# Tricks For Maths To Make Calculation Easy And Fast

### 1) MULTIPLICATION OF 11 WITH ANY NUMBER OF 3 DIGITS.

Let me explain this rule by taking examples

1. 352*11 = 3—(3+5)—(5+2)—2 = 3872

Means insert the sum of first and second digits, then sum of second and third digits between the two terminal digits of the number

2. 213*11 = 2—(2+1)—(1+3)—3 = 2343

Here an extra case arises

Consider the following examples for that

1) 329*11 = 3— (3+2) +1— (2+9-10) —9 = 3619

Means, if sum of two digits of the number is greater than 10, then add 1 to previous digit and subtract 10 to the associated digit.

2) 758*11 = 7+1—(7+5-10)+1—(5+8-10)—8 = 8338

make triplets as written below starting from units place

34………568……….276

now alternate sum = 34+276 = 310 and 568

and difference of these sums = 568-310 = 258

divide it by 7 we get reminder as 6

divide it by 11 we get reminder as 5

divide it by 13 we get reminder as 11

other examples:-

consider the number 4523895099854

triplet pairs are 4…523…895…099…854

alternate sums are 4+895+854=1753 and 523+099=622

difference = 1131

revise the same tripling process

1……131

so difference = 131-1 = 130

divide it by 7 we get reminder as 4

divide it by 11 we get reminder as 9

divide it by 13 we get reminder as 0

### 2) TO CALCULATE REMINDER ON DIVIDING THE NUMBER BY 3

Method:- first calculate the digit sum , then divide it by 3, the reminder in this case will be the required reminder

example:- 1342568

let the number is as written above

its digit sum = 29 = 11 = 2

so reminder will be 2

Take some others

34259677858

digit sum of the number is 64 = 10 = 1

reminder is 1

similarly let the number is 54670329845

then digit sum = 53 = 8

when we divide 8 by 3 we get reminder as 2 so answer will be 2

### 3) SQUARE OF NUMBERS NEAR TO 100

Let me explain this rule by taking examples

96^2 :-

First calculate 100-96, it is 4

so 96^2 = (96-4)—-4^2 = 9216

similarly

106^2 :-

First calculate 106-100, it is 6

so 106^2 = (106+6)—-6^2 = 11236

An other case arises

110^2 = (110+10)—-100 = (120+1)—-00 = 12100

similarly

89^2 = (89-11)—-121 = (78+1)—-21 = 7921

### 4) SQUARE OF ANY 2 DIGIT NUMBER

Let me explain this trick by taking examples

67^2 = [6^2][7^2]+20*6*7 = 3649+840 = 4489

similarly

25^2 = [2^2][5^2]+20*2*5 = 425+200 = 625

Take one more example

97^2 = [9^2][7^2]+20*9*7 = 8149+1260 = 9409

Here [] is not an operation, it is only a separation between initial 2 and last 2 digits

Here an extra case arises

Consider the following examples for that

91^2 = [9^2][1^2]+20*9*1 = 8101+180 = 8281

### 5) MULTIPLICATION OF 2 TWO-DIGIT NUMBERS WHERE THE FIRST DIGIT OF BOTH THE NUMBERS ARE SAME AND THE LAST DIGIT OF THE TWO NUMBERS SUM TO 10

Let me explain this rule by taking examples

To calculate 56×54:

Multiply 5 by 5+1. So, 5*6 = 30. Write down 30.

Multiply together the last digits: 6*4 = 24. Write down 24.

The product of 56 and 54 is thus 3024.

Understand the rule by 1 more example

78*72 = [7*(7+1)][8*2] = 5616

### 6) MULTIPLICATION OF TWO NUMBERS THAT DIFFER BY 6

If the two numbers differ by 6 then their product is the square of their average minus 9.

Let me explain this rule by taking examples

10*16 = 13^2 – 9 = 160

22*28 = 25^2 – 9 = 616

Understand the rule by 1 more example

997*1003 = 1000^2 – 9 = 999991

### 7) MULTIPLICATION OF TWO NUMBERS THAT DIFFER BY 4

If two numbers differ by 4, then their product is the square of the number in the middle (the average of the two numbers) minus 4.

Let me explain this rule by taking examples

22*26 = 24^2 – 4 = 572

98*102 = 100^2 – 4 = 9996

Understand the rule by 1 more example

148*152 = 150^2 – 4 = 22496

### 8) MULTIPLICATION OF TWO NUMBERS THAT DIFFER BY 2

(This trick only works if you have memorised or can quickly calculate the squares of numbers. When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1.Let me explain this rule by taking examples

18*20 = 19^2 – 1 = 361 – 1 = 360

25*27 = 26^2 – 1 = 676 – 1 = 675

Understand the rule by 1 more example 49*51 = 50^2 – 1 = 2500 – 1 = 2499

### 9) MULTIPLICATION OF 125 WITH ANY NUMBER

Let me explain this rule by taking examples

1. 93*125 = 93000/8 = 11625.

2. 137*125 = 137000/8 = 17125.

Understand the rule by 1 more example

3786*125 = 3786000/8 = 473250.

### 10) MULTIPLICATION OF 25 WITH ANY NUMBER

Let me explain this rule by taking examples

1. 67*25 = 6700/4 = 1675.

2. 298*25 = 29800/4 = 7450.

Understand the rule by 1 more example

5923*25 = 592300/4 = 148075.

### 11) MULTIPLICATION OF 5 WITH ANY NUMBER

Let me explain this rule by taking examples

1. 49*5 = 490/2 = 245.

2. 453*5 = 4530/2 = 2265.

Understand the rule by 1 more example

5649*5 = 56490/2 = 28245.

### 12) MULTIPLICATION OF 999 WITH ANY NUMBER

Let me explain this rule by taking examples

1. 51*999 = 51*(1000-1) = 51*1000-51 = 51000-51 = 50949.

2. 147*999 = 147*(1000-1) = 147000-147 = 146853.

Understand the rule by 1 more example

3825*999 = 3825*(1000-1) = 3825000-3825 = 3821175

### 13) MULTIPLICATION OF 99 WITH ANY NUMBER

Let me explain this rule by taking examples

1. 46*99 = 46*(100-1) = 46*100-46 = 4600-46 = 4554.

2. 362*99 = 362*(100-1) = 36200-362 = 35838.

Example.

Understand the rule by 1 more example

2841*99 = 2841*(100-1) = 284100-2841 = 281259

### 14) MULTIPLICATION OF 99 WITH ANY NUMBER

Let me explain this rule by taking examples

1. 46*99 = 46*(100-1) = 46*100-46 = 4600-46 = 4554.

2. 362*99 = 362*(100-1) = 36200-362 = 35838.

Example.

Understand the rule by 1 more example

2841*99 = 2841*(100-1) = 284100-2841 = 281259

### 15) MULTIPLICATION OF 9 WITH ANY NUMBER

Let me explain this rule by taking examples

1. 18*9 = 18*(10-1) = 18*10-18 = 180-18 = 162.

2. 187*9 = 187*(10-1) = 1870-187 = 1683.

Example.

Understand the rule by 1 more example

1864*9 = 1864*(10-1) = 18640-1864 = 16776

### 16) MULTIPLICATION OF 11 WITH ANY NUMBER.

Let me explain this rule by taking examples

1) 234163*11 = 2—2+3—3+4—4+1—1+6—6+3—3 = 2575793

Means insert the sum of 2 successive digits and put 2 terminal digits in its place

2) 45345181*11 = 4—4+5—5+3—3+4—4+5—5+1—1+8—8+1—1 = 498796991

Here an extra case arises

Consider the following examples for that

3) 473927*11 = 4+1— (4+7-10) +1— (7+3-10) +1— (3+9-10) +1— (9+2-10)— (2+7) —7 = 5213197

4) 584536*11 = 5+1—(5+8-10)+1—(8+4-10)—(4+5)—(5+3)—(3+6)—6 = 6429896

### 17) SQUARE OF ANY 2 DIGIT NUMBER

Let me explain this rule by taking examples

27^2 = (27+3)*(27-3) + 3^2 = 30*24 + 9 = 720+9 = 729

In this method, we have to make a number ending with 0, that’s why; we add 3 to 27;

**Example **: Understand the rule by 1 more example

78^2 = (78+2)*(78-2) + 2^2 = 80*76 + 4 = 6080+4 = 6084

### 18) SQUARE OF A 2 DIGIT NUMBER ENDING WITH 5

Let me explain this rule by taking examples

35^2 = 3*(3+1) —25 = 1225;

Other example

95^2 = 9*(9+1) —25 = 9025