Can you do 994 times 997 in your head?

‘Shruti” will explain how to do it, but she doesn’t explain why it works:

Personally, I had never come across this one in my over 40 years of teaching math. She is correct, it does work, but WHY?

I’ll try to explain.

994 is 6 away from 1000, or 10^3 minus 6.

And 997 is 3 away from 1000, or 10^3 minus 3.

If we multiply (10^3 – 6) by (10^3 – 3), we get 10^6 – (6+3)*10^3 + 6*3

So as she explains, we count down from a million by nine thousand, and then we add on 18.

or, if we take away any small number from a thousand, say, a, and subtract any other small number b from a thousand, you have a situation like this if you use the area model for multiplication: