Math ... My 8 year old son came up with a way to do multiplication that makes it easy to do large #s

[masmdu]

So, my 8 year old son was in the bathroom and he calls out to me so we could talk.

He said he found a way to do "hard" multiplication.

I've never heard of this so it may already be out there but even if it is not original to my son, damn if he isn't smart to come up with it independantly.

He explained it to me and then I helped him put it into the language of math.

This will allow you to multiply any number by 6 or factors or multiples of 6.


6*17=102

Here's how:

6*x = x / 2 * 10 + x

6*17 = 17/2 {gives 8.5} * 10 {gives 85} + 17 {gives 102}

Wow!

With multiples of 6 just multiply final answer by the other (non 6)factor.

So, 18*17 = {17/2 {gives 8.5} * 10 {gives 85} + 17 {gives 102}} * 3 (b/c 18/6=3) = 306


Now larger.

6*348

6*348 = 348/2 {gives 174} * 10 {gives 1740} + 348 {2088}


And on and on and on.

I've never been quick with math, especially doing largish multiplication equations in my head but now I can do quite a few thanks to one hell of a cleaver little boy.

[FiveGoodMen]

1. IOW, 6x = 5x + x

[EOTE]

2. Yeah, that hardly seems significant to me.

Also 7x = 5x + 2x
and
8x = 5x + 3x.

On edit: It sure sounds like a smart 8 year old, I just don't know if that will help many people. I find I multiply by five in one step rather than dividing by 10 and multiplying by 2. And if you find it easier to multiply by 5s or 10s, you can always then add the remainder and multiply again.

[masmdu]

7. But 6* 56 = 5*56 + 56 is not as simple to figure out as when it is divided my 2 then multipled 10

[EOTE]

11. I think most adults do that automatically. At least with 5s.

I know that my head is dividing it up into two processes, but I've done it so many times it becomes second nature.

[masmdu]

3. yeah but doing division by 2 and multiplying by 10 is much easier to do

[FiveGoodMen]

10. Yeah, I can see how that might help.

[hunter]

4. Check out Trachtenberg system...

I remember coming up with a few shortcuts on my own when I was a kid, and then my seventh grade teacher showed me this...

http://en.wikipedia.org/wiki/Trachtenberg_system

[masmdu]

9. Very cool...thanks for that

[Rabblevox]

19. BIG rec to the Trachtenburg System! It saved my maths-challenged butt in Middle-School. /nt

[dsc]

5. Here are a couple of more great tricks

If you want to square a number ending in 5, such as 25, then simply take 2*3 = 6 then end with 25 for 625. 75 squared would be 7*8 = 5625 and so on.

If you want to square a number close to 100, say 93, then take 100-93 = 7, first two digits are 93-7 = 86 last two are 7 squared = 49 so 8649. If your number is above 100 then you add instead of subtract. Thus 104 squared is 104 + 4 for 10816.

[TlalocW]

12. Squaring numbers in general

Two digit version

Example: 56
Go to the nearest number that ends with a zero
60
We went up 4 so go down 4.
52
Multiply together. Easier since we're dealing with a number that ends in 0.
3120
Add square of what we went up/down by
3120 + 16
Final answer: 3136

TlalocW

[flying rabbit]

24. OK

that is pretty cool

[buczak]

6. 11 works similiar

11 * x = 10 * x + x

11 * 12 = 120 + 12 = 132

It's good to learn those tricks.

It make learning easier and you'll understand some principles of algebra.

Smart kid. :)

[Fire Walk With Me]

8. It's easier to add large numbers by breaking them down.

Large first, then add the smaller and smaller numbers. This also works for multiplication.

1065 + 943

1000 + 900 = 1900

65 + 43 = 108

1900 + 108 = 2008

Don't have a calculator, hope that's right ;)

[rurallib]

13. great that an 8year old is manipulating numbers like that

We have been working with elementary kids for the past 6 years and the kids have been so scared of numbers. It has taken years for them to realize that multiplication if just fast addition.

I think there are several methods out there, but the big thing is to understand the arithmetic so they can go on to more complex math concepts

way to go kid!

[immoderate]

14. He has discovered the associative and commutative properties of multiplication.

Watch what happens when he learns that you can multiply by 25, by dividing by 4. :think:

--imm

[dipsydoodle]

15. So does that work if you want to

Square Graham's number. :)

[FormerDittoHead]

16. You might find this interesting - Egyptian math.

http://www.youtube.com/watch?v=Ih1ZWE3pe9o

One thing you have to remember, the way we learn math is CULTURAL. This is *not* "only one way" to do a math problem.

For example, we're taught how to subtract numbers and do subtraction, etc.

But when I went to college it was adding negative numbers. Yes, it's the same thing but the FORM was different.

So it is with this example of Egyptian math.

ANOTHER ASPECT of this is to show how the ancients, if you will, were NOT stupid!

For example, while most everywhere we use decimal numbers to represent fractions, they're not as accurate as fractions.

If I wrote 0.3333333333 to represent "one third" there would ALWAY be a degree (no matter how small) of inaccuracy.

If I wrote 1/3, however - that number would be ABSOLUTELY PERFECT - more accurate than any supercomputer can carry out .33333....

I would also check out some books and stuff about games with numbers and such. The more *time* your boys plays around with numbers, the less abstract they will be to him.

[Warpy]

18. AKA, "How to Count with your Fingers"

http://www.youtube.com/watch?v=apCLHmPsC68

It's come in remarkably handy when I've been doing a 40 inch wide, eight end per inch warp on my loom.

[FormerDittoHead]

20. Really?I don't see how you can do on your fingers what's in the video of Egyptian multiplication.n/t

[Warpy]

17. Double and halve served me better when I was a kid

6*17 = 3*34= 102. It's just less cumbersome for me. Teachers disliked the "I did it in my head" and surrounded me with math dunderheads to make sure I wasn't cheating. All it did was point out which of them had cheated since they couldn't explain how they'd gotten the answer without copying it from me.

[EC]

21. Back in 7th grade I was put into an experimental math

class (for math geeks in the 60's) that worked problems like that. We also learned other methods being experimented with at the time. I don't remember any of it of course, the next year I started hanging with the cool kids and didn't have time for that kind of stuff, I was much more into art anyway.

[uppityperson]

22. very good for him to figure this out. Is something evenly divisible by 3? Multiplying by 9....

To find out if something is evenly divisible by 3, add up all the numbers in a number, keep doing so until you end up with 1 number. If it is 3, 6, or 9, it is evenly divisible by 3.
Example: 13,403,204,766. Add up each individual # to get 36. Add up 3+6=9. Yes, this number is evenly divisible by 3.

I use it for smaller numbers in daily use, but it works for all.

9's are great. Notice the right hand numbers. First one goes 012345678, the second goes 987654321. AND if you add up the right hand numbers, they equal 9. (0+9, 1+8, 2+7,etc).
9X1=09
9X2=18
9X3=27
9X4=36
9X5=45
9X6=54
9X7=63
9X8=72
9X9=81

[hfojvt]

23. not exactly chisanbop

How about a formula for addition?

How much is 1 + 2 + 3 + 4?

It's 10 or 4*5/2

Not that cool for just 4, but how about

1+2+3+4+5+6+7+8+9+10

55 or 10*11/2

or how about

1+2+3+....+98+99?

It's 4950 or 99*100/2


That's one of the basic formulas for proof by induction.