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.
How did you use this resource? Can you suggest how teachers could present, adapt or develop it? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world. Click here to enter your comments.
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