NUMBER SYSTEM
You are already familiar with numbers system, natural number, whole numbers, integers, and four fundamental operations on them are well known by you. In this module we would like to introduce you more advance formation of number system, elsewhere there are some initial introduction or refreshment of earlier learning which are described below –
The number used to count things are called Natural Numbers, the Set of natural number is N = { 1, 2, 3, 4, 5, …………………… }
The number 0 (Zero) together with the natural numbers gives us the set of Whole Numbers, that is W = { 0, 1, 2, 3, 4, 5, 6, ………………. }
Integers are described as the members of the collection of numbers such as …………., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,………….. where 1, 2, 3, 4, 5, 6, 7, …………. are called Positive Integers and ………………., -5, -4, -3, -2, -1 are called negative integers. The integers 0 (Zero) is neither positive nor negative.
The entire set of Integers is denoted by I or Z.
So, Z = { ……., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,…………. }, Integers are also called Signed Numbers or Directed Numbers.
Four fundamental operations on directed numbers –
The directed numbers and the integers are the same and we are already familiar with the four fundamental operations on integers.
An expression involving integers (i.e., directed numbers ) is simplified by the rules of BODMAS –
Step.1) First, carry out the operations inside the brackets (B), brackets are removed in the order – a) Line Brackets ( Vinculum ), b) First bracket (Common ), c) Second Brackets (Curly), d) Third brackets ( Rectangular or Square )
Step.2) Then Change ‘OF’ into ‘X’ and multiply (O)
Step.3) Carry out the operations of Division & multiplication, in that order (DM).
Step.4) Finally, carry out the operations of Addition & Subtraction (AS)
Example.1) Simplify 575 – 16 of [ 625 ÷ { 55 – 5 X (9 – 6 – 3)}]
Answer) The given Expression 575 – 16 of [ 625 ÷ { 55 – 5 X (9 – 6 – 3)}]
= 575 – 16 of [ 625 ÷ { 55 – 5 X ( 9 – 3 )}]
= 575 – 16 of [ 625 ÷ { 55 – ( 5 X 6 )}
= 575 – 16 of [ 625 ÷ { 55 – ( 5 X 6 )}]
= 575 – 16 of [ 625 ÷ { 55 – 30}]
= 575 – 16 of [ 625 ÷ 25 ]
= 575 – 16 of 25
= 575 – 400
= 125 (Ans.)