Disclaimer to Disclaimer: Dan does not regularly talk or write in the third person singular, it just ended up that way... that is all.
Occasionally, you know, when I'm sitting around figuring out how things work, I'll come some neat math guava moment. It's pretty cool and I hope you enjoy them. E-mail me at danprime@hotmail.com if you have any suggestions, spot errors or just plain feedback.
This trick is pretty neat and almost trivial in the initial stages but then I started thinking-why can't I use this trick for larger numbers? It was kind of funny because I thought I needed to use my toes, so when I first started wondering I actually tried to count my toes and fingers-and well just read on.
Foreword
You need to know how to count and number fingers... that's it.
Onward
This trick isn't as obvious but it's really handy (sorry couldn't resist:)
We'll do the 9 multiplication table for 1 through 10. Then we'll apply it
for more numbers. Say I want to know what 4 x 9 is (assuming you don't have
it memorized yet).
1)Hold out your two hands in front of you
2)Number your fingers from left to right starting 1 at the left pinky
and ending 10 on the right pinky.
3)If you want to multiply by 4 lower the number four finger (left index).
4)Count the number of fingers to the left of the lowered finger-this
is your first digit. i.e. 3 fingers are left pointing up.
5)Count the number of fingers to the right of the lowered finger-this
is your second digit. i.e. 6 fingers are left pointing up.
6)You now have your answer! 3 6 leads to 36
Why it works
If you ever noticed, you usually have 10 fingers (note this trick only works
with 10 fingers or 10 toes if you're talented:). Note that anytime you multiply
an integer (or whole number by nine) the digits of the product adds to nine
(for the simple cases). For example 2 times 9 is 18 right? Well, take 18 apart
and you get 1 and 8. 1 + 8 = 9. It works with any number try it out.
Now for the more complex cases...
Now what if you wanted to do higher numbers than 10 say 18 or 35? Do you think
you need more or less fingers?
Trick question! you don't need more or less you need the same number of fingers,
you just need to add a step. Watch, say we want to multiply 18 x 9 -you could
whip out your calculator or...
1)Hold your hands out
2)Number your fingers just like you did before
3)Lower the number 8 finger (right ring finger).
4)Count the number of fingers pointing up on the left i.e. 7
NOTE:This isn't your first digit yet!
5)Count the number of fingers pointing up on the right i.e.
2 NOTE: This IS your last digit.
6)Now look at the first digit of your multiplier i.e. 1 and multiply that
by 9, now add that to the number of fingers from step 5. This is your first
set of digits i.e. (1 x 9) + 7 = 16
7)Combine the numbers and bingo! you got 162!!! the right answer
Try 35 x 9:
1)Hold out your hands
2)Number your fingers
3)Lower the number five finger
4)Count to the left... 4
5)Count to the right... 5
6)Multiply the first digit of the multiplier (3) by 9 and add that to the
number on the left
i..e (3 x 9) + 4 = 27 + 4 = 31
7)Combine.... 31 5 leads to 315!!!
Practice and Application
Check out a Flash visualization and
practice!
Multiplying consecutive two-digit-five-ending numbers!
Please E-mail danprime@hotmail.com any questions, comments or things I left out, thanks!