Tabacco created this Spreadsheet Multiplication Table up to 100×100. Even I don’t know this table past 13×13. It is published here to demonstrate what a 70-year-old Math Major will do with his time when he has nothing better to do with his time!
And no, you don’t want to see my Database depicting all numbers up to 1,000! I give the Factors of all non-Primes also. OK, I may as well show you the End of my Database so you can rest assured I’m telling the Truth. I warned you about having too much Free Time! And, NO, I don’t know this Table by heart either!
I do not expect anyone to know the Multiplication Table up to 100×100 or the Primes up to 1,000. But here is the Multiplication Table everyone past the 2nd grade must know:
If the youngsters in your family don’t know this Table by heart without having to count on fingers and toes, your child is being cheated big time by our Educational System.
On Deer Park Avenue near the North Babylon Public Library, I queried 2 white youths on bikes. Neither knew what 7×9 was. One did invite me to attend a meeting that evening at the Upper Room. So much for Religious education (except perhaps Catholic).
2 of 3 cashiers at King Kullen in Sunset Plaza didn’t know! But then those new marvelous cash registers do their thinking for them.
A group of about 10 girls (all ethnicities), having a great noisy time outside at Sunset Plaza, grabbed my attention. They knew 7×9, 9×7, 5×7, 9×11 et al. But it was their Elementary School that taught them. An oasis in a dessert of mediocrity!
1 of 2 guys in the Seafood Department at King Kullen knew the answer. But he learned it at G. Marion ? Elementary School. Good for G. Marion!
A 7th grader (black) didn’t know! But a woman, past 50, thought I didn’t know the answer and responded before she realized I was testing the kid. Her answer: 49! No, the 7th grader didn’t know it either.
I asked a group of boys playing on Sword St. A couple knew, but most didn’t. An Hispanic youth injured his head that day so an ambulance ended my Q&A. That happened in 2011.
A 3rd grader (Hispanic black) on the S25 bus didn’t know, but he figured it out correctly.
A friend in Virginia has started asking basically the same question, “How much is 5×7?” Same results! She has even less confidence in our youth than I do – 5×7? Give me a break!
YOU DO IN YOUR HEAD
7×9 = 63
8×8 = 64
Is there a lesson in that fact? Yes!
Let’s call 8 the letter “n”. Therefore 7 is (n-1) and 9 is (n+1). 8 x 8 (or n x n, which is n2) is 1 more than
(n-1) x (n+1) or 7 x 9. The math goes like this:
(n-1) x (n+1) = n2 –1n+1n-1
-1n and +1n cancel each other out, and we are left with n2 -1 as our Formula. This not only works for 7×9 vis-à-vis 82, it works for all n2 vs. (n-1) x (n+1).
If you don’t believe me, try 86, 87, and 88! Square 87, which will be 1 more than 86 x 88. OK, this only works in your head if you already know what 87×87 is!
The real use here is 19, 20, and 21. Assuming you know that 20×20 = 400, then 19×21 must be what? 399 of course!
Assuming you can figure out that 100×100 = 10,000, then 99×101 must be what? 9,999!
This trick can be expanded! Suppose you have to multiply 18×22 in your head the easy way.
The intermediary number is 20 – that’s a slam-dunk! However the Equation will be different.
If 20 is n, then 18×22 will be (n-2) x (n+2), which equals n2-2n+2n-4. The -2n+2n terms cancel each other out, and we are left with n2-4. Therefore since we know 20×20 = 400, 18×22 must be 396 or 4 less than n2 (400). If you do these math tricks in your head, people will swear you are a relative of Einstein!
If the total at the cashier is $38.43, and you give the cashier $40 cash, all you need do is complement $1.00 with $.43 to get $.57, which takes you to $39.00, and then add $1.00 to make $40.00. Therefore your change will be $1.57!
When cashiers actually had to figure out the change, I used to always beat them to my change total. Oftentimes they got it wrong, but I always got it right. Sometimes they even cheated the store, but I never did because my ego was worth more than $1.00!
This trick is good for checking the register, but it is worthless in trying to beat the cashier to the punch because cashiers don’t even know what 7×9 is!
You probably know what 12×12 is – 144, but how much is 13×13? The answer is 25 more than 12×12. Here’s why:
1×1 = 1
2×2 = 4
3×3 = 9
4×4 = 16
5×5 = 25
6×6 = 36
7×7 = 49
8×8 = 64
9×9 = 81
10×10 = 100
11×11 = 121
12×12 = 144
13×13 = 169, but why?
Because 4 is 3 more than 1
9 is 5 more than 4
16 is 7 more than 9
25 is 9 more than 16
36 is 11 more than 25
49 is 13 more than 36
64 is 15 more than 49
81 is ?? more than 64? (17 of course)
100 is 19 more than 81
121 is 21 more than 100
144 is 23 more than 121
And 169 is 25 more than 144!
Of course 14×14 must be 27 more than 169 or 196! And so on!
That’s enough mind-bending for today! If you are more than 20-years-old, you must be mentally kaput by now!
Next we analyze Calculus Differential Equations and Boundary Value Problems! (I’m just kidding!!)
However, have you discovered the Khan Academy on the Web? Great for College students, High Schoolers and Junior High (as well as us older students)! I don’t think it is useful to many students in Elementary, but who knows! It doesn’t hurt to try! And it’s FREE!
Tabacco: I consider myself both a funnel and a filter. I funnel information, not readily available on the Mass Media, which is ignored and/or suppressed. I filter out the irrelevancies and trivialities to save both the time and effort of my Readers and bring consternation to the enemies of Truth & Fairness! When you read Tabacco, if you don’t learn something NEW, I’ve wasted your time.
Tabacco is not a blogger, who thinks; I am a Thinker, who blogs. Speaking Truth to Power!
In 1981′s ‘Body Heat’, Kathleen Turner said, “Knowledge is power”.