Answer :
We start with the formula that converts degrees Celsius to degrees Fahrenheit:
[tex]$$
F = \frac{9}{5}C + 32
$$[/tex]
Our goal is to rewrite this formula so that it converts Fahrenheit to Celsius (i.e., solve for [tex]$C$[/tex] in terms of [tex]$F$[/tex]).
Step 1. Subtract 32 from both sides
Subtract [tex]$32$[/tex] from each side of the equation:
[tex]$$
F - 32 = \frac{9}{5}C
$$[/tex]
Step 2. Multiply both sides by the reciprocal of [tex]$\frac{9}{5}$[/tex]
The reciprocal of [tex]$\frac{9}{5}$[/tex] is [tex]$\frac{5}{9}$[/tex]. Multiply both sides of the equation by [tex]$\frac{5}{9}$[/tex]:
[tex]$$
\frac{5}{9}(F - 32) = C
$$[/tex]
We can rewrite this equation as:
[tex]$$
C = \frac{5}{9}(F - 32)
$$[/tex]
Thus, the conversion formula from Fahrenheit to Celsius is:
[tex]$$
C = \frac{5}{9}(F - 32)
$$[/tex]
[tex]$$
F = \frac{9}{5}C + 32
$$[/tex]
Our goal is to rewrite this formula so that it converts Fahrenheit to Celsius (i.e., solve for [tex]$C$[/tex] in terms of [tex]$F$[/tex]).
Step 1. Subtract 32 from both sides
Subtract [tex]$32$[/tex] from each side of the equation:
[tex]$$
F - 32 = \frac{9}{5}C
$$[/tex]
Step 2. Multiply both sides by the reciprocal of [tex]$\frac{9}{5}$[/tex]
The reciprocal of [tex]$\frac{9}{5}$[/tex] is [tex]$\frac{5}{9}$[/tex]. Multiply both sides of the equation by [tex]$\frac{5}{9}$[/tex]:
[tex]$$
\frac{5}{9}(F - 32) = C
$$[/tex]
We can rewrite this equation as:
[tex]$$
C = \frac{5}{9}(F - 32)
$$[/tex]
Thus, the conversion formula from Fahrenheit to Celsius is:
[tex]$$
C = \frac{5}{9}(F - 32)
$$[/tex]
