3. Mental Mathematics

Question 1

What is the Addition Method?

Answer 1

1. A method for multiplying numbers by breaking the problem into sums of numbers. For example, 4 x 17 = (4 x 10) + (4 x 7) = 40 + 28 = 68 or 41 x 17 = (40 x 17) + (1 x 17) = 680 + 17 = 697.

Question 2

What is the Associative Law?

Answer 2

1. A law of multiplication that for any numbers a, b, c, (a x b) x c = a x (b x c). For example, 23 x 16 = 23 x (8 x 2) = (23 x 8) x 2. There is also an associative law of addition: (a + b) + c = a + (b + c).

Question 3

What is Benford’s Law?

Answer 3

1. The phenomenon that most of the numbers we encounter begin with smaller digits rather than larger digits. Specifically, for many real-world problems (from home addresses, to tax returns, to distances to galaxies), the first digit is N with probability log(N + 1) - log(N), where log(N) is the base-10 logarithm of N satisfying 10 to the log(N) = N

Question 4

What is the method of Casting out Nines?

Answer 4

1. (also known as the method of digit sums): A method of verifying an addition, subtraction, or multiplication problem by reducing each number in the problem to a 1-digit number obtained by adding the digits. For example, 67 sums to 13, which sums to 4, and 83 sums to 11, which sums to 2. When verifying that 67 + 83 = 150, we see that 150 sums to 6, which is consistent with 4 + 2 = 6. Where verifying 67 x 83 = 5561, we see that 5561 sums to 17 which sums to 8, which is consistent with 4 x 2 = 8

Question 5

What is the Close-Together Method?

Answer 5

1. A method for multiplying two numbers that are close together. When the close-together method is applied to 23 x 26, we calculate (20 x 29) + (2 x 6) = 580 +18 = 598

Question 6

What is a Complement?

Answer 6

1. The distance between a number and a convenient round number, typically, 100 or 1000. For example, the complement of 43 is 57 since 42 + 57 = 100

Question 7

What is the Create-a-Zero, Kill-a-Zero Method?

Answer 7

1. A method for testing whether a number is divisible by another number by adding or subtracting a multiple of the second number so that the original number ends in zero

Question 8

What is the Criss-Cross Method?

Answer 8

1. A quick method for multiplying numbers on paper. The answer is written from right to left, and nothing else is written down

Question 9

What is a Cube Root?

Answer 9

1. A number that, when cubed, produces a given number. For example, the cube root of 8 is 2 since 2 x 2 x 2 = 8

Question 10

What is Cubing?

Answer 10

1. Raising a number to the third power. For example, the cube of 4, denoted 4 to the 3rd, is equal to 64

Question 11

What is the Distributive Law?

Answer 11

1. The rule of arithmetic that combines addition with multiplication, specifically a x (b + c) = (a x b) + (a x c)

Question 12

What is the Factoring Method?

Answer 12

1. A method for multiplying numbers by factoring one of the numbers into smaller parts. For example, 35 x 14 = 35 x 2 x 7 = 70 x 7 = 490

Question 13

What is the Gregorian Calendar?

Answer 13

1. Established by Pope Gregory the 8th in 1582, it replaced the Julian calendar to more accurately reflect the length of the Earth’s average orbit around the Sun; it did so by allowing three fewer leap years for every 400 years. Under the Julian calendar, every 4 years was a leap year, even when the year was divisible by 100

Question 14

What is a Leap Year?

Answer 14

1. A year with 366 days. According to our Gregorian calendar, a year is usually a leap year if it is divisible by 4. However, if the year is divisible by 100 and not by 400, then it is not a leap year. For example, 1700, 1800, and 1900 are not leap years, but 2000 is a leap year. In the 21st century, 2004, 2008, …, 2096 are leap years, but 2100 is not a leap year

Question 15

What is the Left to Right Method?

Answer 15

1. The easiest way to do mental math

Question 16

What is the Major System?

Answer 16

1. A phonetic code that assigns consonant sounds to digits. For example 1 gets the t or d sound 2, gets the n sound, and so on. By inserting vowel sounds, numbers can be turned into words, which make them easier to remember. It is named after Major Beniowski, a leading memory expert in London, although the code was developed by Gregor von Feinagle and perfected by Aime Paris

Question 17

What is Math of Least Resistance?

Answer 17

1. Choosing the easiest mental calculating strategy among several possibilities. For example, to do the problem 43 x 28, it is easier to do 43 x 7 x 4 = 301 x 4 = 1204 than to do 43 x 4 x 7 = 172 x 7

Question 18

What is the Peg System?

Answer 18

1. A way to remember lists of objects, especially when the items of the list are given a number, such as the list of presidents, elements, or constitutional amendments. Each number is turned into a word using a phonetic code, and that work is linked to the object to be remembered.

Question 19

What is the Right to Left Method?

Answer 19

1. The harder way of doing mental math

Question 20

What is the Subtraction Method?

Answer 20

1. A method for multiplying number by turning the original problem into a subtraction problem. For example, 9 x 79 = (9 x 80) - (9 x 1) = 720 - 9 = 711, or 19 x 37 = (20 x 37) - (1 x 37) = 740 - 37 = 703

Question 21

What is Vedic Mathematics?

Answer 21

1. A collection of arithmetic and algebraic shortcut techniques, especially suitable for pencil and paper calculations, that were popularized by Bharati Krishna Tirthaji in the 20th century

Question 22

How do you add a 2 digit number with a 1 digit number?

Answer 22

1. Add the 1’s digits together, then add that sum to the 10’s digit.
2. ((52 +4) = (2 +4) + (50 + 6) = 56)

Question 23

How do you add two 2 digit numbers?

Answer 23

1. Add the 10’s digits, then the 1’s digits
2. ((62 + 24) = (60 + 20) + (2 + 4) = 86)

Question 24

How do you add two 3 digit numbers?

Answer 24

1. Add the first number by the 100’s digit of the other, then the 10’s, and finally the 1’s
2. ((314 + 159) = (314 + 100) + (414 + 59) + (414 + 50) + (464 + 9) = 473)

Question 25

What is the 2nd way to calculate two 3 digit numbers?

Answer 25

1. Find the compliment to make it a simpler problem
2. ((776 + 489) (489 = 500 - 11) (776 + 500 = 1276) - 11)

Question 26

How do you subtract two 2 digit numbers?

Answer 26

1. Subtract the digits in the 10’s place, then subtract the 1’s digits.