I understand how to do it. But how does it work? How does crossing out 9s help you check if a basic arithmetic problem is incorrect?
Something to do with balancing the equation?
Thanks!
In: Mathematics
The process of “crossing 9s” is a simple hack to calculate remainder after division by 9. If two numbers are equal, their remainder after division by 9 is also equal (ANY mathematical operation, performed on two equal numbers, must give equal results). 9 is chosen just because it’s easy to calculate using that hack.
As to why the hack works – it’s because 9 is 1 less than 10, or 9 + 1, if you will. 20 is 2 * (9 + 1), or 18 + 2. 30 is 27 + 3. The first number is always a multiple of 9, the second number is the remainder. We only care about the remainder, which is, as you might notice, simply the digit itself. And since 100 = 99 + 1 and 1000 = 999 + 1 etc., adding up all the digits gives us the remainder for the whole number, no matter how many digits it has.
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