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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