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Feb. 8th, 2012
Casting out nines
It's a different way to check your math work than "doing it backwards". It's not perfect (you have a 1 in 9 chance of getting a false positive, and it seems that if you transpose two numbers it won't make a difference to the end result), but if you're mostly competent at basic arithmetic or just need a quick check, it's a lot of fun.
I taught it to Ana, but because "casting out" isn't a term in her vocabulary and because it's unlikely she'll ever learn it in school (so she doesn't really need to know the correct term) I called it "throwing away" the nines instead.
For multiplication, I stumbled across something called "Indian hand multiplication" (which is exactly what it sounds like, and even the "Indian" part seems to be accurate, not like "French" toast or "German" measles!) which is much niftier than the nines trick everybody knows. (That'd be the nines trick with your fingers, not the nines trick where you add up the digits. Fun fact, that second trick works with ANY base system. If you're working in base N, multiples of n-1 will always add up to n-1. So in base 12, multiples of 11 will always add up to 11, and in base 16 multiples of 15 will add up to 15 and so on.)
I can't describe it, I've yet to master it, but when I do you can bet I'm going to show the nieces!
http://www.murderousmaths.co.uk/books/BKMM3xft.htm
http://jollymaths.com/?page_id=7
SERIOUSLY. CLICK THE LINKS. It is absolutely worth it, especially if multiplication is your vexation.
It's a different way to check your math work than "doing it backwards". It's not perfect (you have a 1 in 9 chance of getting a false positive, and it seems that if you transpose two numbers it won't make a difference to the end result), but if you're mostly competent at basic arithmetic or just need a quick check, it's a lot of fun.
I taught it to Ana, but because "casting out" isn't a term in her vocabulary and because it's unlikely she'll ever learn it in school (so she doesn't really need to know the correct term) I called it "throwing away" the nines instead.
For multiplication, I stumbled across something called "Indian hand multiplication" (which is exactly what it sounds like, and even the "Indian" part seems to be accurate, not like "French" toast or "German" measles!) which is much niftier than the nines trick everybody knows. (That'd be the nines trick with your fingers, not the nines trick where you add up the digits. Fun fact, that second trick works with ANY base system. If you're working in base N, multiples of n-1 will always add up to n-1. So in base 12, multiples of 11 will always add up to 11, and in base 16 multiples of 15 will add up to 15 and so on.)
I can't describe it, I've yet to master it, but when I do you can bet I'm going to show the nieces!
http://www.murderousmaths.co.uk/books/BKMM3xft.htm
http://jollymaths.com/?page_id=7
SERIOUSLY. CLICK THE LINKS. It is absolutely worth it, especially if multiplication is your vexation.