 I'm going to start with an example of Fahrenheit to Celsius where we have 340 degrees Fahrenheit and we want to convert that into a temperature in Celsius. The equation we use for that is this temperature Celsius is five-ninths of the quantity the temperature Fahrenheit minus 32 degrees Fahrenheit. Now you might recognize this equation looks similar to another one, the one that's often shown in textbooks gives us the nine-fifths the temperature in Celsius plus 32 degrees Fahrenheit. And this is really just doing the algebra of subtracting the 32 over to the other side and then you've got your quantity of the temperature in Fahrenheit minus 32. And then you cross multiply the nine-fifths becomes five-ninths. We go to plug in our equation, we put our temperature in Fahrenheit in and we've got the quantity of 350 degrees Fahrenheit minus 32 degrees Fahrenheit. So we're taking care of the offset here before we take care of the scale changes there. And that's going to give us a value of still our five-ninths out front of 318 degrees Fahrenheit. Now remember our scales over here this is really five degrees Celsius is the same size as nine degrees Fahrenheit. So when we multiply that five-ninths times the 318 we've got a temperature of 177 degrees Celsius. So it becomes Celsius now instead of Fahrenheit because that was five degrees Celsius and nine degrees Fahrenheit. You'll also notice if you plug this in your calculator I've rounded it off. It was actually 176.667 but since we started off with two or three significant digits we should make sure that we don't have too many decimal places. If you're doing other calculations you may want to keep the extra decimal places and then round at the very end. As a second example we're going to take a look at a starting temperature of minus 40 Fahrenheit and again we're taking that into Celsius. When you use our same equation here we did last time and plug in our negative making sure in the calculator we're using the negative sign correctly. Negative 40 minus negative 32 that's going to give us a negative 72 then multiply by our scaling factors of the five divided by the nine and our final answer is minus 40. Nope that's not a mistake minus 40 and minus Celsius are actually the same temperature. If you were to look at a thermometer that goes that cold you'd see that the numbers are actually aligned at that point.