Concept:The Fahrenheit and Celsius scales have different zero points (32°F vs 0°C for the freezing point of water) and different scale intervals (180 degrees vs 100 degrees between freezing and boiling points of water).
Formula:$$ \frac{^\circ C}{100} = \frac{^\circ F - 32}{180} $$
Solution:- To isolate Celsius (\( ^\circ C \)), multiply both sides by 100.
- \( ^\circ C = \frac{100}{180} \times (^\circ F - 32) \).
- Simplify the fraction \( \frac{100}{180} \) by dividing the numerator and denominator by 20.
- This reduces exactly to \( \frac{5}{9} \).
- Therefore, the correct formula is \( ^\circ C = \frac{5}{9}( ^\circ F - 32) \).
Why other options are incorrect:- Option A & D: Adding 32 instead of subtracting it is mathematically incorrect (water freezes at +32°F, so we must subtract it to reach the 0°C baseline).
- Option B: The fraction 9/5 is used when converting from Celsius to Fahrenheit (\( ^\circ F = \frac{9}{5} ^\circ C + 32 \)).
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