Any two- or more-digit number can be placed in so-called "expanded" notation, that is, by expressing it as a sum of multiples of ones, tens, hundreds etc. Expanded notation's the sort of thing you learn in third grade and never use again, but it happens to be useful here.
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branchandroot
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Date: 2022-01-02 01:50 pm (UTC)Any two- or more-digit number can be placed in so-called "expanded" notation, that is, by expressing it as a sum of multiples of ones, tens, hundreds etc. Expanded notation's the sort of thing you learn in third grade and never use again, but it happens to be useful here.
11 = 10 + 1
22 = 20 + 2
1963 = 1000 + 900 + 60 + 3
So then 11 + 22 + 1963 = (10 + 1) + (20 + 2) + (1000 + 900 + 60 + 3).
Addition is associative, so we can remove the parentheses:
11 + 22 + 1963 = 10 + 1 + 20 + 2 + 1000 + 900 + 60 + 3
...and zeroes in the number don't affect it when you're adding up digits, so...
11 + 22 + 1963 "=" 1 + 1 + 2 + 2 + 1 + 9 + 6 + 3 (when the digits are summed recursively to a single-digit number)