The Celsius to Fahrenheit formula: F=9/5 C + 32

Question

Solve this formula for C. Check all answers that are true.

(4 points)
Responses

First step is to multiply by 9 on each side.

First step is to add 32 to both sides.

The next step from F - 32 = 9/5 C, could be to multiply both sides by 5

The next step from F - 32 = 9/5 C, could be to divide both sides by 5

Solution: 5/9F - 32 = C

To solve this equation for C, you would have to distribute at some point.

Answer 1

To solve the Celsius to Fahrenheit formula \( F = \frac{9}{5} C + 32 \) for \( C \), we can follow these steps:

1. Subtract 32 from both sides: \[ F - 32 = \frac{9}{5} C \]

2. Multiply both sides by \( \frac{5}{9} \) to isolate \( C \): \[ C = \frac{5}{9} (F - 32) \]

3. Distribute \( \frac{5}{9} \): \[ C = \frac{5}{9}F - \frac{5}{9} \times 32 \]

So, the final solution is: \[ C = \frac{5}{9}F - \frac{160}{9} \]

Evaluating the Responses:

1. First step is to multiply by 9 on each side.

   • False. The first step is to subtract 32 from both sides, not to multiply.

2. First step is to add 32 to both sides.

   • False. The correct first step is to subtract 32 from both sides.

3. The next step from \( F - 32 = \frac{9}{5} C \) could be to multiply both sides by 5.

   • False. The correct step is to multiply both sides by \( \frac{5}{9} \), not just 5.

4. The next step from \( F - 32 = \frac{9}{5} C \) could be to divide both sides by 5.

   • False. Dividing by 5 wouldn't correctly isolate \( C \) since it is currently multiplied by \( \frac{9}{5} \).

5. Solution: \( \frac{5}{9}F - 32 = C \)

   • False. The correct solution should distribute the \( \frac{5}{9} \) to both terms: \( C = \frac{5}{9}F - \frac{160}{9} \).

6. To solve this equation for \( C \), you would have to distribute at some point.

   • True. Distributing the \( \frac{5}{9} \) is necessary to arrive at the final equation in terms of \( C \).

Summary of True/False Statements:

• 1: False
• 2: False
• 3: False
• 4: False
• 5: False
• 6: True