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Maths Tricks

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Submitted By pavan0531
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Maths Tricks , shortcut tricks for maths to make calculation easy and fast
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To calculate reminder on dividing the number by 27 and 37
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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
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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
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Is this maths trick helpful? (1217) (444)
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To calculate reminder on dividing the number by 7, 11, 13
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Let me explain this rule by taking examples consider number 34568276, we have to calculate the reminder on diving this number by 7, 11, 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
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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
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Is this maths trick helpful? (495) (195)
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To calculate reminder on dividing the number by 3
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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
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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
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Is this maths trick helpful? (379) (142)
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To calculate reminder on dividing the number by 3
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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
-------------------------------------------------
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
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Is this maths trick helpful? (216) (103)
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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
-------------------------------------------------
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
-------------------------------------------------
Is this maths trick helpful? (197) (94)
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Square of numbers near to 100
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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
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Example.
An other case arises
110^2 = (110+10)----100 = (120+1)----00 = 12100 similarly 89^2 = (89-11)----121 = (78+1)----21 = 7921
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Is this maths trick helpful? (414) (159)
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Square of any 2 digit number
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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
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Example.
Here an extra case arises
Consider the following examples for that
91^2 = [9^2][1^2]+20*9*1 = 8101+180 = 8281
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Is this maths trick helpful? (660) (231)
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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 (You can’t use this rule for other numbers)
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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.
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Example.
Understand the rule by 1 more example
78*72 = [7*(7+1)][8*2] = 5616
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Is this maths trick helpful? (335) (105)
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Multiplication of two numbers that differ by 6 (This trick only works if you have memorized or can quickly calculate the squares of numbers.
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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
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Example.
Understand the rule by 1 more example
997*1003 = 1000^2 - 9 = 999991
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Is this maths trick helpful? (231) (94)
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Multiplication of two numbers that differ by 4 (This trick only works if you have memorized or can quickly calculate the squares of numbers.
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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
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Example.
Understand the rule by 1 more example
148*152 = 150^2 - 4 = 22496
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Is this maths trick helpful? (203) (64)
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Multiplication of two numbers that differ by 2 (This trick only works if you have memorized or can quickly calculate the squares of numbers.
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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
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Example.
Understand the rule by 1 more example
49*51 = 50^2 - 1 = 2500 - 1 = 2499
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Is this maths trick helpful? (169) (47)
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Multiplication of 125 with any number (You can't use this rule for other numbers)
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Let me explain this rule by taking examples
1. 93*125 = 93000/8 = 11625.
2. 137*125 = 137000/8 = 17125.
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Example.
Understand the rule by 1 more example
3786*125 = 3786000/8 = 473250.
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Is this maths trick helpful? (221) (88)
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Multiplication of 25 with any number (You can't use this rule for other numbers)
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Let me explain this rule by taking examples
1. 67*25 = 6700/4 = 1675.
2. 298*25 = 29800/4 = 7450.
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Example.
Understand the rule by 1 more example
5923*25 = 592300/4 = 148075.
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Is this maths trick helpful? (205) (53)
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Multiplication of 5 with any number (You can't use this rule for other numbers)
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Let me explain this rule by taking examples
1. 49*5 = 490/2 = 245.
2. 453*5 = 4530/2 = 2265.
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Example.
Understand the rule by 1 more example
5649*5 = 56490/2 = 28245.
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Is this maths trick helpful? (178) (57)
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Multiplication of 5 with any number (You can't use this rule for other numbers)
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Let me explain this rule by taking examples
1. 49*5 = 490/2 = 245.
2. 453*5 = 4530/2 = 2265.
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Example.
Understand the rule by 1 more example
5649*5 = 56490/2 = 28245.
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Is this maths trick helpful? (143) (56)
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Multiplication of 999 with any number (You can\'t use this rule for other numbers)
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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.
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Example.
Understand the rule by 1 more example
3825*999 = 3825*(1000-1) = 3825000-3825 = 3821175
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Is this maths trick helpful? (161) (45)
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Multiplication of 99 with any number (You can't use this rule for other numbers)
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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.
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Example.
Example.
Understand the rule by 1 more example
2841*99 = 2841*(100-1) = 284100-2841 = 281259
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Is this maths trick helpful? (149) (40)
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Multiplication of 99 with any number (You can't use this rule for other numbers)
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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.
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Example.
Example.
Understand the rule by 1 more example
2841*99 = 2841*(100-1) = 284100-2841 = 281259
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Is this maths trick helpful? (119) (40)
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Multiplication of 9 with any number (You can't use this rule for other numbers)
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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.
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Example.
Example.
Understand the rule by 1 more example
1864*9 = 1864*(10-1) = 18640-1864 = 16776
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Is this maths trick helpful? (163) (42)
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Multiplication of 11 with any number. (You can't use this rule for other numbers)
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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
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Example.
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
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Is this maths trick helpful? (427) (237)
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Square of any 2 digit number (You can't use this rule for other numbers)
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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.
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Example.
Understand the rule by 1 more example
78^2 = (78+2)*(78-2) + 2^2 = 80*76 + 4 = 6080+4 = 6084
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Is this maths trick helpful? (261) (163)
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Square of a 2 digit number ending with 5 (You can't use this rule for other numbers)
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Let me explain this rule by taking examples
35^2 = 3*(3+1) ---25 = 1225
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Example.
Other example
95^2 = 9*(9+1) ---25 = 9025
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Is this maths trick helpful? (334) (46)
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Multiplication of 11 with any number of 3 digits. (You can't use this rule for other numbers)
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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
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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
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Is this maths trick helpful? (227) (53)
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Multiplication of 11 with any number of 2 digits. (You can’t use this rule for other numbers)
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Let me explain this rule by taking examples
35*11 = 3---(3+5)---5 = 385
Means insert the sum of first and second digits between the two digits of the number
27*11 = 2---(2+7)---7 = 297
-------------------------------------------------
Example.
Here an extra case arises
Consider the following examples for that
39*11 = 3+1---(3+9-10)---9 = 429
Means, if sum of two digits of the number is greater than 10, then add 1 to first digit and subtract 10 to the inserted term.
78*11 = 7+1---(7+8-10)---8 = 858
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Is this maths trick helpful? (251) (52)
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Multiplication of any two numbers, both ranging from 11 to 19. (You can’t use this rule for other numbers)
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Let me explain this rule by taking examples
13*19 = (13+9)*10 + (3*9) = 220 + 27 = 247
Means add first number and last digit of the second number take zero in the third place of this number then add product of last digit of the two numbers in it.
-------------------------------------------------
Example.
18*14 = (18+4)*10 + (8*4) = 220 + 32 = 252

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...| Business Ethics | Individual Case 1 – The Lost Coupon | | | Table of Content I. Case Briefing 2 II. The Ethical Cycle 2 1.1 Moral Problem Statement 2 1.1.1. What is the problem? 2 1.1.2. Who has the problem? 2 1.1.3. What is the moral nature of the problem? 2 1.2 Problem Analysis 3 1.2.1. What are the stakeholders and their interests? 3 1.2.2. What are the moral values that are relevant in the situation? 3 1.2.3. State the relevant facts from the case, but also look for uncertain possible missing facts? 3 1.3 Options for Action 4 1.3.1. Black-and-white strategy 4 1.3.2. Creative middle way solutions 4 1.3.3. Cooperation strategy 4 1.3.4. Whistle blowing 4 III. Intuition 4 I. Case Briefing Joe and Ellen were in the elevator of the hotel which they invest in. In that elevator, there were also a group of three others and an individual. Joe, Ellen and the individual all overheard the group talked about how to play a scam on the hotel. The scam was planed based on a hotel policy, if one stays an additional night as a registered guest, one can receive an additional night coupon for half price; guests also can check in for one night only with half price, if they have a coupon from friend. This group of three was going to lie to the hotel, they had the coupon but they lost it. Afterwards, they all got front desk and waited in the line. The group was in the front, followed by Joe and...

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