Mathematics worksheet for converting temperatures between Celsius and Fahrenheit.

To solve the temperature conversion problems, we will use the following formulas:

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

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

Part 1: Convert Temperatures from Celsius to Fahrenheit

#### Problem 1: \( 53^\circ C \)
\[
F = \left( 53 \times \frac{9}{5} \right) + 32
\]
\[
F = \left( 53 \times 1.8 \right) + 32
\]
\[
F = 95.4 + 32
\]
\[
F = 127.4
\]

#### Problem 2: \( 40^\circ C \)
\[
F = \left( 40 \times \frac{9}{5} \right) + 32
\]
\[
F = \left( 40 \times 1.8 \right) + 32
\]
\[
F = 72 + 32
\]
\[
F = 104
\]

Part 2: Convert Temperatures from Fahrenheit to Celsius

#### Problem 1: \( 208^\circ F \)
\[
C = \left( 208 - 32 \right) \times \frac{5}{9}
\]
\[
C = 176 \times \frac{5}{9}
\]
\[
C = 176 \times 0.5556
\]
\[
C \approx 97.78
\]

#### Problem 2: \( 110^\circ F \)
\[
C = \left( 110 - 32 \right) \times \frac{5}{9}
\]
\[
C = 78 \times \frac{5}{9}
\]
\[
C = 78 \times 0.5556
\]
\[
C \approx 43.33
\]

Part 3: Solve the Word Problems

#### Problem a: Yesterday it was \( 50^\circ C \) in Miami. What was the temperature in Fahrenheit?
Using the formula for Celsius to Fahrenheit:
\[
F = \left( 50 \times \frac{9}{5} \right) + 32
\]
\[
F = \left( 50 \times 1.8 \right) + 32
\]
\[
F = 90 + 32
\]
\[
F = 122
\]

#### Problem b: Australia was \( 100^\circ F \) earlier today. What was the temperature in Celsius?
Using the formula for Fahrenheit to Celsius:
\[
C = \left( 100 - 32 \right) \times \frac{5}{9}
\]
\[
C = 68 \times \frac{5}{9}
\]
\[
C = 68 \times 0.5556
\]
\[
C \approx 37.78
\]

Final Answers:

1. \( 53^\circ C = 127.4^\circ F \)
2. \( 40^\circ C = 104^\circ F \)
3. \( 208^\circ F = 97.78^\circ C \)
4. \( 110^\circ F = 43.33^\circ C \)
5. \( 50^\circ C = 122^\circ F \)
6. \( 100^\circ F = 37.78^\circ C \)

\[
\boxed{127.4, 104, 97.78, 43.33, 122, 37.78}
\]