The multiplication rule for equations says that if I multiply both sides of an equation by the same number, I’m not affecting the value or the balance of that equation. This helps us solve problems like you see here: x over two equals six. X over two is the same as saying "x divided by two," and to do the opposite operation, I must multiply x divided by two times two is equal to six times two. So I get x is equal to twelve. And checking my work, substitute back into the equation, twelve over two or twelve divided by two is six, so the solution is correct.

In this equation, x over six is x divided by six, so I can multiply by six. And I get twelve times six. Notice this a different way to write the same problem. So I could write this x divided by six times six or I can leave it with the fraction bar and do it that way. It’s the same thing—this and this are the same thing. So, x over six times six gives me x, and twelve times six equals seventy-two. I can check my work by substituting seventy-two in for x and seventy-two divided by six is equal to twelve, so my solution is correct.