In this activity, you will rewrite a formula to solve for a different variable and then find specific values of unknowns.
Part A:
You are measuring temperature using a thermometer that gives degrees in Fahrenheit. You want to know what the temperature is in degrees Celsius. This formula converts temperatures from degrees Celsius to degrees Fahrenheit: [tex]F = \frac{9}{5} C + 32[/tex].
Rewrite this formula to convert Fahrenheit to Celsius. In your answer, use fractions instead of decimal numbers.
To convert the given formula [tex]\( F = \frac{9}{5}C + 32 \)[/tex] from Fahrenheit to Celsius, we need to isolate [tex]\( C \)[/tex] on one side. Let's go through this step by step:
1. Start with the given formula: [tex]\[
F = \frac{9}{5}C + 32
\][/tex]
2. Subtract 32 from both sides to keep terms involving [tex]\( C \)[/tex] on one side: [tex]\[
F - 32 = \frac{9}{5}C
\][/tex]
3. Multiply both sides by the reciprocal of [tex]\(\frac{9}{5}\)[/tex] to isolate [tex]\( C \)[/tex]. The reciprocal of [tex]\(\frac{9}{5}\)[/tex] is [tex]\(\frac{5}{9}\)[/tex]: [tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
Therefore, the formula to convert Fahrenheit to Celsius is: [tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
This is the correct conversion formula where [tex]\( C \)[/tex] (Celsius) is expressed in terms of [tex]\( F \)[/tex] (Fahrenheit).
