Number System: Fraction, Proper, Improper , Mixed and Decimal fraction

by Wonder Boy · Published April 10, 2020 · Updated May 9, 2020

Fraction : A fraction is a number in the form $\frac{x}{y}$ , where x & y are both integers and y $\ne$ 0. In the form $\frac{x}{y}$ , ‘x’ is called the numerator of the fraction and ‘y’ is called the denominator of the fraction.

We can also describe a fraction as a part of a whole. The denominator denotes how many equal parts the whole is divided into & the numerator denotes how many of the parts we are taking.

For. eg. $\frac{5}{6}$ is a fraction.
5 is the numerator of the fraction & 6 is the denominator of the fraction.

We may also call it as 5 of 6 equal parts.

We can classify fraction as:
Proper Fraction: A fraction in which the numerator is smaller than the denominator.
For e.g. $\frac{5}{6}$ , $\frac{9}{11}$

Improper Fraction : A fraction is which the numerator is greater than the denominator.
For e.g. $\frac{13}{5}$ , $\frac{17}{7}$

Mixed Number or Mixed Fraction : Mixed number is composed of a whole number and a proper fraction.
For e.g. $5\frac{3}{4}$ , $7\frac{2}{5}$

Decimal Fraction: A fraction where the denominator can be expressed as a power of ten (such as 10, 100, 1000, etc).
For e.g. $\frac{8}{10}$ , $\frac{11}{100}$ , $\frac{9}{1000}$ …

Decimal fraction can be written as a decimal point and no denominator. In decimal point form, it is easier to make calculations such as addition, subtraction etc.
$\frac{8}{10}$ can be written as 0.8
$\frac{11}{100}$ can be written as 0.11
$\frac{9}{1000}$ can be written as 0.009

Converting Improper fractions to Mixed numbers:
~ Divide the numerator by the denominator.
~ Use the quotient as the whole number.
~ And the remainder as the numerator of the proper fraction.
~ The denominator will remain the same.
~ If there is no remainder the result is simply a whole number.

Let’s convert $\frac{51}{5}$ into mixed number.
$\frac{51}{5}$ = $\frac{50+1}{5}$ = $\frac{50}{5}$ + $\frac{1}{5}$
=10+ $\frac{1}{5}$
=10 $\frac{1}{5}$

Let’s convert $\frac{30}{5}$ into a mixed number.
$\frac{30}{5}$ = 6 which is a whole number.

Converting Mixed numbers to Improper fractions.
~ Multiply the whole number by the denominator.
~ Add the product to the numerator of the proper fraction. The sum total is the numerator of the improper fraction.
~ The denominator will remain the same.

Let’s convert $4\frac{3}{5}$ into an improper fraction.
$4\frac{3}{5}$ = $\frac{20+3}{5}$ = $\frac{23}{5}$