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Yes, and it's pretty easy to prove. Multiplying any rational number by the inverse of another gives you a new rational number. (Zero doesn't have an inverse).
by Dove 14y ago
Yes, and it's pretty easy to prove. Multiplying any rational number by the inverse of another gives you a new rational number. (Zero doesn't have an inverse).
A rational number is a number that can be represented as one integer divided by another. Take two rational numbers, A = a/b, and B = c/d. If B has an inverse, then A/B = a/b * d/c = ad/bc. ad and bc are both integers, so A/B is rational.
- crntaylor 14y agoMy point was that you can only divide one rational by another to produce a new rational if the denominator is nonzero. This is not what it says in the book, so there's potential for a newbie to get confused (and anyone reading the book in order to learn from it is, by definition, a newbie).
- Dove 14y agoOh, then that seems like a pretty pedantic worry. You can't divide by zero in any context; even children know that. It's such an obvious exception that it didn't even occur to me that's what you thought was wrong with the statement.