Teachers frequently get questions from students who are very astute or just curious. A math question that seems simple may have a difficult answer or the answer may connect in unexpected ways to other ideas. This text aims to address commonly asked questions about the middle school math curriculum that require expert knowledge to answer.

Questions addressed:

• Why is 1 not a prime integer?
• How many prime integers are there?
• Why is 0 times 7 equal to 0?
• Why is -1 times 2 equal to -2?
• Is 2 + 2 always equal to 4?
• Why is odd plus odd an even, but odd times odd an odd?
• Why is a negative times a negative equal to a positive?
• Why can't we divide by 0?
• Why do fractions have to have a common bottom before we can add them?
• Why do we flip the bottom fraction in a compound fraction?
• What is the square root of a negative number?
• Why is a^0=1 for a not equal to 0?
• Why is 0^0 not defined?
• Why does 0.99999... = 1?
• Is there a smallest positive real number?
• Why does multiplying by a negative number make the inequality change directions?
• Why do rational numbers have repeating decimal representations?
• Why does the decimal representation of certain fractions terminate while others have repeating decimals?
• Why is 3/2 called an improper fraction?
• Why do we use certain symbols for multiplication and division in elementary and middle school and not in high school?
• Why is the distance formula in one dimension |x| and the distance formula in two dimensions the square root of (x^2 + y^2) ?
• If I pick any real number between 0 and 1, what is the probability of picking 0.5?
• If I have a 1 in 100 chance of winning every time I try and I try 100 times, what is the probability I win at least once?

If you have a burning question that requires a technical answer, leave it as a comment and I may consider writing an answer to it in an update.