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# Subtract 345 from 678 using the method of complements (a technique used to subtract one number from another using only addition o

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567
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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
+27052
+18

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
#1
+27052
+18

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
+93677
+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
+90023
0

I have to agree, Melody......I see how  this works, but I don't understand the rationale for wanting to do it.....!!!

CPhill  Jun 18, 2015
#4
+27052
+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
#5
+90023
0

Thanks, Alan......that method seemed a little convoluted for everyday practicality......IMHO.....!!!!

CPhill  Jun 18, 2015
#6
+93677
0

Thanks Alan :)

Melody  Jun 18, 2015