You posted, in part: That process isn’t available for kids who haven’t memorized their multiplication tables. You and I don’t really multiply 9 times 9. We know that the answer is 81 because we once memorized it.
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And what about 10 times 10? Do we actually multiply that? I am not sure there is any difference in not multiplying 9 times 9 and not multiplying 10 times 10.
Probably not. Most people don't need to even think about calculating it.
Calculating 10 times 10 can be done, though, by two different methods:
You can append a zero to any number to multiply it by 10. This is a shortcut which is only available for the base of the number system. (I work with hexadexcimal, base 16, a lot. I know that I can multiply a hex number by 16 by simply appending a zero to it.)
You can also multiply it out longhand as you would do with any other multi-digit numbers.
1 0I am not sure there is any difference in not multiplying 9 times 9 and not multiplying 10 times 10.
x 1 0
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0 0
+1 0
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1 0 0
What steps can you follow to multiply 9 times 9? How would you teach someone how to do it?
You can either:
1) Count up by 9s until you reach 81. (This is actually addition, not multiplication.)
or
2) Multiply 9 times 10 by adding a 0 and then subtract 9 from the result. (This is just a shortcut for adding up the 9s.)
or
3) Remembering that it's 81 from having memorized the multiplication tables.