- Identify the given temperature as \(77^{\circ}\text{F}\) and the conversion formula as \(T_{\left(^{\circ}\text{C}\right)} = (T_{\left(^{\circ}\text{F}\right)} - 32) \times \frac{5}{9}\).
- Substitute \(77\) into the formula and perform the subtraction: \(77 - 32 = 45\).
- Multiply by \(\frac{5}{9}\) to get \(45 \times \frac{5}{9} = 25\).
- The final temperature is \(\boxed{25^{\circ}\text{C}}\).
Explanation
- Understanding the Problem and Data
The goal is to convert the temperature from Fahrenheit to Celsius using the given conversion formula:
\[T_{\left(^{\circ}\text{C}\right)} = \left( T_{\left(^{\circ}\text{F}\right)} - 32 \right) \times \frac{5}{9}\]
We are given that the temperature in degrees Fahrenheit is \(T_{\left(^{\circ}\text{F}\right)} = 77\). Our task is to substitute this value into the formula and evaluate it to find the equivalent temperature in degrees Celsius.
- Calculation and Evaluation
We substitute \(T_{\left(^{\circ}\text{F}\right)} = 77\) into the conversion formula:
\[T_{\left(^{\circ}\text{C}\right)} = \left( 77 - 32 \right) \times \frac{5}{9}\]
First, perform the subtraction inside the parentheses:
\[77 - 32 = 45\]
Now, substitute this result back into the formula:
\[T_{\left(^{\circ}\text{C}\right)} = 45 \times \frac{5}{9}\]
Next, multiply 45 by \(\frac{5}{9}\). We can simplify this by dividing 45 by 9 first:
\[45 \div 9 = 5\]
Then multiply by 5:
\[5 \times 5 = 25\]
Thus, the temperature is \(25^{\circ}\text{C}\).
Examples
Temperature conversion is essential in daily life for understanding weather forecasts and scientific measurements. For example, if you are traveling to a country that uses the Celsius scale, knowing how to convert temperatures can help you pack appropriate clothing or understand the climate. Converting \(77^{\circ}\text{F}\) (a pleasant room temperature) to \(25^{\circ}\text{C}\) helps in adjusting to local environmental standards effectively.