Mental Math with Tricks and Shortcuts

Addition

Method: Add left to proper

326 + 678 + 245 + 567 = 900, 1100, 1600, 1620, 1690, 1730, 1790, 1804, & 1816

Be aware: Search for alternatives to mix numbers to scale back the variety of steps to the answer. This was accomplished with 6+8 = 14 and 5+7 = 12 above. Search for alternatives to type 10, 100, 1000, and and many others. between numbers that aren’t essentially subsequent to one another. Apply!

Multiplication & Squaring

Some helpful formulae                                                 Examples

(a+b)² = a² + 2ab + b²                                                    49² = (40 + 9) ² = 1600 + 720 + 81 = 2401

(a-b) ² = a² –2ab + b²                                                      56² = (60 – 4) ² = 3600 – 480 + 16 = 3136

(a+b) (a-b) = a² – b²                                                       64 x 56 = (60 – 4) (60 + 4) = 3600 – 16 = 3584

(a+b) (c+d) = (ac + advert) + (bc + bd)                23 x 34 = (20 + 3) (30 + 4) = 600 + 80 + 90 + 12 = 782

(a+b) (c-d) = (ac – advert) + (bc – bd)                  34 x 78 = (30 + 4) (80 – 2) = 2400 –60 + 320 – 8 = 2652

(a-b) (c-d) = (ac – advert) – (bc – bd)                   67 x 86 = (70 – 3) (90 – 4) = 6300 – 280 – 270 + 12 = 5762

 

X = 1 to 9 & Y = Any Quantity

(X5) ² = 100X(X+1) + 25                                65² = 600(7) + 25 = 4200 + 25 = 4225

25 x Y = (Y x 100)/4                                      25 x 76 = 7600/4 = 1900

50 x Y = (Y x 100)/2                                      50 x 67 = 6700/2 = 3350

75 x Y = 3(Y x 100)/4                                    75 x 58 = (5800 x 3)/4 = 17400/4 = 4350

Sq. any Two Digit Quantity (a = 10’s digit & b = 1’s digit)

(ab)² = 100a² + 20(a x b) + b²                                   67² = 100(36) + 20(42) + 49 = 4489

Multiply any Two 2 Digit Numbers (a & c = 10’s digit, b & d = 1’a digit)

ab x cd = 100(a x c) + 10[(b x c) + (a x d)] + (b x d)                         53 x 68 = 3000 + 580 + 24 = 3604

Methods utilizing (X5) 2

(X5 – a) ² = (X5) ² – X5(2a) + a²)                    63² = (65 – 2) ² = 4225 – 260 + 4) = 3969

(X5 + a) ² = (X5) ² + X5(2a) + a²)                    67² = (65 + 2) ² = 4225 + 260 + 4) = 4489

Squaring Numbers 52 to 99

a² = [a – (100 – a)]100 + (100 – a) ²                       93² = (93 – 7)100 + 7² = 8649

Squaring Numbers 101 to 148

a² = [a + (a – 100)]100 + (a – 100) ²                     108² = (108 + 8)100 + 8² = 11664

Squaring Numbers close to 1000

a² = [a – (1000 – a)]1000 + (1000 – a) ²              994² = (994 – 6)1000 + 6 ² = 988036

a² = [a + (a – 1000)]1000 + (a – 1000) ²             1007² = (1007 + 7)1000 + 7² = 1014049

Squaring Numbers that finish in 1

a² = (a – 1) ² + 2a – 1                                        61 ² = 60 ² + 122 – 1 = 3600 + 121 = 3721

Squaring Numbers that finish in 4

a² = (a + 1)² – (2a + 1)                                      44² = 45² – (88 + 1) = 2025 – 89 = 1936

Squaring Numbers that finish in 6

a² = (a – 1)² + (2a – 1)                                       56² = 55² + 112 – 1 = 3025 + 111 = 3136

Squaring Numbers that finish in 9

a² = (a + 1) ² – (2a + 1)                                     79² = 80² – (158 + 1) = 6400 – 159 = 6341

 

Utilizing Squares to Assist Multiply

Two Numbers that Differ by 1

If a > b then a x b = a² – a                               35 x 34 = 1225 – 35 = 1190

If a < b then a x b = a² + a                               35 x 36 = 1225 + 35 = 1260

Two Numbers that Differ by 2

a x b = [(a + b)/2]² -1                                       26 x 28 = 27² -1 = 729 – 1 = 728

Two Numbers that Differ by 3 (a < b)

a x b = (a + 1)² + (a – 1)                                  26 x 29 = 27² + 25 = 729 + 25 = 754

Two Numbers that Differ by 4

a x b = [(a + b)/2]² – 4                                     64 x 68 = 66² – 4 = 4356 – 4 = 4352

Two Numbers that Differ by 6

a x b = [(a + b)/2]² – 9                                     51 x 57 = 54² – 9 = 2916 – 9 = 2907

Two Numbers that Differ by an Even Quantity: a < b and c = (b – a)/2

a x b = [(a + b)/2]² – c²                                                 59 x 67 = 63² – 4² = 3969 – 16 = 3953

Two Numbers that Differ by an Odd Quantity: a < b and c = [1 + (b – a)]/2

a x b = (a + c)² – [b + (c –1)²]              79 x 92 = 86² – (92 + 36) = 7396 – 128 = 7268

 

Different Multiplying Strategies

Multiplying by 11

a x 11 = a + 10a                                              76 x 11 = 76 + 760 = 836

a x 11 = If a > 9 insert a 0 between digits and

add sum of digits x 10                                    76 x 11 = 706 + 130 = 836

Multiplying by Different Two Digit Numbers Ending in 1 (X = 1 to 9)

a x X1 = a + X0a                                            63 x 41 = 63 + (40 x 63) = 63 + 2520 = 2583

Multiplying with Numbers Ending in 5 (X = 1 to 9)

a x X5 = a/2 x 2(X5)                                       83 x 45 = 41.5 x 90 = 415 x 9 = 3735

Multiplying by 15

a x 15 = (a + a/2) x                                          10 77 x 15 = (77 + 38.5) x 10 = 1155

Multiplying by 45

a x 45 = 50a – 50a/10                                      59 x 45 = 2950 – 295 = 2655

Multiplying by 55

a x 55 = 50a + 50a/10                                                 67 x 55 = 3350 + 335 = 3685

Multiplying by Two Digit Numbers that Finish in 9 (X = 1 to 9)

a x X9 = (X9 + 1)a – a                                    47 x 29 = (30 x 47) – 47 = 1410 – 47 = 1363

Multiplying by Multiples of 9 (b = a number of of 9 as much as 9 x 9)

a x b = spherical b as much as subsequent highest 0               29 x 54 = 29 x 60 – (29 x 60)/10 = 1740 – 174 = 1566

multiply then subtract 1/10 of end result

Multiplying by Multiples of 99 (b = a number of of 99 as much as 99 x 10)

a x b = spherical as much as subsequent highest 0                  38 x 396 = 38 x 400 – (38 x 400)/100 = 15200 – 152 = 15048

multiply after which subtract 1/100 of end result

SUBTRACTION

 

Strategies:

1) Study to calculate from left to proper: 1427 – 698 = (800 – 100) + (30 – 10) + 9 = 729

2) Assume by way of what quantity added to the smaller equals the bigger: 785 – 342 = 443 (left to proper)

3) Add a quantity to the bigger to spherical to subsequent highest 0; then add similar quantity to the smaller and subtract:

496 – 279 = (496 + 4) – (279 + 4) = 500 – 283 = 217 (left to proper)

4) Add a quantity to the smaller to spherical to the following highest 10, 100, 1000 and and many others.; then subtract and add

the identical quantity to the end result to get the reply: 721 – 587 = 721 – (587 + 13) = (721 – 600) + 13 = 134

5) Subtract a quantity from every quantity after which subtract: 829 – 534 = 795 – 500 = 295

 

DIVISION

 

Strategies:                                                    Examples

Divide by components of divisor one by one:        1344/24 = (1344/6)/4 = 224/4 = 56

Methodology of Brief Division

340 ————— Remainders (3, 4, and 0 throughout calculations)

7)1792

256 ———————Reply

Divide each divisor and dividend by similar quantity to get a brief division drawback

                                                     10

972/27 divide each by 9 = 3)108

                                                 36

Dividing by 5, 50, 500, and and many others.: Multiply by 2 after which divide by 10, 100, 1000, and and many others.

365/5 = 730/10 = 73

Dividing by 25, 250, 2500, and and many others.: Multiply by 4 and divide by 100, 1000, 10000, and and many others.

Dividing by 125: Multiply by 8 after which divide by 1000

36125/125 = 289000/1000 = 289

It may be divided evenly by:

2 if the quantity ends in 0, 2, 4, 6, and eight

3 if the sum of the digits within the quantity is divisible by 3

4 if the quantity ends in 00 or a 2 digit quantity divisible by 4

5 if the quantity ends in 0 or 5

6 if the quantity is even and the sum of the digits is divisible by 3

7 sorry, you will need to simply do this one

8 if the final three digits are 000 or divisible by 8

9 if the sum of the digits are divisible by 9

10 if the quantity ends in 0

11 if the quantity has an excellent variety of digits which might be all the identical: 33, 4444, 777777, and and many others.

11 if, starting from the best, subtracting the smaller of the sums of the even digits and odd digits

ends in a quantity equal to 0 or divisible by 11:

406857/11 Even = 15 Odd = 15 = 0

1049807/11 Even = 9 Odd = 20 = 11

12 if check for divisibility by 3 & 4 work

15 if check for divisibility by 3 & 5 work

Others by utilizing checks above in numerous multiplication combos

USE ESTIMATES Use estimates to examine your solutions. Get within the behavior of doing this for all calculations.

Video

Cash and Finance

• $1/hour = $2000/12 months** (derivation)

• Earn $25/hour? That’s about 50k/12 months.

• Make 200k/12 months? That’s about $100/hour. This assumes a 40-hour work week.

• $20/week = $1000/12 months** (derivation)

• Spend $20/week at Starbucks? That’s a cool grand a 12 months.

Rule of 72: Years To Double = 72/Curiosity Price (derivation)

• Have an funding rising at 10% curiosity? It should double in 7.2 years.
• Need your funding to double in 5 years? You want 72/5 or about 15% curiosity.
• Rising at 2% every week? You’ll double in 72/2 or 36 weeks. You need to use this rule for any period of time, not simply years.
• Inflation at 4%? It should halve your cash in 72/4 or 18 years.

Infographic: Psychological Math Shortcuts for Poker – Pink Chip Poker

https://redchippoker.com/infographic-mental-math-shortcuts-for-poker

Revealed: Aug 24, 2015Author: Doug HullEstimated Studying Time: 1 min

Infographic: Psychological Math Shortcuts for Poker. 6. Poker is a recreation of math, however not everyone thinks math is a recreation. Doug Hull got down to change that with Poker Work Guide for Math Geeks, a “Sudoku e-book for poker” that presents the reader with a bevy of poker-specific mathematical workout routines to flex their grey matter. In the event you’re already geeked …

Arthur T. Benjamin, Ph.D. –

iranischool.com

2017-7-25 · Psychological Math: The Mathemagician’s Information to Lightning Calculation and Wonderful Math Methods. Proli¿ c math and science author Martin Gardner calls it “the clearest, easiest, most entertaining, and greatest e-book but on the artwork of calculating in your head.” An avid recreation participant, Professor Benjamin was winner of the American Backgammon Tour in 1997.

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The distinction between two sq. numbers is the product of their sq. roots

If you recognize the sq. of a quantity, you may simply discover the sq. of the following quantity. Say you recognize that 10*10=100. So 11*11 = 100+10+11 = 121. So 12*12 = 121+11+12 = 144. So 13*13 = 144+12+13 = 169. And so forth.

Math Trick For Multiplying 2-Digit 3-Digit Numbers

https://www.onlinemathlearning.com/math-trick-multiply-2-digit.html

Find out how to do psychological math for multiplying 2-digit numbers and 3-digit numbers shortly and effectively, train or reinforce some math ideas and expertise, Enjoyable Quick Multiplication Trick, multiply 3 digit numbers by 2 digit numbers mentally, …

7 Fraction ideas and tips –

www.moomoomath.com

For some folks the phrase "Fractions" just isn’t a cheerful phrase. Many individuals don't like including fractions,or subtracting fractions as a result of it has all the time been very complicated or irritating. Listed below are 10 confirmed ideas,tips, or useful data that may assist everybody perceive slightly bit higher.

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Convert temperatures

To roughly convert from Celsius to Fahrenheit, multiply by 2 and add 30. From Fahrenheit to Celsius, subtract 30 and divide by 2. (To extra exactly convert C to F, multiply by 1.8 and add 32.)

The order is vital: The addition/subtraction is all the time nearer to the Fahrenheit facet of the conversion. In the event you neglect the order, you recognize that 32° F = 0° C, so you may check your system in opposition to that.

Or simply memorise that room temperature is about 20–22 °C or 68–72 °F, and regular physique temperature is round 36-37° C or 97-99° F, depending on several factors.

Vital Psychological Heuristics

Tversky and Kahneman’s 1974 work, Judgment under Uncertainty: Heuristics and Biases, launched three key traits: representativeness, anchoring and adjustment, and availability. 

The representativeness heuristic permits folks to evaluate the chance that an object belongs in a common class or class based mostly on how comparable the thing is to members of that class.

To elucidate the representativeness heuristic, Tversky and Kahneman supplied the instance of a person named Steve, who’s “very shy and withdrawn, invariably useful, however with little curiosity in folks or actuality. A meek and tidy soul, he has a necessity for order and construction, and a ardour for element.” What’s the likelihood that Steve works in a selected occupation (e.g. librarian or physician)? The researchers concluded that, when requested to evaluate this likelihood, people would make their judgment based mostly on how comparable Steve appeared to the stereotype of the given occupation.

The anchoring and adjustment heuristic permits folks to estimate a quantity by beginning at an preliminary worth (the “anchor”) and adjusting that worth up or down. Nevertheless, totally different preliminary values result in totally different estimates, that are in flip influenced by the preliminary worth.

To exhibit the anchoring and adjustment heuristic, Tversky and Kahneman requested contributors to estimate the proportion of African international locations within the UN. They discovered that, if contributors got an preliminary estimate as a part of the query (for instance, is the actual share greater or decrease than 65%?), their solutions have been moderately near the preliminary worth, thus seeming to be "anchored" to the primary worth they heard.

The availability heuristic permits folks to evaluate how usually an occasion happens or how probably it would happen, based mostly on how simply that occasion will be delivered to thoughts. For instance, somebody would possibly estimate the proportion of middle-aged folks liable to a coronary heart assault by considering of the folks they know who’ve had coronary heart assaults.

Tversky and Kahneman's findings led to the event of the heuristics and biases analysis program. Subsequent works by researchers have launched plenty of different heuristics.

Who this course is for:

• These making ready for Math Olympiad, GMAT, GRE, CAT, MAT, SAT, Banking exams and another Math aggressive examination
• Anybody who needs to study brief tips to crack difficult issues in a goal time

Sources

• Gigerenzer, G., and Gaissmeier, W. “Heuristic choice making.” Annual Evaluation of Psychology, vol. 62, 2011, pp. 451-482.
• Hertwig, R., and Pachur, T. “Heuristics, history of.” In Worldwide Encyclopedia of the Social & Behavioral Sciences, 2 Version^nd, Elsevier, 2007.
• “Heuristics representativeness.” Cognitive Consonance.
• Simon. H. A. “A behavioral model of rational choice.” The Quarterly Journal of Economics, vol. 69, no. 1, 1955, pp. 99-118.
• Tversky, A., and Kahneman, D. “Judgment under uncertainty: Heuristics and biases.” Science, vol. 185, no. 4157, pp. 1124-1131.

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