Hi everyone. Today in my Alg.2 class I was given an extra credit assignment of proving The Law of Reciprocals using a 2-column proof method. Here is the problem I was given:

Prove : if 1/x = a/b, then x = b/a ; a, x, & b do not equal 0. If anybody knows how to solve this problem or could help me it would be appreciated!

(p.s. my 1/x symbols are supposed to look like upright fractions but I don't know how to type them upright on my keyboard)

The 2-col proof would start with your premise: \frac{1}{x}\ =\ \frac{a}{b} . In the right column, your listed justification would be "Premise" or "Hypothesis".

After that, just solve for x algebraically, one step at a time. For each step, indicate the justification, which will be typically one of the basic properties or axioms of real numbers.