Mental Math

Question 1

How do you determine the even divisibility of a number by 3 through 12?

Answer 1

3: sum of digits divisible by three
4: last two digits divisible by 4
5: last digit is 0 or 5
6: if ones digit is even, same as 3
7: starting at ones, multiply each digit following the pattern (1, 3, 2, -1, -3, -2). If sum of results is divisible by 7.
8: if hundreds place is even, divide last two digits by 8. If odd, subtract 4 from last two digits and divide them by 8
9: sun of digits divided by 9
10: doi
11: subtract the ones digit from the rest of the number, continue until end. If final result is 0, then yes.
12: if divisible by 4 and divisible by 3…

Question 2

How do you quickly calculate:
N / 5
N x .2
20% of N

Answer 2

(N * 2) / 10

Question 3

How can you quickly multiply two-digit numbers up to 19x19?

Answer 3

1. Add the second digit from the smaller number to the entire larger number.
2. Multiply by ten.
3. Add the product of the ones digits.

Question 4

How do you calculate the area of a circle? Circumference?

Volume of a sphere? Surface area?

Answer 4

2 pi r || pi d

pi r-squared || pi ( d-squared/4)

sphere
(4 pi r-cubed)/3

4 pi r-squared

Question 5

How can you roughly convert temperature from C to F? And vice versa?

Answer 5

Double C and add 30, or subtract 30 and halve.

Question 6

What’s a way to approximate the time it takes a number to double given an annual growth of N%, where N is aroundish 2-10?

Answer 6

72 / N

Question 7

How do you quickly calculate:

N * 9

Answer 7

(N * 10) - N

Question 8

How do you quickly calculate
N * 4
N * 8

Answer 8

N * 2 * 2

N * 2 * 2 * 2

Question 9

What’s a fantastic way to simplify multiplication and division problems?

Answer 9

Use factors

Question 10

How do you quickly calculate
N / 4
N / 8

Answer 10

(N / 2) / 2

((N /2) / 2 ) / 2

Question 11

What’s one potentially powerful way of multiplying two even numbers?

Answer 11

Halve one and double the other until it’s solved simply.

Question 12

Come up with an optimal multiplication/division strategy for each number from 2 to, say, 100?

Answer 12

Ok…

Question 13

What is my personal, genius, unproven method for add/subtract/multiply/divide?

Answer 13

Deal with numbers as sets of pairs.

So 1256 / 2 is really
12 / 2 next to 56 / 2
6 28
628

Question 14

How do you quickly find the sum of 1+2+3+…N?

Answer 14

(N + 1) * N/2