 or any whole number.

Description of Fraction

A fraction is usually expressed in the form of $\frac{a}{b}$, where "a" represents "Numerator" and "b" represents "Denominator". Examples of fractions are $\frac{1}{2}$, $\frac{3}{4}$, $\frac{7}{5}$, $\frac{9}{8}$ and so on.

It can be said, therefore, that the upper part of all fractions is known as a "Numerator" while the lower part of all fractions is known as a "Denominator". In the fraction $\frac{3}{4}$, "3" is known as a "Numerator" while "4" is a "Denominator".

Types of Fraction

There are three (3) types of fraction namely:

1. Proper Fractions
2. Improper Fractions
3. Mixed Numbers (This is not usually called a fraction.)

(1) A proper fraction is a fraction which has its denominator (i.e. the lower part of any fraction) greater than its numerator (i.e. the upper part of any fraction). Examples of proper fractions are $\frac{7}{9}$, $\frac{2}{3}$, $\frac{3}{4}$ and so on.

(2) An improper fraction is a fraction which has its numerator less than its denominator. Examples of improper fractions are $\frac{7}{5}$, $\frac{3}{2}$, $\frac{4}{3}$, $\frac{9}{4}$ and so on.

(3) A mixed number is defined as the combination (or coming together) of a "whole number" and a "proper fraction". Examples of mixed numbers are $3\frac{1}{4}$, $7\frac{1}{3}$, $2\frac{1}{5}$ and so on.