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Number System Part-1

Natural Numbers: 

They are denoted by N

N= 1,2,3,4,5..... 

Whole Number:

When We include "0" in the natural number is denoted as "W" . W= 0,1,2,3,4......

Primary Number:

 Numbers other than 1 are divisible by only 1 are called Primary Numbers. Ex. 2,5,7,11,13 etc.

How to know a number Primary or not!

1. Is 881 a primary number?

Sol: The approximate sq root is 30. A prime number less than 30 is 2,3,5,7,11,13,17,19,23,19, and 881 is not divisible by any of these. so 881 is primary number.

Do it yourself- Is 349 the primary number? (Hint: what is the nearest square number of 349; it's 19)

Lists of square roots:


Ex. Please check the 509, 757, and 647 primary numbers or not?


Composite Numbers:

Numbers other than 1 which are not primary numbers are called composite numbers. Ex: 4,6,8,9,10 etc

Even Numbers: 

The numbers are divisible by 2. Ex: 2,4,6,8,10,12etc.

Odd Numbers:

Numbers not divisible by 2. Ex: 3,5,7,9,11,13,15 etc.

Integers:

The numbers consist of whole numbers and negative numbers.

Ex: (-4,-3,-2,-1,0,1,2,3,4..) etc

Rational numbers:

When the numbers are written in a fraction is called rational numbers

Ex: 2/3, 8/9, 11/14, etc.

Irrational numbers: 

When numbers can not be written as fractions. Ex: Root over 3= 1.732732.... rootover 2= 1.414...

Rule of Simplification :

VBODMAS rule:

V= Vinculum(Bar)

B=Bracket

O= Of

D= Division

M=Multiplication

A=Addition

S= Subtraction

Example:


Some important Formula:


Ex1: Which is Greatest: 3/4, 4/5, 5/6?

Sol:  the difference in numerators and denominators is 1 or equal in each case. Always remember the higher number is always the greatest. (thumb rule )

Ex.2 Which is greatest 2/5, 4/4, 6/9

Sol: Greatest is 6/9 ( same logic applied as before )

Ex3: Which is greatest 1/8, 4/9, 7/10?

Sol: As numerators increase by 3 and denominators increase by 1 (At constant value) Higher is always greater. So 7/10 is the greatest.

Ex4; Which is greatest2/7, 4/15, 6/23?

Sol: Here is a little bit confusing. So Numerator increased by 2 and denom. increased by 8 . Stick to the rule ---

1. if (Increase in Nom.)/(Increase in Den.) > the First fraction then the last value is the greatest.

2. if (Increase in Nom.)/(Increase in Den.) < the First fraction then the last value is Least.

3. if (Increase in Nom.)/(Increase in Den.) = the First fraction then all values are equal.

For Ex-4 we can write 2/8 or 1/4. is it greater or lesser than 2/7? the answer is lesser. So rule 2 will be applied and 6/23 is the least among these numbers.

Let's do it: 

5/8 or 9/14 Which is greater? ( Do it you own )


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Location: West Bengal, India

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