I love little number tricks. This page is to help me remember them.
They’re very difficult to describe in words, and I don’t have any nice mathematical or graphical tools, so it is a bit hard to follow some of them. But go practice. They’re a lot of fun once you get the hang of them.
If you are genuinely interested and want something explained better, or if you have any more neat tricks for me., please leave a message below. But if you are a robot, don’t bother, I have a robot policing this site for spam 😉
Number Divisible by 3?
- Add all the digits of the number
- If the result is greater than 10, add the digits of the result
- When you get down to a one-digit number, if the number is 3, 6 or 9,
- Then the original number is divisible by 3
eg 123456789
- digits total 45
- 4 + 5 = 9
- therefore it is divisible by 3
eg 1236262
- digits total 22
- 2 + 2 = 4
- therefore it is not divisible by 3
Multiply by 5
- Divide the number by 2.
- Multiply the answer by 10.
eg 234 * 5
- 234 / 2 = 117
- 117 * 10 = 1170
- therefore the answer is 1170
eg 751 * 5
- 751 / 2 = 375.5
- 375.5 * 10 = 3755
- therefore the answer is 3755
Divide by 5
- Multiply the number by 2
- Divide the answer by 10.
eg 2340 / 5
- 2340 * 2 = 4680
- 4680 / 10 = 468
- therefore the answer is 468
eg 7515 / 5
- 7515 * 2 = 15030
- 15030 / 10 = 1503
- therefore the answer is 1503
Square a Number Ending in 5
Multiply the number that precedes the 5 by the next number higher than it, and then tack on 25.
- Remove the 5
- Multiply what is left by (itself + 1)
- Append 25
eg 75 squared
- the number without the 5 is 7
- 7 * 8 = 56
- therefore the answer is 5625
Number Divisible by 9?
- Add all the digits of the number
- If the result is greater than 10, add the digits of the result
- When you get down to a one-digit number, if the number is 9,
- Then the original number is divisible by 3
eg 123456789
- digits total 45
- 4 + 5 = 9
- therefore it is divisible by 9
eg 1236262
- digits total 22
- 2 + 2 = 4
- therefore it is not divisible by 9
Multiply by 11
- Take any number
- The digits of the number is as follows:
- If the number has digits abcde
- The answer has digits as follows:
- a(a+b)(b+c)(c+d)(d+e)e
- If any single calculation is greater than 10
- Carry the one as per normal rules of addition
Another way of saying it is, working right to left:
- The right-most digit is the last digit of the original number
- Add each number to the digit immediately preceding it
- Write down the answer
- If the answer is greater than 10, then carry one to the next sum to the left
- When there is only one number left, write that down, optionally adding any carried one
eg 12342 * 11
- 1(1+2)(2+3)(3+4)(4+2)2
- simplifies to 135762
- therefore the answer is 135762
eg 75382 * 11
- 7(7+5)(5+3)(3+8)(8+2)2
- simplifies to 7(2 carry 1)(8)(1 carry 1)(0 carry 1) 2
- move the carries left gives (7+1)(2)(8+1)(1+1)(0)2
- and the answer is 829202
Number Divisible by 11?
- For any number with more than 1 digit
- Add up all the digits in positions 1, 3, 5 etc
- Add up all the digits in positions 2, 4, 6 etc
- If the two answers are equal, then the number is divisible by 11
- If the two numbers are not equal, subtract one from the other.
- If the result is divisible by 11, then the original number is divisible by 11
eg 5896
- 5 + 9 = 14
- 8 + 6 = 14
- therefore it is divisible by 11
eg 6235
- 6 + 3 = 9
- 2 + 5 = 7
- 9 – 7 = 2
- therefore it is not divisible by 11
eg 74688636
- 7 + 6 + 8 + 3 = 24
- 4 + 8 + 6 + 6 = 24
- therefore it is divisible by 11
eg 746886415
- 7 + 6 + 8 + 4 + 5 = 30
- 4 + 8 + 6 + 1 = 19
- 30 – 19 = 11
- therefore it is divisible by 11
Multiplication in your head
Working right to left:
- Multiply the rightmost digits together
- Write the last digit of the answer, carry the 10s
- In your mind, draw an X over the last two digits of both numbers
- Multiply the digit at top left corner with the digit at bottom right corner of the X
- Multiply the digit at the right corner with the digit at bottom left corner of the X
- Add the two numbers above
- Add any carries
- Right down the last digit and carry the 10s
- eg abCD * efGH – the result is (C * H) + (D * G)
- Move the X 1 place to the left, and repeat until you reach the end of the number
- Finally multiply the two digits on the left, and add the carries.
- If your final answer is greater than 10, now put in the carries.
If you’re doing this as a party trick, keep the digits low. It’s the carries that fall out of your head more than anything else.