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 256 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 form 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 we need 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 there's 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 five ninths x times the Fahrenheit temperature the Fahrenheit temperature is 56 56 degrees Fahrenheit minus 32 minus 32 well 56 minus 32 is 24 so this is going to be equal to is going to be equal to 5/9 times 24 times 24 and this is the same thing as five times 24 over nine and we can divide the numerator and the denominator by three 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 as a number that makes a little bit more sense in terms of temperature let's divide 3 into 40 degrees or so sorry 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 nine subtract you get a 1 and then you could bring down another zero we now have a decimal point over here you're going to get a zero 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 this is equal to thirteen point three three three it'll just keep repeating this little line on top means repeating degrees Celsius or you could say that look three goes into forty three goes into forty 13 times with a remainder of one with a remainder of one so you could say that this is also equal to 13 remainder one so 13 and one third degrees Celsius either way it works but that's our Celsius temperature when our Fahrenheit temperature is 56 degrees