Just thought of this tonight. It took me 34 years to come up with sure, but I did it.
I have the 5 times tables memorized up to about five. Once I'm past 5 I tend to resort to adding and tricks meaning 5 x 7 isn't 35 but actually it's 5 x 6 and then 30 + 5 and then finally it's 35. Slow but it gets done.
It struck me tonight however that there's a much easier way. Make the 5 a .5 and then it's .5 x 7, right? That's 3.5. Then move the decimal point one space to the right. It's 35! But it's even simpler than that. When you multiply by .5 you're simply splitting the the number you're multiplying in half. So anytime you need to multiply by 5 just split the number in half and move your decimal point over one.
5 x 6493? Easy. Half of 6493 I can do in my head, it's 3246.5. Move the decimal and the answer to the original question is 32,465. Whoo hoo! Thrilling stuff! And never mind the implications for multiplying by 50, 500, 5000...
I know those people who've got the tables memorized will be slapping their foreheads over the awkwardness of this (trust me, compared to some of the gymnastics I go through to multiply things this is elegantly simple) but those who, like me, have never really memorized the times tables will thank me.
If they hadn't already figured this trick out that is. But it did take me 34 years and I am unusually bright and clever so I'm betting they didn't.
3 comments:
I love tricks like that. There are so many different ways to solve Math problems, and if you want to get anywhere with higher Math you need to be good at finding the "easy ways".
Of course, things like that don't get you too far when you need to show your work. That's something I did learn in school!
Unfortunately, the way schools teach, and the way we have accepted, is the "standard" (read: good enough for government work). Real math is based on the personal discovery you have made. All basic operations have methods that are better the the awful, rote Junk-Ed we learned in school. Those methods are only considered "tricks" by people who know no valuable mathematics. You discovered a pattern, and a logical way to use it. It's not a trick. You did a great thing.
"Showing the work" is what you did when you explained it. Unfortunately, (again) schools don't want to see good work, they want to see the work they are programmed to see, regardless of its value.
Take your Idea further. To multiply any whole number, no matter how large, tack a zero onto the end of the number, start from the left and divide by two (no, for crapsake don't show work!) Now see if you can use that method to figure out how to multiply 24*84,358 in your head. It's easier than learning the "five-times-table."
Why don't they teach this in school? Are you kidding? What if they taught kids to think, and then graduated them? They'd create a population that wouldn't support the BS that they are fed. What kind of little consumers would we have then?
Keep up the good work!
Brian (a.k.a. Professor Homunculus) at MathMojo.com
Thank you! Your comment threw a whole new light on the matter for me. I've been working under the impression that rote memorization is the proper way and those of us with 'tricks' were just getting by.
I'm off to visit your site!
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