# How to do 1565 x 1197 in 10 seconds without a calculator and paper?

1. Nov 12, 2007

### Jekertee

How to do this in 10 seconds without a calculator and scratch paper?

1565 x 1197 = ?

2. Nov 12, 2007

### mgb_phys

Call it 1565 * 1200 which is just (1565 * 2 *100) + 1565*1000
The subtract 1565 three times.

3. Nov 13, 2007

### Jekertee

Do you know how to apply Indian's classic calculation method to this ?

4. Nov 13, 2007

### mgb_phys

Sorry never heard of it.

5. Nov 15, 2007

### Rogerio

6. Nov 16, 2007

### Jekertee

I don't think that'll work.

7. Nov 16, 2007

### Jimmy Snyder

I googled 1565 x 1197, and got the answer: 1 873 305.
It didn't take 10 seconds. Then I googled "India's classic calculation method" but I got nothing I could use.

Jekertee, are you willing to teach us the method?

Last edited: Nov 16, 2007
8. Nov 16, 2007

### DaveC426913

Here's a question: how randomly chosen is that pair of numbers? After you demonstrate the method, I want to see you do the same thing with numbers provided by an audience member.

9. Nov 17, 2007

### Jekertee

:shy , Jim, I din't know that method also, I made a quizz thinking that someone knew to tell me too

I input random numbers into the search box of google but found only strange result. It's amazing to me the example I gave works on your search

10. Nov 17, 2007

### Rogerio

Only numbers? Didn't you specify an operator?

What about an expression like (into the search box):
2*17.9 + 3**3

11. Nov 17, 2007

### Jimmy Snyder

Is there any information you could give us to help search for it?

12. Nov 25, 2007

### BlackWyvern

1565 x 1200 - (1565 x 3) = ?

4 x 1565 = 6000 + 240 + 20 = 6260
6260 x 300 - (1565 x 3) = ?
6260 x 3 = 18000 + 600 + 180 = 18780
18780 x 100 = 1878000 - (1565 x 3)
1565 x 3 = 4500 + 180 + 15 = 4695
1878000 - 4695 = ?
=1873305

This is one way, and it's probably not the fastest, but it uses an ancient technique of multiplying where one number was halved, and the other was doubled. Or multiplied by 3, and divided by 3.

13. Feb 20, 2008

### nabeelr

it's called vedic math. if you google it, you'll find a ton of sites with math tricks here and there. but usually, they don't involve numbers that big.
for example:
when multiplying 2, 2-digit numbers with the same tens digits and two ones digits that add up to 10, (ex. 23 x 27 ) the vedic stuff is useful.
you just multiply the tens digit by the next number up, so multiply 2 by 3 and get 6.
then multiply the two ones digits, and get 21.

there's tons of little things like that that you can find on google.

14. Feb 21, 2008

### Jimmy Snyder

Yes, here's a proof. Let a be the common tens place digit (2 in this case), and b one of the ones place digits (either 3, or 7 in this case). Then
$$(10a + b)(10a + 10 - b)$$
$$= 100a^2 + 100a - 10ab + 10ba + 10b - b^2$$
$$= 100a(a + 1) + b(10 - b)$$
That is to say, multiply a by the next number up, multiply by 100 and add the product of the two numbers in the respective ones places.