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------------------------------------------------ Rewrite the formula to convert Fahrenheit to Celsius. Use fractions instead of decimal numbers in your answer.

Given the formula to convert Celsius to Fahrenheit:

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

Rearrange the formula to solve for [tex]C[/tex] in terms of [tex]F[/tex].

We start with the formula that converts Celsius to Fahrenheit:
[tex]$$
F = \frac{9}{5}C + 32.
$$[/tex]

Our goal is to solve for [tex]$C$[/tex] in terms of [tex]$F$[/tex]. Here are the steps:

1. Subtract 32 from both sides:

Subtract [tex]$32$[/tex] from both sides of the equation:
[tex]$$
F - 32 = \frac{9}{5}C.
$$[/tex]

2. Multiply by the reciprocal of [tex]$\frac{9}{5}$[/tex]:

To isolate [tex]$C$[/tex], we 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]

3. Express as a single fraction (optional):

Distribute [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}F - \frac{5 \times 32}{9} = \frac{5}{9}F - \frac{160}{9}.
$$[/tex]

Thus, the formula that converts degrees Fahrenheit to degrees Celsius is:
[tex]$$
C = \frac{5}{9}(F - 32) \quad \text{or equivalently} \quad C = \frac{5F}{9} - \frac{160}{9}.
$$[/tex]