Answer :
To find the formula for converting from degrees Fahrenheit to degrees Celsius, you want to express Celsius [tex]\( C \)[/tex] in terms of Fahrenheit [tex]\( F \)[/tex]. Let's go through the steps to find this formula:
1. Start with the original conversion formula:
The formula to convert Celsius to Fahrenheit is:
[tex]\[
F(C) = \frac{9}{5}C + 32
\][/tex]
2. Set up the equation to solve for Celsius:
We're looking to convert from Fahrenheit back to Celsius, so we need to rearrange the formula to solve for [tex]\( C \)[/tex]. Start with the equation:
[tex]\[
F = \frac{9}{5}C + 32
\][/tex]
3. Isolate the term with [tex]\( C \)[/tex]:
To isolate the term with [tex]\( C \)[/tex], subtract 32 from both sides:
[tex]\[
F - 32 = \frac{9}{5}C
\][/tex]
4. Solve for [tex]\( C \)[/tex]:
To solve for [tex]\( C \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
So, the formula for converting a temperature from degrees Fahrenheit [tex]\( F \)[/tex] to degrees Celsius [tex]\( C \)[/tex] is:
[tex]\[
C(F) = \frac{5}{9}F - \frac{5}{9} \cdot 32
\][/tex]
Simplifying further gives:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
This formula allows you to convert any temperature in Fahrenheit to its equivalent in Celsius.
1. Start with the original conversion formula:
The formula to convert Celsius to Fahrenheit is:
[tex]\[
F(C) = \frac{9}{5}C + 32
\][/tex]
2. Set up the equation to solve for Celsius:
We're looking to convert from Fahrenheit back to Celsius, so we need to rearrange the formula to solve for [tex]\( C \)[/tex]. Start with the equation:
[tex]\[
F = \frac{9}{5}C + 32
\][/tex]
3. Isolate the term with [tex]\( C \)[/tex]:
To isolate the term with [tex]\( C \)[/tex], subtract 32 from both sides:
[tex]\[
F - 32 = \frac{9}{5}C
\][/tex]
4. Solve for [tex]\( C \)[/tex]:
To solve for [tex]\( C \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
So, the formula for converting a temperature from degrees Fahrenheit [tex]\( F \)[/tex] to degrees Celsius [tex]\( C \)[/tex] is:
[tex]\[
C(F) = \frac{5}{9}F - \frac{5}{9} \cdot 32
\][/tex]
Simplifying further gives:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
This formula allows you to convert any temperature in Fahrenheit to its equivalent in Celsius.
