Subtract 345 from 678 using the **method of complements** (a technique used to subtract one number from another using only addition of positive numbers).

Guest Jun 18, 2015

#1**+18 **

Best Answer

The 9's complement of 678 is 321

321 + 345 = 666

The 9's complement of 666 is 333 which is the desired result.

(i.e. 678 - 345 = 333)

.

Alan
Jun 18, 2015

#2**+10 **

Thanks Alan

It took me ages to work out what you did!

The question is 678-345

NOW

678+321=999 (1)

345+321=666 (2)

so thinking of this like simultaneous equations using elimination method.

(1)-(2)

678-345=999-666

678-345=333

That is really weird.

Why would anyone want to do that for?

Melody
Jun 18, 2015

#3**0 **

I have to agree, Melody......I see* how * this works, but I don't understand the rationale for

CPhill
Jun 18, 2015

#4**+5 **

This method can be found in computers that use binary arithmetic (where they use 2's complement of course).

I've never come across 9's complement being used for real in normal base 10 arithmetic though!

.

Alan
Jun 18, 2015