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# Amazing Mathematics

1 x 8 +1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 +5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 =9876543

12345678 x 8 + 8 =98765432

123456789 x 8 + 9 =987654321

1 x 9 + 2 =11

12 x 9 + 3 = 111

123 x 9 + 4 =1111

1234 x 9 +5= 11111

12345 x 9 +6=111111

123456 x9 +7 = 1111111

1234567 x 9 +8 =11111111

12345678 x 9 +9 =111111111

123456789 x 9 +10 =1111111111

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 =888888

987654 x 9 + 2 =8888888

9876543 x 9 + 1 =88888888

98765432 x 9 + 0 = 888888888

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

Shortcuts for Mathematical operations (Multiplication)

1. Multiplication: is nothing but repetitive addition.

87 x 93 =?

Traditionally we know how to deal with this.

87 x 93

————

261

783

————–

8091

————–

this is done in another way is

87 is 13 difference to 100

93 is 07 difference to 100

87 – 13

93 – 07 ( apply cross subtraction here)

i.e 87-07 = 80

93- 13 =80

and multiply the differences 07 x 13 = 91

2. 76 x 82 =?

76 is 24 diff to 100

82 is 18 diff to 100

so as per apply cross subtraction 76-18 and 82-24 is 58

and multiply the difference 24 x 18 = 432 here take 32 and 4 as carry it is added to the 58

so the answer is (58+4)32 = 6232

Fundamental Rules for Arithmetic Operations

Four Fundamental Rules for Addition, Subtraction, Multiplication and Division (+,-,x,%)
Before that have a quick look at Number System:

Even numbers—The number which is divisible by 2 are called even numbers. Such as 2,4,6,8,10,etc.
Odd numbers—The numbers which are not divisible by 2 are called odd numbers. Such as I 3,5,7,9,11,13,15 etc.
Prime numbers—A number,if it is divisible by 1 and itself only is called Prime number. Such as 2,3,5,7,11,13,17,19,23,etc.
Composite Numbers—A number ,other than 1 and which is not a prime, is a composite number. Such as 4,6,8,9,10etc. 6 is combination of 2 and 3 i.e 2 x3 = 6
Whole number– All positive, negative and including Zero(0) numbers are called whole number. Such as 0,1,2,3,4,-1,-2,-3,-4etc.
Natural number– Counting numbers generally called as Natural Numbers, These are used to counting things . such as 1,2,3,4,5,6………..Zero(0) is not a positive integer or natural number.
Rational Number—A number is said to be a rational number which can be written in the P/q
Form, where p and q be a integer but Q be not a Zero. Such as 3/5,-3/5,0/4,2/-5,-3/7.
Irrational Number—The number which can not be expressed in the p/q form is called a irrational number, where p and q are a integer.(Q≠0) such as √5 ,√5+R3, ╥ etc.

Real Number – The numbers which are either rational or irrational, are called real number.Real numbers can shown on the numbers line. 