Irrational Numbers
Numbers can not written in the form a/b with a&b as an integers...
Irrational Numbers are not #terminating & #not_repeating.

Eg. π, √5 & numbers in the form 0.26383518.... etc Are irrational Numbers

Prime Numbers
Numbers Divisible by 1& Itself are nothing but the #prime numbers.

Composite Numbers
Numbers other than prime & divisible by 1, Number itself & #by_other numbers also

The numbers 0 and 1 are neither prime nor composite. They are too special because they represent nothingness (zero) and wholeness (one), so the idea of having factors for 0 and 1 does not make sense....

Real Numbers
Numbers On line... Its set of numbers contains...
#Natural Numbers
#Whole Numbers
#Prime Numbers
#Composite Numbers
#Rational_&_Irrational Numbers... also🤘

Encircled are #Prime_numbers Other are #Composites Except '1'...

Compex Numbers
Numbers expressed in the form a + bi where a & b are real Numbers & #_i is imaginary number (i.e. i=√(-1) )...

Even Numbers
Numbers Divisible by 2...
Eg. 4, 6, 8, 10,......

Odd Numbers
Numbers not Divisible by 2
Eg. 1, 3, 5, 7,...

Operations...

1.Addition of two numbers...

1. (+a)+(+b)=+ve
Eg. (2+3)=+5

2. (-a)+(+b)= -ve/+ve...sign of greater number...
Eg. (-3)+(+4)=(-3+4)=(+1)

3. (+a)+(-b)= (a-b) = -ve/+ve... Sign of greater number...
Eg. (+5)+(-7)=(5-7)=(-2)

4. (-a)+(-b)=(-a-b)= -ve...
Eg. (-3)+(-2)= -(3+2)=-(5)
Or = (-3-2)=(-5) #same


2. Substraction of two numbers

1. (+a)-(+b)= +ve If_(a>b) & -ve If_(a<b)
Eg. (+2)-(+6)=(2-6)=(-4)

2. (+a)-(-b)=(a+b)=+ve
Eg. (6-(-3)= (6+3) =+9

3. (-a)-(-b)=(-a+b)= Sign of greater number
Eg. (-2)-(-5)=-(2-5)=-(-3)=3

4. (-a)-(+b)=(-a-b)=-ve(a+b)
eg. (-5)-(+3)=(-5-3)=-(5+3)= -(8)
Or =(-8)... #Same

3.Multiplication

1. (+a)×(+b)=+be
Eg. (8×2)=+16
i.e.Product of two positive numbers carries positive number.

2. (+a)×(-b)=-ve
Eg. (6×(-4))=(-24)

3. (-a)×(+b)=-ve
Eg. (-7)×(+5)=(-35)
⏫ Product of two numbers must be negative iff one of the number is Negative.

4. (-a)×(-b)=+ve
Eg. (-8)×(-2)= +16
i.e Product of two Negative numbers carries Positive Number.


4. Division

1. (+a)÷(+b)=+ve
Eg. (+1)÷(+4)= +0.25

2. (+a)÷(-b)= -ve
Eg. (+2)÷(-4)= -0.5

3. (-a)÷(+b)= -ve
Eg. (-4)÷(+4)= -1

4. (-a)÷(-b)= +ve
Eg. (-6)÷(-3)= +2

( Division of two numbers must be positive...iff both the numbers are either positive or negative.)

( Division of two numbers will be equal to Negative... If n only if one of the number is Negative.)

5. Exponentiation
i.e Numbers in the form bn or b^n...
We can say 'b to the power n'.


1. (+a)^n=+ve
Eg. (+5)^3=5×5×5= (+125)

2. (-a)^n= +ve Or -ve
#depends on the value of 'n'... If 'n' is Even result will be Positive.
If 'n' is Odd result will be Negative.

Eg.1.Even power (-4)^4=(-4)×(-4)×(-4)×(-4)=(+128)

2.Odd power
(-5)^3=(-5)×(-5)×(-5)=(-125)

Simplification of Expressions

Order of Operations in Maths...#PEMDAS
BODMAS

1.Parenthesis i.e Bracket(),[],{} first
From innermost to outer

2. Exponent i.e power (like square)

3. Multiplication & Division (left to right)

4. Addition & Substraction (left to right)

5.Distribute when brackets exist.
Example:
2(x + y) + 3(x - y)
= 2x + 2y + 3x - 3y
= 5x - y

Example #order of operations...

Eg. 1: 6+(14-3)×5-5²+22÷2=??
Ans:-
Solve Bracket first,
=6+(11)×5-5²+22÷2
Now,Exponent
=6+11×5-25+22÷2
Now,Multiply&Divide from left to right,
=6+55-25+11
Now, Addition & Subtraction from left to right,
=61-25+11
=36+11
=47...!

Divisibility Rules 👆

Important formulas

1. a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)

2. (a+b)³= a³+3a²b+3ab²+b³

3. a³+b³= (a+b)(a²-ab+b²)

4. a³-b³= (a-b)(a²+ab+b²)

5. (a+b+c)²= a²+b²+c²+2ab+2bc+2ca

6. (a+b)²= a²+2ab+b²

7. (a-b)²= a²-2ab+b²

8. a²-b²= (a-b)(a+b)
...

You should know the tables from 1-25...!

Assuming that, We know square of each number from 1-25. We are going to find square of of any number bigger than 25. By assuming base as 50, 100, 150, 200, 250, 300......

Base 50 : i.e for numbers between 26-75.
1. Get the difference between 50 and given number and square it(Write it on right side such that it will consume last two digits.
2. Subtract the difference( if number < 50) or Add the difference (if number > 50) in 25. And Write result in front of result of case 1.

e.g (46)^2 = (25-4)=21 and (4^2)=16 i.e 2116