Temperature Conversion Worksheet - Free Printable

Problem Overview:

The task involves converting temperatures between Fahrenheit (°F) and Celsius (°C). The formulas for conversion are as follows:

1. From Fahrenheit to Celsius:
\[
C = \frac{5}{9} \times (F - 32)
\]

2. From Celsius to Fahrenheit:
\[
F = \left( \frac{9}{5} \times C \right) + 32
\]

The worksheet provides a series of conversions, and the answers are already filled in. Our task is to verify these conversions using the formulas and explain the process.

---

Step-by-Step Verification:

#### Part 1: Convert to Celsius
We will use the formula:
\[
C = \frac{5}{9} \times (F - 32)
\]

1. 140°F:
\[
C = \frac{5}{9} \times (140 - 32) = \frac{5}{9} \times 108 = 60.0^\circ C
\]
Answer: \(60.0^\circ C\)

2. 66°F:
\[
C = \frac{5}{9} \times (66 - 32) = \frac{5}{9} \times 34 = 18.9^\circ C
\]
Answer: \(18.9^\circ C\)

3. 45°F:
\[
C = \frac{5}{9} \times (45 - 32) = \frac{5}{9} \times 13 = 7.2^\circ C
\]
Answer: \(7.2^\circ C\)

4. 263°F:
\[
C = \frac{5}{9} \times (263 - 32) = \frac{5}{9} \times 231 = 128.3^\circ C
\]
Answer: \(128.3^\circ C\)

5. 20°F:
\[
C = \frac{5}{9} \times (20 - 32) = \frac{5}{9} \times (-12) = -6.7^\circ C
\]
Answer: \(-6.7^\circ C\)

6. 58°F:
\[
C = \frac{5}{9} \times (58 - 32) = \frac{5}{9} \times 26 = 14.4^\circ C
\]
Answer: \(14.4^\circ C\)

7. 350°F:
\[
C = \frac{5}{9} \times (350 - 32) = \frac{5}{9} \times 318 = 176.7^\circ C
\]
Answer: \(176.7^\circ C\)

8. 10°F:
\[
C = \frac{5}{9} \times (10 - 32) = \frac{5}{9} \times (-22) = -12.2^\circ C
\]
Answer: \(-12.2^\circ C\)

9. 0°F:
\[
C = \frac{5}{9} \times (0 - 32) = \frac{5}{9} \times (-32) = -17.8^\circ C
\]
Answer: \(-17.8^\circ C\)

10. 420°F:
\[
C = \frac{5}{9} \times (420 - 32) = \frac{5}{9} \times 388 = 215.6^\circ C
\]
Answer: \(215.6^\circ C\)

---

#### Part 2: Convert to Fahrenheit
We will use the formula:
\[
F = \left( \frac{9}{5} \times C \right) + 32
\]

11. 35°C:
\[
F = \left( \frac{9}{5} \times 35 \right) + 32 = 63 + 32 = 95.0^\circ F
\]
Answer: \(95.0^\circ F\)

12. 2°C:
\[
F = \left( \frac{9}{5} \times 2 \right) + 32 = 3.6 + 32 = 35.6^\circ F
\]
Answer: \(35.6^\circ F\)

13. -8°C:
\[
F = \left( \frac{9}{5} \times (-8) \right) + 32 = -14.4 + 32 = 17.6^\circ F
\]
Answer: \(17.6^\circ F\)

14. 72°C:
\[
F = \left( \frac{9}{5} \times 72 \right) + 32 = 129.6 + 32 = 161.6^\circ F
\]
Answer: \(161.6^\circ F\)

15. 160°C:
\[
F = \left( \frac{9}{5} \times 160 \right) + 32 = 288 + 32 = 320.0^\circ F
\]
Answer: \(320.0^\circ F\)

16. -18°C:
\[
F = \left( \frac{9}{5} \times (-18) \right) + 32 = -32.4 + 32 = -0.4^\circ F
\]
Answer: \(-0.4^\circ F\)

17. 57°C:
\[
F = \left( \frac{9}{5} \times 57 \right) + 32 = 102.6 + 32 = 134.6^\circ F
\]
Answer: \(134.6^\circ F\)

18. 210°C:
\[
F = \left( \frac{9}{5} \times 210 \right) + 32 = 378 + 32 = 410.0^\circ F
\]
Answer: \(410.0^\circ F\)

19. 17°C:
\[
F = \left( \frac{9}{5} \times 17 \right) + 32 = 30.6 + 32 = 62.6^\circ F
\]
Answer: \(62.6^\circ F\)

20. -5°C:
\[
F = \left( \frac{9}{5} \times (-5) \right) + 32 = -9 + 32 = 23.0^\circ F
\]
Answer: \(23.0^\circ F\)

---

#### Part 3: Mixed Conversions
We will alternate between the two formulas as needed.

21. -1°C:
\[
F = \left( \frac{9}{5} \times (-1) \right) + 32 = -1.8 + 32 = 30.2^\circ F
\]
Answer: \(30.2^\circ F\)

22. 42°F:
\[
C = \frac{5}{9} \times (42 - 32) = \frac{5}{9} \times 10 = 5.6^\circ C
\]
Answer: \(5.6^\circ C\)

23. 33°C:
\[
F = \left( \frac{9}{5} \times 33 \right) + 32 = 59.4 + 32 = 91.4^\circ F
\]
Answer: \(91.4^\circ F\)

24. 95°C:
\[
F = \left( \frac{9}{5} \times 95 \right) + 32 = 171 + 32 = 203.0^\circ F
\]
Answer: \(203.0^\circ F\)

25. 340°F:
\[
C = \frac{5}{9} \times (340 - 32) = \frac{5}{9} \times 308 = 171.1^\circ C
\]
Answer: \(171.1^\circ C\)

26. 25°F:
\[
C = \frac{5}{9} \times (25 - 32) = \frac{5}{9} \times (-7) = -3.9^\circ C
\]
Answer: \(-3.9^\circ C\)

27. -10°C:
\[
F = \left( \frac{9}{5} \times (-10) \right) + 32 = -18 + 32 = 14.0^\circ F
\]
Answer: \(14.0^\circ F\)

28. 12°F:
\[
C = \frac{5}{9} \times (12 - 32) = \frac{5}{9} \times (-20) = -11.1^\circ C
\]
Answer: \(-11.1^\circ C\)

29. 190°C:
\[
F = \left( \frac{9}{5} \times 190 \right) + 32 = 342 + 32 = 374.0^\circ F
\]
Answer: \(374.0^\circ F\)

30. 95°F:
\[
C = \frac{5}{9} \times (95 - 32) = \frac{5}{9} \times 63 = 35.0^\circ C
\]
Answer: \(35.0^\circ C\)

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Final Answer:

All the conversions have been verified using the appropriate formulas. The provided answers in the worksheet are correct.

\[
\boxed{\text{All answers are correct.}}
\]