There is nothing more that The Study Dude wants for you than to use your fingers to store and recall three digit numbers.
Well, in these articles, as The Study Dude, I’ll try to give you the study tips you need to help make your learning easier. I’ll also give you straight and honest opinions and personal anecdotes?even the embarrassing ones that you wouldn’t ever dare read about from any other study tip guru.
Arthur J. Benjamin, PhD and mathemagican, and Michael Shermer wrote the book The Secrets of Mental Math, which leads us to part two of the Study Dude’s examination of mathemagics.
Using Fingers to Remember Two or Three digit Numbers
I once saw a little child math prodigy who resourcefully used her tiny fingers to calculate the hardest math problems. Once, she appeared on television, calculating at lightning speed on her hand, but got the answer wrong. Her eyes welled with tears, and my heart leapt for her. Little did she know, everyone watching stood in awe, irrespective of her error. She mastered instant calculations to the extent that she appeared numerous times on national television. No shame in that, even if one of her varied appearances yielded a wrong answer.
I often wondered how she used her fingers to calculate. Although, Benjamin and Shermer give some indication, they don’t quite capture this little girl’s system. Yet, Benjamin and Shermer assist you in recording on your fingers two or three digit numbers so that you too can make instant calculations.
– the number six is represented by your thumb touching your pinkie.
– The number seven is represented by your thumb touching your ring finger.
– The number eight is represented by your thumb touching your middle finger.
– The number nine is represented by your thumb touching your index finger.
– With the above tools, you can store the hundred’s digit place of a three-digit number on your left hand and store the tens digit place of a three-digit number on your right hand. The ones digit place you store in your brain. Where else?
Divisibility by 2, 3, 4 and so on
In junior high school, we learned little tricks to determine a number’s divisibility by the numbers from two to nine. The whirlwind of rules and tricks overwhelmed me, and I walked away with knowledge of how to determine a number’s divisibility by, of course, 2, but also by 3. I retained the divisibility by 3 rule all throughout my university experience, and it often came in handy. Yet, I felt slightly disadvantaged not knowing the rest of the rules to determine the divisibility of numbers from 4 to 9. If I had known these rules by heart, I’m certain my math experience would have yielded even greater results, although I did end up with the highest grade in seven out of nine math classes.
Now, Arthur Benjamin and Michael Shermer open the doors for you, too, to learn the tricks for determining divisibility by the numbers from 2 to 9. I’m omitting 7 and 5, as the rules for 7 are too complex and those for 5 are too simplistic.
– Numbers divisible by 2 are even numbers.
– Numbers divisible by 3 have digits that add up to a multiple of 3. For the number 216, 2+1+6=9, and nine is a multiple of 3, so 216 is divisible by 3.
– Numbers divisible by 9 have digits that add up to a multiple of 9. For the number 216, 2+1+6=9, which is a multiple of 9, therefore it is divisible by 9.
– Numbers divisible by 6 are even and have digits that add up to a multiple of 3.
– Numbers divisible by 4 have the last two digits divisible by 4. The number 45680 is divisible by 4, because the last two digits, 80, are divisible by 4.
– Numbers divisible by 8 have the last three digits divisible by 8.
Guessing Done Right
Do you stare down a long list of shopping items to collect, marking down the cost of each item in the next column? That may seem easy to do, but you also need to mentally tally the total of those grocery items. While carrying a calculator proves to be the best solution in any situation, some advantages exist for making calculations in your head on the fly.
Even if you lack math craftiness, you can always learn simple tricks for not only calculating grocery lists, but also for determining the tip on a restaurant meal.
If you ever wanted to defer paying the automated 15% that comes up shining on the Interact machine, take heed in Benjamin and Shermer’s advice on how to guesstimate most any everyday calculation:
– When guesstimating grocery bills, round the digits to the nearest 50 cent increment. In other words, $1.19 is closest to $1, while $1.60 is closest to $1.50. Add this easier calculation in your head.
– When multiplying two digit numbers by two digit numbers, round each number to the nearest 10s place. So, 88 X 54 would be rounded to 90 X 50.
– An even better method of multiplying two digit numbers by two digit numbers involves rounding up or down one number to the nearest tens place and then rounding the second number up or down the same increment in the opposite direction. In other words, 88 X 54 would become 90 X 52 (88 + 2 = 90 and 54 – 2 = 52).
– When you need to calculate a 15% tip, take 10% of the total and 20% of the total, and then take the average of the two. Alternatively, take 10% and half of 10% and add the values together.
– When you need to calculate a 25% tip, divide the amount by 4.
So, there’s nothing to fear. The Study Dude is determined to make right for you all the wrongs I made in grad school?one A+ at a time.
Benjamin, Arthur, & Shermer, Michael. (2006). Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks. New York, NY: Three Rivers Press.