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

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

1565 x 1197 = ?

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

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

mgb_phys
Homework Helper
Sorry never heard of it.

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

1565 x 1197 = ?

I don't think that'll work.

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:
DaveC426913
Gold Member
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.

.....
Jekertee, are you willing to teach us the method?
: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

...I input random numbers into the search box of google but found only strange result.
Only numbers? Didn't you specify an operator?

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

I din't know that method also, I made a quizz thinking that someone knew to tell me too
Is there any information you could give us to help search for it?

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.

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.

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.
$$(10a + b)(10a + 10 - b)$$
$$= 100a^2 + 100a - 10ab + 10ba + 10b - b^2$$
$$= 100a(a + 1) + b(10 - b)$$