Celsius and Fahrenheit are two different *temperature
scales*, which people use to describe how hot or cold things are. Centigrade
is another name which is used to describe the Celsius temperature scale. A
typical use of these temperature scales is to describe what the maximum
temperature is going to be each day. In Australia a weather forecaster might
say something like, “The maximum temperature today is going to reach 32 degrees
Celsius.” However, in America, the Fahrenheit temperature scale is used. In America,
a weather reporter might say something like, “The maximum temperature today is
going to reach 84 degrees Fahrenheit.”

If you do any travelling, or watch the news, quite often you’ll want to convert between a temperature in Fahrenheit and a temperature given in Celsius. For instance, you might see a news report on how there’s a heatwave sweeping California and that temperatures have reached 105 degrees Fahrenheit. You might be sitting at home wondering whether that’s any hotter than you get in Australia. Here is one formula telling us the relationship between Celsius and Fahrenheit:

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This isn’t much use for you sitting at home, because you want to convert from Fahrenheit into Celsius. This formula only makes it easy for you to convert from Celsius into Fahrenheit. What you’d need to do is rearrange the equation so that it was in the form “C = something…”:

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So now we have a formula telling us the equivalent temperature in Celsius, if we’re given a temperature in Fahrenheit. We can now work out what 105 degrees Fahrenheit is:

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So that is a pretty hot temperature, even by Australian standards.

Handy Hint #1 - General formulas – rearranging them to fit your needs

Mathematical formulas exist for all
sorts of different things. There are formulas for the *areas* of plane
shapes and *volumes* of solid shapes. There are formulas telling you how
much *interest* is earned on a certain amount of money. In order to do
well at mathematics, you need to be able to quickly rearrange the formulas so
that they are in a *useful form* for you. The last example showed how to
rearrange the temperature formula so that we could work out something of
interest to us. In general, you need to be able to do this quickly with any
formula.