Content material of the fabric

- Addition
- Video
- Money and Finance
- Infographic: Mental Math Shortcuts for Poker – Red Chip Poker
- Arthur T. Benjamin, Ph.D. –
- The difference between two square numbers is the product of their square roots
- Math Trick For Multiplying 2-Digit 3-Digit Numbers
- 7 Fraction tips and tricks –
- Convert temperatures
- Significant Psychological Heuristics
- Who this course is for:
- Sources

## 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} = a^{2} + 2ab + b^{2} 49^{2} = (40 + 9) ^{2} = 1600 + 720 + 81 = **2401**

(a-b) ^{2} = a^{2} –2ab + b^{2} 56^{2} = (60 – 4) ^{2} = 3600 – 480 + 16 = **3136**

(a+b) (a-b) = a^{2} – b^{2} 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 65^{2} = 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} = 100a^{2} + 20(a x b) + b^{2} 67^{2} = 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) + a^{2}) 63^{2} = (65 – 2) ^{2} = 4225 – 260 + 4) = **3969**

(X5 + a) ^{2} = (X5) ^{2} + X5(2a) + a^{2}) 67^{2} = (65 + 2) ^{2} = 4225 + 260 + 4) = **4489**

Squaring Numbers 52 to 99

a^{2} = [a – (100 – a)]100 + (100 – a) ^{2} 93^{2} = (93 – 7)100 + 7^{2} = **8649**

Squaring Numbers 101 to 148

a^{2} = [a + (a – 100)]100 + (a – 100) ^{2} 108^{2} = (108 + 8)100 + 8^{2} = **11664**

Squaring Numbers close to 1000

a^{2} = [a – (1000 – a)]1000 + (1000 – a) ^{2} 994^{2} = (994 – 6)1000 + 6 ^{2} = **988036**

a^{2} = [a + (a – 1000)]1000 + (a – 1000) ^{2} 1007^{2} = (1007 + 7)1000 + 7^{2} = **1014049**

Squaring Numbers that finish in 1

a^{2} = (a – 1) ^{2} + 2a – 1 61 ^{2} = 60 ^{2} + 122 – 1 = 3600 + 121 = **3721**

Squaring Numbers that finish in 4

a^{2} = (a + 1)^{2} – (2a + 1) 44^{2} = 45^{2} – (88 + 1) = 2025 – 89 = **1936**

Squaring Numbers that finish in 6

a^{2} = (a – 1)^{2} + (2a – 1) 56^{2} = 55^{2} + 112 – 1 = 3025 + 111 = **3136**

Squaring Numbers that finish in 9

a^{2} = (a + 1) ^{2} – (2a + 1) 79^{2} = 80^{2} – (158 + 1) = 6400 – 159 = **6341**

** **

**Utilizing Squares to Assist Multiply**

Two Numbers that Differ by 1

If a > b then a x b = a^{2} – a 35 x 34 = 1225 – 35 = **1190**

If a < b then a x b = a^{2} + a 35 x 36 = 1225 + 35 = **1260**

Two Numbers that Differ by 2

a x b = [(a + b)/2]^{2} -1 26 x 28 = 27^{2} -1 = 729 – 1 = **728**

Two Numbers that Differ by 3 (a < b)

a x b = (a + 1)^{2} + (a – 1) 26 x 29 = 27^{2} + 25 = 729 + 25 = **754**

Two Numbers that Differ by 4

a x b = [(a + b)/2]^{2} – 4 64 x 68 = 66^{2} – 4 = 4356 – 4 = **4352**

Two Numbers that Differ by 6

a x b = [(a + b)/2]^{2} – 9 51 x 57 = 54^{2} – 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} – c^{2} 59 x 67 = 63^{2} – 4^{2} = 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 = 86^{2} – (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-pokerRevealed: 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.

Seen 168 instances

## 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.htmlFind 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.

Seen 115 instances

## 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.