## MATHS TRICKS , SHORT CUT TRICKS FOR MATHS TO MAKE CALCULATION EASY AND FAST

**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 EXAMPLE. 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

__TO CALCULATE REMINDER ON DIVIDING THE NUMBER BY 27 AND 37__Let me explain this rule by taking examples

consider number 34568276, we have to calculate the reminder on diving this number by 27 and 37 respectively.

make triplets as written below starting from units place

34.........568..........276

now sum of all triplets = 34+568+276 = 878

divide it by 27 we get reminder as 14

divide it by 37 we get reminder as 27 EXAMPLE. other examples for the clarification of the rule

let the number is 2387850765

triplets are 2...387...850...765

sum of the triplets = 2+387+850+765 = 2004

on revising the steps we get

2......004

sum = 6

divide it by 27 we get reminder as 6

divide it by 37 we get reminder as 6

__TO CALCULATE REMINDER ON DIVIDING THE NUMBER BY 7 11 AND 13__Let me explain this rule by taking examples

consider number 34568276, we have to calculate the reminder on diving this number by 7 11 and 13 respectively.

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 EXAMPLE. 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

__TO CALCULATE REMINDER ON DIVIDING THE NUMBER BY 3 Method:-__first calculate the digit sum , then divide it byMULTIPLICATION 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. EXAMPLE. Understand the rule by 1 more example

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

__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 EXAMPLE. Understand the rule by 1 more example

997*1003 = 1000^2 - 9 = 999991

__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 EXAMPLE. Understand the rule by 1 more example

148*152 = 150^2 - 4 = 22496

__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 EXAMPLE. Understand the rule by 1 more example 49*51 = 50^2 - 1 = 2500 - 1 = 2499

__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. EXAMPLE. Understand the rule by 1 more example

3786*125 = 3786000/8 = 473250.

__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. EXAMPLE. Understand the rule by 1 more example

5923*25 = 592300/4 = 148075.

__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. EXAMPLE. Understand the rule by 1 more example

5649*5 = 56490/2 = 28245.

__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. EXAMPLE. Understand the rule by 1 more example

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

__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. Example.

Understand the rule by 1 more example

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

__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. Example.

Understand the rule by 1 more example

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

__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. Example.

Understand the rule by 1 more example

1864*9 = 1864*(10-1) = 18640-1864 = 16776 Is this m 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 EXAMPLE. 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

__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 EXAMPLE. An other case arises

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

similarly

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

__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

EXAMPLE. Here an extra case arises

Consider the following examples for that

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

__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. EXAMPLE. Understand the rule by 1 more example

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

__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 EXAMPLE. Understand the rule by 1 more example

997*1003 = 1000^2 - 9 = 999991

__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 EXAMPLE. Understand the rule by 1 more example

148*152 = 150^2 - 4 = 22496

__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 EXAMPLE. Understand the rule by 1 more example 49*51 = 50^2 - 1 = 2500 - 1 = 2499

__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. EXAMPLE. Understand the rule by 1 more example

3786*125 = 3786000/8 = 473250.

__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. EXAMPLE. Understand the rule by 1 more example

5923*25 = 592300/4 = 148075.

__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. EXAMPLE. Understand the rule by 1 more example

5649*5 = 56490/2 = 28245.

__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. EXAMPLE. Understand the rule by 1 more example

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

__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. Example.

Understand the rule by 1 more example

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

__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. Example.

Understand the rule by 1 more example

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

__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. Example.

Understand the rule by 1 more example

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

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