Reverse Connection

An Advanced Mathematics Lesson Starter Of The Day

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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    Answer

    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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