Choose a 2-digit number of different digits and don’t reveal it! Reverse the digits to get another number. Find their difference. Divide the result by 9. In the trick given above, what is the quotient when you divide by 9? Is there a relationship between the two numbers and the quotient?
The quotient when dividing by 9 equals the absolute difference between the two digits of the original number.
If the original 2-digit number is 'ab' (where a and b are its digits), then the quotient is |b - a|.
Explanation
The chapter shows that when we take a 2-digit number ab (value 10a + b), reverse it to get ba (value 10b + a), and find their difference, we get 9(b - a) or 9(a - b). Dividing by 9 gives (b - a) or (a - b), which is the absolute difference of the digits.
Solution Steps
The quotient when dividing by 9 equals the absolute difference between the two digits of the original number.
If the original 2-digit number is 'ab' (where a and b are its digits), then the quotient is |b - a|.
When we take a 2-digit number ab (value 10a + b), reverse it to get ba (value 10b + a), and find their difference, we get 9(b - a) or 9(a - b).
Dividing by 9 gives (b - a) or (a - b), which is the absolute difference of the digits.