• Simple fahrenheit to celsius: `(F - 30) / 2 = C` , and `C*2 + 30 = F`
• Simple mph to kph or Miles to Kilometers : Just go up one on the fibonnaci sequence: `0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144`. So 80 mph = 130 kph, 130 miles = 210 km, etc.

Percentanges: e.g. 30% of 70 = 70% of 30 and this is always true. 40% of 60 is 60% of 40 and so on.

Multiplying by 9 with your hands: hold out your hands, palms down. You want to know 1x9, roll up your left pinkie… 9 fingers left so, the answer is 9. 2x9, lower the left ring finger. You have 1 finger, a space, then 8 fingers…answer is 18. 3x9, lower middle finger on left hand. 2 fingers, space, 7 fingers…27. 9x9, lower right ring finger, 8 fingers, space, 1 finger…81. This is not a great concept to explain with text.

Sum of series of numbers: what is the sum of 1 to 10…half way between 1 and 10 is 5. 1+10 is 11. 11x5=55. 1 to 100=(50x(100+1))=5050.

I used to know more but it has been about 15 years since I graduated from uni.

@joule
71Y

Divisibility tricks :) here are some of the more interesting ones:

• 3: digit sum is divisible by 3 (can repeatedly calculate the digit sum until you get to a single-digit number)
• 4: last two digits are divisible by 4
• 6: number is divisible by 2 and 3
• 7: pop the last digit off the number, multiply it by 2 and subtract it from what’s left of the number. Then, check if the new number is divisible by 7 (can repeat if the number is still pretty big) (you might end up with a negative number but it doesn’t really matter, just check whether or not it’s divisible by 7)
• 8: last 3 digits are divisible by 8
• 9: digit sum is divisible by 9

7 is probably the most confusing so I’ll add an example. Say you want to check if 161 is divisible by seven.

1. pop off the last digit, 1, leaving you with 16
2. multiply it by 2: 1 * 2 = 2
3. subtract it from what’s left: 16 - 2 = 14
4. 14 is divisibly by 7, so 161 is also divisible by 7
5. if you really wanted to keep going you could ( 1 - 4 * 2 = -7 which is also divisible by 7)

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@ster
31Y

It’s not used in computing large primes. We use computers for that and to check divisibility, you just divide and check the remainder.

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Ephera
31Y

Well, they do kind of do that, but in a more explicit way. We know that a number is not prime, if it’s a multiple of, well, anything but itself and 1. So, you can for example “sieve out” all even numbers, because all of those are multiples of two. And you can take choose a number that’s a multiple of 3 and then just sieve out all numbers that are that number+3, +6, +9 etc…

The actual sieving techniques are a little more crazy still, but that’s the general idea: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

@Doug
41Y

Most multiplication tables of 1-11 follow a pattern (Excluding 3 and 7). This helps me to know how a number might be divisible by something, or help me remember a multiplication table if I forget it.

• 1: Pretty obvious
• 2: The one’s place digit will end in 0, 2, 4, 6, 8
• 4: The one’s place digit only goes in the order of 0, 4, 8, 2, 6
• 5: The one’s place digit can only be 0 or 5
• 6: The one’s place digit can only be 0, 6, 2, 8, 4
• 8: Follows the one’s place digit restriction of 4, just in a different pattern.
• 9: Where N < 10, adding (N * 9)'s digits together will always make 9.
• 10: The one’s digit is always 0
• 11: Where N < 10, (N * 11)'s digits are always the same.
• 12: Where N < 5, (N * 12)'s one’s digit is double the ten’s digit.

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Mental calculation of decimal lorgarithms. Ye, not that cool unless you mess with pH. @ster
2
edit-2
1Y

What do you mean by “reduce” numbers? Divide them by 9?

EDIT: RIP I meant taking the remainder on division by 9

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@ster
21Y

Oh yeah that’s equivalent to taking the remainder on division by 9

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Ephera
21Y

I was gonna ask, how often that trick is relevant. I think, the last time I needed to calculate the digit sum was when I was taught in school about the digit sum.

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