Science Friday: Converting Fahrenheit to Celsius

I've used the fact that my step-daughter will probably take chemistry this summer as an excuse perhaps to dabble a little in chemistry this spring: http://moleculestutorials.blogspot.com/

Here's an excerpt for my "Science Friday":
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... 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...