Converting Fahrenheit to Celsius

A thermometer in a science lab displays the temperature in both Celsius and Fahrenheit. If the mercury in the thermometer rises to 56 degrees Fahrenheit-- they're giving us the Fahrenheit temperature-- what is the corresponding Celsius temperature? And then they give us the two formulas, that if we know the Celsius temperature, how do we figure out the Fahrenheit temperature, or if we know the Fahrenheit temperature, how do we figure out the Celsius temperature. And these are actually derived from each other, and you'll learn more about that when you do algebra. And we also-- maybe in another video-- will explain how to derive these. It's actually kind of interesting, involves a little bit of algebra. But they gave us the formula. So they really just want us to apply it, and maybe make sure we understand which one we should apply. Well, they're giving us the Fahrenheit temperature right here, so F is going to be equal to 56. And they're asking us for the Celsius temperature, so we need to figure out what the Celsius temperature is. Well, in this one over here, if you know the Fahrenheit temperature, then you can solve for the Celsius temperature. So let's use this right over here. So our Celsius temperature is going to be 5/9 times the Fahrenheit temperature-- the Fahrenheit temperature is 56 degrees Fahrenheit-- minus 32. Well, 56 minus 32 is 24. So this is going to be equal to 5/9 times 24. And this is the same thing as 5 times 24, over 9. And before I even multiply out 5 times 24, we can divide the numerator and the denominator by 3. So let's do that. If we divide the numerator by 3 and the denominator, we're not changing the value. 24 divided by 3 is 8. 9 divided by 3 is 3. So it becomes 5 times 8, which is 40, over 3 degrees. And if we want to write this as a number that makes a little bit more sense in terms of temperature, let's divide 3 into 40 to get the number of degrees we have. 3 goes into 4 one time. 1 times 3 is 3. Subtract. 4 minus 3 is 1. Bring down the 0. 3 goes into 10 three times. 3 times 3 is 9. Subtract. Get a 1. And then you could bring down another 0. We now have a decimal point over here. You're going to get a 0 here. 3 goes into, once again, 10 three times. And this 3 is going to repeat forever. So you could view this-- this is equal to 13.333-- it'll just keep repeating. This little line on top means repeating-- degrees Celsius. Or you could say that, look, 3 goes into 40 13 times with a remainder of 1. So you could say that this is also equal to 13, remainder 1. So 13 and 1/3 degrees Celsius. Either way, it works. But that's our Celsius temperature when our Fahrenheit temperature is 56 degrees.