How do you evaluate #89767\times 98654#?

1 Answer
George C.
Dec 7, 2017

#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#

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