| Math Logic |
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| Question : |
| What
is meant by 'Casting out nines' ? |
Answer : |
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Casting out the nine is a method of checking answers to multiplication, addition and subtraction. |
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Casting out nines was known to the Roman bishop Hippolytos as early as the third century.
It was employed by Twelfth-century Hindu mathematicians. |
| It is
based on the idea of finding the sum of the digits in a number
and then adding the digits in the resulting sum, etc., until
a one digit number results. This addition of the digits in a
number is further simplified by first discarding or casting
away any digits whose sum is 9. The remainder is set down, in
each case as the check number. |
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For example, |
8216 x 4215 = 34630440, this is how you proceed.
4 + 2 + 1 + 5 = 12, casting out the nines leaves 3 as check number.
8 + 2 + 1 + 6 = 17, casting out the nines leaves 8 as check number.
3 + 4 + 6 + 3 + 0 + 4 + 4 + 0 = 24, casting the nines leaves 6 as check number.
3 x 8 = 24, 2 + 4 = 6 which was the check number of the original product. So the multiplication is correct. |
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Casting out nines is not in wide use today, mainly because of the widespread use of calculators and computers.
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