Choose any two digit number (E.g. 37)
Reverse the order of the digits (E.g. 73)
Find the difference between the two numbers (E.g. 73 - 37 = 36)
Repeat this operation for many different two digit numbers. Do you notice any connection between the answers? Can you explain the reason for this connection using algebra?
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Let the first digit be a
Let the second digit be b
The two digit number has a value of 10a + b
The number with the digits reversed has a value of 10b + a
The difference between these numbers is either 9a - 9b or 9b - 9a depending on which of a or b is the largest.
In either case there is a factor of 9 in the answer.
So the difference will always be a multiple of 9.
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Numbers and the Making of Us
I initially heard this book described on the Grammar Girl podcast and immediately went to find out more about it. I now have it on my Christmas present wish list and am looking forward to receiving a copy (hint!).
"Caleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists." more...