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My book derives relationship between Celsius and Fahrenheit scale as

F-32/212-32 = C-0/100

F-32/180 = C/100

but I don't understand why F-32 is divided by 180? What does 180 and 100 indicate in both respectively?

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    $\begingroup$ chemistry.stackexchange.com/questions/15488/… $\endgroup$ – Mithoron Jun 30 '17 at 18:27
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    $\begingroup$ Order of operations matter. You are supposed to do division before subtraction. Also, there are some parentheses missing, so the overall expression is wrong. $\endgroup$ – Zhe Jun 30 '17 at 18:41
  • $\begingroup$ They don't indicate anything. That's just the way it is. There is no physical reason behind it. $\endgroup$ – Ivan Neretin Jun 30 '17 at 19:25
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    $\begingroup$ I'm voting to close this question as off-topic because this is not a question dealing with chemistry in the slightest. $\endgroup$ – Jan Sep 20 '17 at 2:19
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Water boils at $100\ ^{\circ}\mathrm{C}$ and $212\ ^{\circ}\mathrm{F}$, while it freezes at $0\ ^{\circ}\mathrm{C}$ and $32\ ^{\circ}\mathrm{F}$. The numerators in formula provides the correct shift based on freezing point. The denominators provide the correct scaling between units by noting that a $180\ ^{\circ}$ increase on the Fahrenheit scale is equal to a $100\ ^{\circ}$ increase on the Celsius scale.

Note that your formula is missing some parentheses for correctness:

$$\frac{F-32}{212-32} = \frac{C-0}{100}$$ should be written as $$(F-32)/(212-32) = C/100$$

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