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#1 2007-10-02 13:30:11

Mitchell3
Member
Registered: 2007-09-12
Posts: 2

Casting out nines to check addition, multiplication and division.....

Could someone please explain this to a frustrated parent?   It seems like it would just be easier to check for the correct answer by doing the opposite.  This is in a traditional math text - - not a "reformed" text.  dunno

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#2 2007-10-02 17:05:52

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Casting out nines to check addition, multiplication and division.....

I just learned it for you so I doubt you really must know this, but...

Cast out nines addition example.
14 + 23 = 37
5 + 5 = 1
9 + 1 = 1
1 = 1
Cast out nines 2nd addition example.
5 + 6 = 11
11 = 11
9 + 2 = 9 + 2
2 = 2
Cast out nines 3rd addition example.
21 + 34 = 55
(2 + 1) + (3 + 4) =  5 + 5
3 + 7 = 10
9 + 1 = 9 + 1
1 = 1
You can also cast out elevens, which is weirder, I just learned on internet...
Cast out elevens addition example.
For elevens casting you go right to left and go plus minus plus minus...
38 + 124 = 162
(8 - 3) + (4 - 2 + 1) = (2 - 6 + 1)
5 + 3 = -3
8 = -3
8 = 11 - 3
8 = 8


igloo myrtilles fourmis

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#3 2007-10-03 00:58:07

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Casting out nines to check addition, multiplication and division.....

I dunno really, probably because casting out nines is a lot faster than doing it backwards. But I must say, I'm against it (unless they know how to prove it works). If they don't even know how to prove it works, then they're much better off just doing the opposite. No maths should be taken for granted.

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#4 2007-10-03 02:17:06

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Casting out nines to check addition, multiplication and division.....

Casting out nines is an important tool in checking addition/multiplication.
Example, to check whether 523x13=6699,
First add all the digits of 523. You get 5+2+3=10, 1+0=1
Then, add all the digits of 13. 1+3=4.
Since 1x4=4, the sum of the digits of the resultant must also be 4.
However, it can be seen that 6+6+9+9=30, 3+0=3.
Hence, the multiplication is wrong.
The correct answer is 6799. 6+7+9+9=31, 3+1=4.
Although this method can be used as a check, it doesn't guarantee correct results. For example, if your answer was 6979, the total would still be 4, and you may be led to believe that the answer is correct!!! However, if the sum or product fails the test by this method, the answer is certainly wrong.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#5 2007-10-08 14:39:44

Mitchell3
Member
Registered: 2007-09-12
Posts: 2

Re: Casting out nines to check addition, multiplication and division.....

"Casting out nines is an important tool in checking addition/multiplication."

ganesh, if it doesn't work all the time, and it seems to take as much time - or longer - than to just do the opposite, what makes it important? I think I understand HOW to do it, but I'm unsure why they should be learning this. 

At the fourth grade level, I doubt they would understand why this works (I don't even know why it works) sometimes.  And if it only works sometimes and not all the time - like doing the opposite operation, then of what use is it?

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