Mental Math


Everybody has been stuck at some point in their lives without a calculator and too lazy to draw out 72 x 11 on paper to figure it out.  Or how about figuring out 9% of 60 in an instinct?  125 x 125?  No problem.  This week Perek brings a handful of useful tips and techniques to help you increase speed and ease for all your mental math needs.  As pointed out in the audio, at the beginning, it may help to write a couple things down.  Grab a paper and pen and follow along, the GoodGuys are already getting promotions and sportscars due to their newfound math skillz.  Below are some brief explanations of the techniques discussed.  Also check out the video below about the Soroban (abacus) we discuss at the end of the show.

Multiplying by 9

Multiply by 10 and subtract the original number from that result.  7×9?  taxe 7×10, and then subtract 7.  This helps more and more as numbers get larger.

Multiply by 11

For 2 digit numbers this couldn’t be easier.  Add the 2 digits together, and place that result in between the original 2 numbers.  72×11?  7 plus 2 is 9, put that 9 in between the original 7 and 2, to get 792.  To carry a 1 when the 2 numbers add up to more than 10, just add that 1 to the next digit to the left.  86×11?  8 plus 6 is 14, so keep the 4 and carry the 1.  Out the 4 in the middle and add 1 to the next digit to the left.  Did you get 946?  good.  You are already better than Mitch at mental math.

Multiply by 5

To increase the probability of doing this in your head, divide the number by 2.  If the original number is even, tag a 0 on the end of the halved result.  That’s it.  If the original number is odd, you will end up with a .5 once you divide by 2.  Just get rid of that decimal and you are done!  This is awesome on big numbers.  2,682×5?  Well, what’s half of 2682.  Most people can do THAT better than they could attempt to do that whole problem in their head.  Half of 2,682 = 1341.  Since 2682 is even, tag on a zero.  13,410.  There’s your answer.  For odd numbers, how about 4,215.  Half of that is 2,107.5.  Drop the decimal for 21,075.  Easy as pie.

Divide by 5

This is even easier to remember than multiplying by 5.  All you have to do is double the number, and then move the decimal one to the left.  193/5 seems difficult on its own.  but doubling 193 is easier.  193 doubled is 386.  Move that decimal over and you get 38.6.  193/5 is 38.6.

Square any number ending in 5

This one is a little more interesting, but still easier than the long way.  Take any number ending in 5, and forget about the 5.  So, 95×95?  That’s 95 squared.  forget about that 5, and all you have left is the 9.  Multiply the 9 by 1 + itself, so 9+1 = 10.  multiplying 9×10 is easy right?  90.  The last step is to tack on a 25 at the end.  9025.  95 squared is 9,025.  A little practice on this and you can do it in a couple of seconds.

Criss Cross Multiplication 

This concept I absolutely love.  It is so much easier to do in your head than the way we learned in school.  It’s going to be tough to describe it properly in words, so here’s a link to a video that can help!  This site has other examples that I duscussed as well.


Percentage flip rule

9% of 80, go!  That’s hard for me.  But the flip rule says that 9% of 80 is EQUAL to 80% of 9.  That’s easier for me.  I would take 10% of 9 (.9), and then multiply that times8 to get up to that 80%.  .9×8 = 7.2 (9×8 is 72, move that decimal back to get 7.2).  This is only really useful when one number is a multiple of 5 or 10.

 Day of week calculation

Warning!  Advanced maneuver in your head.  Not so bad, but just not exactly a clearly logical path (if you break it down it is, of course, totally logical).  Here is a link to a good site that lays it out:  http://www.eccentricgenius.com/wp/2008/10/29/any-day-of-the-week-the-perpetual-calendar-made-easy/

So – as I mention too many times in the show – these are all going to seem a little weird or difficult at first.  The important thing to remember is that these methods, although they will need practice, will pay off later because (IMO) they are much easier to keep track of in your head.  I’m gonna start practicing now.  Quick!  What is 127 divided by 5?

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