LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

NUMBER SYSTEM

__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.)**