Just a list of cool little mathematical tricks and other cool things I wanted to make.
Every number divisible by three (to give whole numbers) has a digit sum that is a multiple of 3.
Eg. 186/3=62 (1+8+6=15, 15/3=5 and 1+5=6, 6/3=2)
For dividing by four the last two digits have to either by 00 or equal something divisible by four itself.
Eg. 400 or 35644/4=8911 (44/4=11)
Dividing by six is the same as for dividing by 3 but the number must be even!
Now for numbers divisible by seven it gets a bit trickier. Multiply the last number by 2 and then subtract this number from the remaining digits, if this is a multiple of seven you can divide the original number by seven.
Eg. 287. 7x2=14, 28-14=14 (which is of course 7x2). 287/7=41.
Dividing by 8 is similar to that of 4, the last 3 digits either have to be 000 or equal a number that itself is divisible by 8.
Every number divisible by 9 has a digit sum equal to a multiple of 9 (which in turn has a digit sum equal to another multiple of 9 and so forth until you reach 9 itself).
Eg. 27/9=3 (2+7=9), 513/9=57 (5+1+3=9)
An interesting application of this is to get someone to think of a number that has 2 or more digits, next get them to reverse this number and subtract the smaller one from the larger one. From this number get them to select a digit and get them to tell you all the other digits. In this scenario the number they arrived at is divisible by 9, so to calculate which number they picked simply add up and then work out the remaining number to get to the closest multiple of 9.
Similarly the nine times table can be worked out using your fingers. Hold your fingers out in front of you and read them from left to right. If you want to multiply 9 by 3 lower your 3rd finger (middle finger of your left hand) this leaves you with 2 fingers stretched out to the left and 7 on the right to give 27!
An interesting trick for calculating people’s ages. Get a volunteer to take their age, multiply by 10 and then subtract any multiple of 9 up to (9x9). At this stage you can then work out their age by adding the number made by the first two digits to the latter.
Eg. Say the person is 32 years old. 32x10=320, 320-(9x3)=293, 29+3=32.
A not so amazing (but incredibly useful) tool is that percentages work both ways, for example 43% of 50 dollars is the same as 50% of 43 dollars (but easier to calculate).
Another trick that is quite interesting is the 1089 trick. For this pick any three digits to give a number, reverse this number and subtract the smaller number from the larger one. Next reverse the answer of the last step and add it to the actual answer of the last step, every time you will arrive at the same answer: 1089 (or the square of 33 as I like to call it).
Eg. 356. 653-356=297, 297+792=1089.
A nice little trick to impress people by cheating at addition is to get a person to write down two single digit numbers, one above the other. Then add and continue to add the numbers to the number above it. Once you reach a list of 10 have a competition to add up the numbers as fast as possible, or cheat by simply multiplying the 4th number from the bottom by 11.
The first ten squares can be calculated by adding consecutive primes.
Eg. 2x2=4 (1+3) or 4x4=16 (1+3+5+7)
There’s also a fairly neat trick for multiplying by 11 (for numbers greater than 10). Say I want to multiply 11 by 34, instead of simply saying 34x10+34 I could do 3|(3+4)|4=374 but for another such as 11x66 (6|(6+6)|6) there is a trick. The answer is not 6666 but in fact 726 ((6|(12)|6) but carry the one and add it to the first 6).
