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CASTING OUT NINES

1938

To say that Arithmetic was not my long shot would be an understatement. Whether I missed so many classes due to Bronchitis in childhood or later Menstrual horrors, or whether “I was behind the door when the brains were passed out” would be debatable.

I do remember that ‘Casting Out Nines’ was taught in grammar school, and I learned it before I moved to Pacific Beach, so I’d say I was in fourth or fifth grade...which would make it about 1937 or 1938.

Whenever we got a wrong answer while working at the blackboard, the teacher would say, “Did you ‘cast out your nines’?”

“No,” I’d say, twisting one leg around the other and biting my lip.

“If you had, you would’ve known the answer was wrong.”

I thought it was exactly like doing a problem twice, and I didn’t like doing it once! It was very time consuming, and I’d rather have been writing a story at my desk.

Here’s an example:

Say you have an addition problem 1297 +3468 _____ 4765

Add the digits together until you have only one digit. (1+2+9+7=19 - cast out the 9 and you have 1). This is a simpler way of expressing the old system of removing or “casting out nines: or multiples of nine. The second row would (3+4+6+8=21 or 3) You can look at the second row as (3+6=9) and (4+8=12). Disregard or cast out the 9 and add the 1 & 2 of 12 to equal 3. Either way, the answer is 3. Add that 3 plus the 1 from the first row and your answer is 4. Now if you cast out nines from the answer row, you have (4+7+6+5=22) Add the 2 and 2 from 22 and the answer is 4 which matches the addition of the single digits added together from rows 1 and 2.

So you know by doing this that your addition is probably correct.

If your individual row of digits add up to more than 9, cast out nines again to equal the sum answer. This also works on multiplication, subtraction and division that has whole number answers. This whole idea was to give a simple way of checking arithmetic problems for accuracy.

Needless to say, this was before calculators were in every pocket or purse! However, I have caught myself , in this electronic day and age, ‘casting out nines’ to prove my addition or multiplication when I did not have a trusty calculator in hand.

Tedious and time consuming? Yes! But it works...for any generation!

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