Celsius and Fahrenheit 3

Well, that was enough chemistry for the day.  Later that evening was a football game, and Stef was looking forward to some time just hanging out with friends...

... That is, until she got a text from her mom saying that they were all on their way down to go to the game with her.  It's not that family wasn't nice too... at home. It was just more work when they visited college!

So sure enough, the family SUV pulled up to Stefanie's house just in time to walk down to the stadium.  Out jumped her eleven and twelve year old sister and brother, Sophia and Tom, along with her mom and step-dad. Her little brother and sister ran up and gave her a hug.

Then there were the usual, "How are you?" "How are classes going?" and finally the expected question from her step-dad, "How's chemistry?"

"Not bad so far," she said honestly, "although the prof is going to make us memorize how to convert Fahrenheit into Celsus, pounds into kilograms, and all that stuff."

"Oh, that's easy," said Tom.  "We had to do that all the time in Germany."  Stefanie's mom and step-dad had just spent four months in Germany while she and her sister Stacy mostly stayed home to go to work in the summer. "To go from Celsius to Fahrenheit," Tom continued, "you multiply by 9, divide by 5, then add 32."

Her step-father took out his pocket notebook and wrote down the formula: F=9/5C+32.

"Yep, that's one of them," she said.  "Then going the other direction it's C=5/9(F-32).

It was too much for her step-dad to resist.  While they walked on, he launched into a lecture about why the formulas made sense.  Mind you, no one was listening to him.  Stefanie and her mom were whispering to each other in the front.  Tom and Sophia were competing to see who could count more birds. Meanwhile, Stefanie's step-dad Ken muttered on and on to himself.

"It's easy to figure out the formulas if you forget them," he said.  "It has to do with the fact that on the Celsius scale, 0 degrees (0°) is where water freezes and 100 degrees (100°) is where water boils.  What the conversion formula does is it matches these temperatures to the places where water freezes in Fahrenheit (32°) and where water boils in Fahrenheit (212°).

"So if you're going from Fahrenheit to Celsius, first you subtract 32, like you were going from 32° in Fahrenheit to 0° in Celsius.  Taking away 32 aligns the Fahrenheit scale with the Celsius scale.  Or when you're going from Celsius to Fahrenheit, adding 32 at the end aligns the two scales.

"The other part of the conversion has to do with how much bigger a Celsius degree is or how much smaller a Fahrenheit degree is.  If you subtract the 32° from the boiling point of water, 212°, then you can compare how the two types of degree relate to each other.  180 degrees on the one scale corresponds to 100 degrees on the other.  So you can figure out how big a degree is in one scale compared to the other.  Fahrenheit degrees are 180/100 times more (which reduces to 9/5). Celsius degrees are 100/180 times less (which reduces to 5/9).

"That's the ratio.  You multiply a Celsius degree by 9/5 to get a Fahrenheit degree.  You multiply the aligned Fahrenheit by 5/9 to get a Celsius degree.  It all makes sense."

"Oh, I see," Stefanie cleverly responded as they arrived at the ticket booth, where her other sister Stacy was waiting.  But of course no one had paid any attention to Ken's lovely explanation...