Question

Use the formula \(C=\frac{5}{9}(F-32)\) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature. \(F=77^{\circ}\)

Short answer

The Celsius measure for \(77^{\circ}F\) is \(25^{\circ}C\).

Step-by-step solution

- Write Down the Formula

Start with the given formula for converting Fahrenheit to Celsius: \[ C = \frac{5}{9}(F - 32) \]

- Substitute the Given Fahrenheit Value

Substitute \( F = 77^{\circ} \) into the formula: \[ C = \frac{5}{9}(77 - 32) \]

- Simplify the Expression Inside the Parentheses

Calculate the value inside the parentheses first: \[ 77 - 32 = 45 \] So the equation now looks like: \[ C = \frac{5}{9} \times 45 \]

- Perform the Multiplication

Multiply \( \frac{5}{9} \) with 45: \[ C = 5 \times 5 = 25 \] (since \( \frac{45}{9} = 5 \)).

- State the Final Answer

The Celsius measure for \( 77^{\circ}F \) is \( 25^{\circ}C \).

Key concepts

Fahrenheit to Celsius

Many students find temperature conversions confusing. One of the most common conversions is from Fahrenheit to Celsius. Fahrenheit and Celsius are two different scales to measure temperature. To convert from Fahrenheit to Celsius, we can use the formula: \( C = \frac{5}{9}(F - 32) \). This formula takes the Fahrenheit temperature, subtracts 32, and then multiplies the result by \( \frac{5}{9} \). This way, we can accurately convert temperatures from the Fahrenheit scale to the Celsius scale. Let's understand this step-by-step conversion process with an example.

temperature conversions

Temperature conversions are important in various fields like science, everyday life, and travel. To convert temperatures, we use mathematical formulas that relate different temperature scales, like Fahrenheit, Celsius, and Kelvin. Here's how it works for Fahrenheit to Celsius:

• Start with the formula: \( C = \frac{5}{9}(F - 32) \).
• Substitute the Fahrenheit temperature you want to convert.
• Simplify the expression inside the parentheses, which means you first subtract 32 from the Fahrenheit temperature.
• After this, multiply the result by \( \frac{5}{9} \) to get the Celsius temperature.

Using this method ensures that you get accurate results in your temperature conversions.

algebraic expressions

When converting temperatures, we often deal with algebraic expressions. Understanding these expressions is crucial to solving temperature conversion problems. In our given formula, \( C = \frac{5}{9}(F - 32) \), we see several algebraic components:

• \( F - 32 \): This part inside the parentheses represents the initial adjustment to the Fahrenheit temperature.
• \( \frac{5}{9} \): This fraction is the multiplier used to convert the adjusted Fahrenheit value to Celsius.

Remember, when you substitute a value and simplify, you're just following basic algebraic principles: substitute, simplify, and multiply. Grasping these concepts can make temperature conversion problems much easier to solve.