Question

How do you evaluate `89767\times 98654`?

Answer 1

`89767 xx 98654 = 8855873618`

Explanation:

Note that the digits of these numbers are generally larger than `5`, so straight long multiplication will result in quite a few carries.

So let's try another way...

`89767 xx 98654`

`= (100000-10233) xx (100000 - 1346)`

`= 10000000000-100000(10233+1346)+(10233xx1346)`

`= 10000000000-1157900000+(10233xx1346)`

`= 8842100000+(10233xx1346)`

`1346 xx 2 = 2692`

`1346 xx 3 = 2692 + 1346 = 4038`

So:

`10233xx1346 = 13460000+269200+40380+4038`

`13460000`
`color(white)(00)269200`
`color(white)(000)40380`
`underline(color(white)(0000)4038)`
`13773618`

`color(white)(10233xx1346) = 13773618`

So:

`89767 xx 98654 = 8842100000+13773618`

`8842100000`
`underline(color(white)(00)13773618)`
`8855873618`

`color(white)(89767 xx 98654) = 8855873618`