Answer :
We start with the formula for converting Celsius to Fahrenheit:
[tex]$$
F = \frac{9}{5} C + 32.
$$[/tex]
To rewrite this formula so that it converts Fahrenheit ([tex]$F$[/tex]) to Celsius ([tex]$C$[/tex]), follow these steps:
1. Subtract 32 from both sides:
Subtracting 32 from both sides of the equation gives
[tex]$$
F - 32 = \frac{9}{5} C.
$$[/tex]
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]. Multiplying both sides by [tex]\(\frac{5}{9}\)[/tex] isolates [tex]\(C\)[/tex]:
[tex]$$
\frac{5}{9} (F - 32) = C.
$$[/tex]
Thus, the formula for converting Fahrenheit to Celsius is
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
3. Verification with a sample value:
If we take a sample Fahrenheit temperature [tex]\(F = 68\)[/tex], then
- First, compute [tex]\(F-32\)[/tex]:
[tex]$$
F - 32 = 68 - 32 = 36.
$$[/tex]
- Next, calculate [tex]\(C\)[/tex]:
[tex]$$
C = \frac{5}{9} \times 36 = \frac{5 \times 36}{9} = \frac{180}{9} = 20.
$$[/tex]
Thus, using the rewritten formula, a Fahrenheit temperature of 68 degrees corresponds to a Celsius temperature of 20 degrees.
In summary, the conversion formula from Fahrenheit to Celsius is:
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
[tex]$$
F = \frac{9}{5} C + 32.
$$[/tex]
To rewrite this formula so that it converts Fahrenheit ([tex]$F$[/tex]) to Celsius ([tex]$C$[/tex]), follow these steps:
1. Subtract 32 from both sides:
Subtracting 32 from both sides of the equation gives
[tex]$$
F - 32 = \frac{9}{5} C.
$$[/tex]
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]. Multiplying both sides by [tex]\(\frac{5}{9}\)[/tex] isolates [tex]\(C\)[/tex]:
[tex]$$
\frac{5}{9} (F - 32) = C.
$$[/tex]
Thus, the formula for converting Fahrenheit to Celsius is
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
3. Verification with a sample value:
If we take a sample Fahrenheit temperature [tex]\(F = 68\)[/tex], then
- First, compute [tex]\(F-32\)[/tex]:
[tex]$$
F - 32 = 68 - 32 = 36.
$$[/tex]
- Next, calculate [tex]\(C\)[/tex]:
[tex]$$
C = \frac{5}{9} \times 36 = \frac{5 \times 36}{9} = \frac{180}{9} = 20.
$$[/tex]
Thus, using the rewritten formula, a Fahrenheit temperature of 68 degrees corresponds to a Celsius temperature of 20 degrees.
In summary, the conversion formula from Fahrenheit to Celsius is:
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
