High School

You are measuring temperature using a thermometer, and the temperature is in degrees Celsius. The formula to convert Celsius to Fahrenheit is given by:

[tex] F = \frac{9}{5} C + 32 [/tex]

Rewrite this formula to convert Fahrenheit to Celsius.

Answer :

We start with the formula that converts Celsius to Fahrenheit:

[tex]$$
F = \frac{9}{5}C + 32.
$$[/tex]

Our goal is to rewrite this equation so that it converts Fahrenheit to Celsius—that is, to solve for [tex]$C$[/tex] in terms of [tex]$F$[/tex].

Step 1: Isolate the term with [tex]$C$[/tex].
Subtract [tex]$32$[/tex] from both sides of the equation:

[tex]$$
F - 32 = \frac{9}{5}C.
$$[/tex]

Step 2: Solve for [tex]$C$[/tex].
Multiply both sides by the reciprocal of [tex]$\frac{9}{5}$[/tex], which is [tex]$\frac{5}{9}$[/tex]:

[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]

This is the exact expression for the conversion from Fahrenheit to Celsius.

To express the conversion in decimal form, note that

[tex]$$
\frac{5}{9} \approx 0.555555555555556,
$$[/tex]

so the formula can also be written as:

[tex]$$
C = 0.555555555555556\,F - 17.7777777777778.
$$[/tex]

Thus, the final formula to convert Fahrenheit to Celsius is:

[tex]$$
\boxed{C = \frac{5}{9}(F - 32) \quad \text{or equivalently} \quad C = 0.555555555555556\,F - 17.7777777777778.}
$$[/tex]

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