Thread: Math Tricks

Do you all know of any cool math tricks? Basically shortcuts for basic ( or maybe not so basic ) math?

For example :
do you know the trick for any single digit number multiplied by 9?
hold out your hands so you can see all 10 fingers
then, let's say you want to know what 9x4 is
put down the 4th finger from the left.
the number of fingers remaining to the left of the finger that's down is the first digit of the answer
and the number of fingers to the right is the 2nd digit of the answer

Cool! I always remember it this way:

First digit is one less than the number being multiplied by 9.

Second digit is 10 minus the number being multiplied by 9.

At least until 9 x 9, anyway.

Reminds me of the movie Stand and Deliver.

I used to use a sort of short cut with the number 11 where you can write the answer out immediately no matter how large the multipying number is. You start from the right of the multiplying number, keep the first and last digit of that number at the beginning and end, but add numbers next to each other, carrying the one over to the next pair (or left hand number) when needed. It's not really a trick, just a sort of short hand way to do it with basic addition instead of writing it all out.

11x34=374 11x374=4114 11x374546253594=4020008789534

Not very useful though and it can be hard to keep your place with larger numbers.

Originally Posted by mugaliens

Cool! I always remember it this way:

First digit is one less than the number being multiplied by 9.

Second digit is 10 minus the number being multiplied by 9.

At least until 9 x 9, anyway.

There are only nine possibilities (or ten, if you count multiplication by zero), and I have them all pretty much permanently stamped into my brain . . .

Memorizing squares is easy, there aren't a lot of them, and there is a regular pattern. Once you've memorized them, you can use them to do more complicated products. I first read about this when I was a kid, in the book Cheaper By the Dozen.

For instance, to multiply 37 times 43, find the number halfway between, and add/subtract 3: (40-3) x (40+3), which equals 40^2 - 3^2 or 1591.

Determining whether a number is divisible by 9 (or 3, or 5, or 10, or 2, or 11) is pretty easy, most of us learn how early on. Here is a webpage that tackles divisibility tricks for all numbers:
Nerd Paradise : Divisibility Rules for Arbitrary Divisors

I always liked the 1/7ths decimals...
1/7 = 0.142857142857...
2/7 = 0.285714285714...
3/7 = 0.428571428571...
4/7 = 0.571428571428...
5/7 = 0.714285714285...
6/7 = 0.857142857142...

and another fun one is the 1/13 fractions. Work these out and look at them. Similar to this but with one more feature.

In fact, all recurring decimal expansions of fractions of 1/f (doesn't apply to 1/2 and 1/5 because they divide the base 10) have f-1 digits recurring or an exact fraction of this.

The one I like is 1/89 = .011235... Fibonnacci numbers!

Originally Posted by grapes

The one I like is 1/89 = .011235... Fibonnacci numbers!

But it only allows 1 column per member of the series, so we have to overlap 13, 21, 34 etc and add the digits together. It really does keep working!

Another very similar one to this is 1/81 which gives 0.012345679012345679... with the digit 8 missing! But if we apply the same logic of actually putting in 8, 9, 10, 11, 12 etc moving just one column to the right each time, then we get the decimal expansion correctly. "8" is just hiding in there.

Originally Posted by RayTomes

But it only allows 1 column per member of the series, so we have to overlap 13, 21, 34 etc and add the digits together. It really does keep working!

All the way to infinity!

Another very similar one to this is 1/81 which gives 0.012345679012345679... with the digit 8 missing! But if we apply the same logic of actually putting in 8, 9, 10, 11, 12 etc moving just one column to the right each time, then we get the decimal expansion correctly. "8" is just hiding in there.

But I think that system only goes so far before it breaks down...