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« I guess this was inevitable | Main | Ladakh: Shangri La on the Silk Route »

August 22, 2011

Comments

Due to non-use most of my science and math knowledge is now rusty or forgotten. Of everything that I have forgotten, I most regret the loss of calculus and statistics. Perhaps one of these days I should sit down and crack open an old text book and begin learning again.

Norm, why did you just show off your computational skills and not tell us the actual "tricks?"

@ Ruchira:

I was waiting for someone to ask. I'll tell you the second procedure. It is so easy it is embarrassing.

To multiply an arbitrary number of any length by 25:

1. You have to be able to look at the number. (If you can do this procedure by simply holding the number in your head, you will really amaze your friends and confuse your enemies.)

2. Mentally, place 2 zeros at the end of the number.

3. HERE'S THE MAGIC!!! Now divide the number by 4. Proceed as in long division, but you should be able to do the arithmetic and carry numbers in your head. A divisor of 4 is relatively easy to handle in your head.

Try this with the example above.

9,880,981,445

988098144500

4 Divided into 9 8 8 0 9 8 1 4 4 5 0 0

Give it a try.

9 8 8 0 9 8 1 4 4 5 0 0
_ _ _ _ _ _ _ _ _ _ _ _

@ Ruchira:

Have you tried the above example. It hardly takes any practice at all, and friends and family will gaze in wondrous admiration - as long as you don't tell them your secret.

Do you want to try the multiplication of numbers ending in 5? It's a little more taxing on your memory and concentration and doing some calculations in your head. With a little bit of practice you will amaze your friends and confuse your enemies.

I did try it, Norman. Thanks! It's a neat little trick. And yes, do tell me about multiplying numbers ending in 5.

Let me guess, to multiply arbitrarily large numbers by 5, you just add one 0 at the end, and divide the whole thing by 2?


@ Ruchira and Sujatha:

Sujatha, you are generalizing from the earlier example, correctly, if the multiplier is only a single digit, 5.

I have a more general solution when the numbers being multiplied have any length, but the units digit is 5, in both cases. However, the mental arithmetic beyond two or three digits is difficult.

Let's take the example of 165 x 35.

1. Both numbers end in 5.

2. Ignore, completely, the units digits 5 and 5.

Here's where do everything in your head.

3. Multiply 3 x 16 = 48.

4. Now add 3 + 16 = 19.

5. Take half 19, dropping any numbers after the decimal point. 19 / 2 = 9.5 (drop the .5 and you are left with 9)

6. Add 9 + 48 = 57.

7. All that is left is to determine the final two digits of the answer. If the sum of 16 + 3 = 19 is an odd number, the last two digits are 75. If the sum is even, the last two digits are 25.

8. So we concatenate 57 with 75. 5,775 is the answer.

This speed calculation becomes quite easy after only a little practice. I use it rarely, that's why I need about 15-20 seconds. I have to remind myself of what to do. Otherwise, I would knock them off in about 5-10 seconds.

The length of the numbers you can handle is dependent on your facility with mental multiplication and adding.

How about 155 X 155....24,025

How about 185 x 115....21,275

Quick. What's 95 x 35?

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