Converting Celsius to Fahrenheit

A weather report shows $25°C$. What is this in Fahrenheit?

Write the formula: $°F = (°C \times \frac{9}{5}) + 32$ = Formula identified

Substitute the Celsius value: $°F = (25 \times \frac{9}{5}) + 32$ = Values substituted

Multiply by 9/5: $25 \times \frac{9}{5} = 25 \times 1.8 = 45$ = $45$

Add 32: $45 + 32 = 77$ = $77°F$

Answer: $25°C = 77°F$ — a pleasant warm day!

Converting Fahrenheit to Celsius

The oven is set to $350°F$. What is this in Celsius?

Write the formula: $°C = (°F - 32) \times \frac{5}{9}$ = Formula identified

Subtract 32 from the Fahrenheit value: $350 - 32 = 318$ = $318$

Multiply by 5/9: $318 \times \frac{5}{9} = \frac{1590}{9} \approx 176.67$ = $\approx 177°C$

Round appropriately: Oven temperatures are typically rounded to the nearest 5 = $\approx 175°C$ or $180°C$

Answer: $350°F \approx 177°C$ — a common baking temperature

Converting Body Temperature

Normal body temperature is $98.6°F$. What is this in Celsius?

Write the formula: $°C = (°F - 32) \times \frac{5}{9}$ = Formula identified

Subtract 32: $98.6 - 32 = 66.6$ = $66.6$

Multiply by 5/9: $66.6 \times \frac{5}{9} = \frac{333}{9} = 37$ = $37°C$

Verify the answer: This is a well-known medical reference point = Confirmed: $37°C$

Answer: $98.6°F = 37°C$ — normal human body temperature

Mistake: Forgetting to add or subtract 32

Why: The 32 accounts for the different zero points of the two scales (water freezes at 32°F but 0°C).

Correct: Always remember: C to F, add 32 at the END. F to C, subtract 32 at the START.

Mistake: Using 9/5 instead of 5/9 (or vice versa)

Why: The two conversions use reciprocal fractions. Fahrenheit degrees are smaller, so there are more of them.

Correct: C to F: multiply by 9/5 (makes the number bigger). F to C: multiply by 5/9 (makes the number smaller).

Mistake: Doing operations in the wrong order

Why: Order of operations matters! The formulas have a specific sequence.

Correct: C to F: first multiply, then add. F to C: first subtract, then multiply.

International Travel

When traveling between countries using different temperature scales, you need to understand local weather forecasts.

If Paris reports a high of $28°C$, that's $(28 \times 1.8) + 32 = 82.4°F$ — bring light clothes!

Cooking and Baking

Recipes from different countries use different temperature scales. Converting correctly is essential for cooking success.

A British recipe calls for $200°C$. That's $(200 \times 1.8) + 32 = 392°F$, so set your oven to $400°F$.

Q: Why are there two different temperature scales?

A: Fahrenheit was developed first (1724) by Daniel Fahrenheit. Celsius was developed later (1742) by Anders Celsius using water's freezing and boiling points as reference. Most of the world switched to Celsius, but the US still uses Fahrenheit.

Q: Is there a temperature where Celsius equals Fahrenheit?

A: Yes! At $-40$, both scales show the same number: $-40°C = -40°F$. You can verify: $(-40 \times 1.8) + 32 = -72 + 32 = -40$.

Q: What is the quick estimation trick?

A: For a rough estimate: C to F: double it and add 30. F to C: subtract 30 and halve it. Example: $20°C$ → roughly $(20 \times 2) + 30 = 70°F$ (actual: $68°F$).