Powerful Math Magic

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By Mike O’Hern, Center Director of Mathnasium of West Knoxville

 

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Math tricks can come in handy on occasion. There are some fun ones for amazing your friends and the like. There are some that can be kind of useful in doing your math, like the one for multiples of nine using your fingers. Unfortunately, for learning and using your math in general, learning and using tricks ain’t gonna get it!

But, I’ve got some “tricks” that aren’t really tricks. That is, these are ways to find your answer using mathematical reasoning, and they work like a trick because they’re so simple! Often, when I’m teaching these to my students, I lean in close and say, “Don’t tell anyone about this, because this is far too powerful to put into the hands of just anybody…” So, in that spirit, I’ll let you read it, but only you, okay?

Multiply by four. So you want to know what 13 x 4 is. First, let’s recognize that 4 = 2 x 2. So 13 x 4 = 13 x 2 x 2, right? Okay, understanding that, we can see that in order to multiply by 4, we can instead multiply by 2 twice. But here’s the linguistic twist to this thing. Multiplying by 2 is called “doubling,” and when we say “double it,” it seems to be even easier! So 13 doubled is 26, and 26 doubled is 52. Just that easy. Can’t remember your 4 x 7 math fact? 7 doubled is 14 and 14 doubled is 28 – you got your fact back, jack!

Multiply by eight. Same as four, but double it again. 9 x 8 = 9 x 2 x 2 x 2. 9 doubled is 18, 18 doubled is 36, 36 doubled is 72.

(You might not have noticed this right off the bat, but those two work in reverse as well. Need to split the $24 check four ways? Cut it in half twice. Half of $24 is $12 and half of $12 is $6. Eight people sharing the cost of the $600 beach house rental? Half of $600 is $300, half of $300 is $150 and half of $150 is $75.)

I’ve got some ‘tricks’ that aren’t really tricks. That is, these are ways to find your answer using mathematical reasoning, and they work like a trick because they’re so simple!

Multiply by five. We can use the same principle we used with four and eight to multiply by five. But this time instead of multiplying twice, we’ll divide once and multiply once. Since 5 is 10 divided by 2, we can take our number and either cut it in half and multiply by 10 or multiply by 10 and then cut it in half. So what’s 12 x 5? Since 12 is even (thus easy to cut in half), I’ll say half of 12 is 6 and 6 x 10 is 60. What about 15? Since it’s odd, I think I’ll say 10 x 15 is 150, then half of 150 is 75. Either way you win!

As I’ve been writing this it has occurred to me that these are only simple methods, if one is already good at doubling and cutting in half. Then, I started thinking that I’m pretty good at the doubling thing, but that’s because it is natural for me to think about numbers. But, you don’t have to be a natural to end up with the same skill! Think how quickly you would get good at doubling numbers, if you were to practice doubling any number you saw – in your head – as you went through the day. Five birds in the air? Ten! Suite number 17? 34! Candy bar for 89 cents? $1.78! Gas for $3.33? $6.66! (But if the gas is $3.799 you’re allowed to round it off to $3.80, okay?)

Numerical fluency is not innate. It is learned by use. I might add that it will not be strong or permanent if you just memorize math facts – it comes with practice, and practice in varying circumstances makes it as strong as it can be!

Mike O’Hern, Center Director of Mathnasium of West Knoxville, earned his Bachelor’s Degree in Metallurgical Engineering at the University of Tennessee, Knoxville in 1988. He pursued graduate studies in Materials Science & Engineering while on the Research Staff at Oak Ridge National Laboratory. Mike has had a life-long love of mathematics and teaching, and feels that math is not about learning to be ready for the next math class – it’s about learning to think.

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