Problem 117 - Introductory Algebra for College Students

Question

Use the formula \(C=5(F-32)\) to express each Fahrenheit temperature, \(F,\) as its equivalent Celsius temperature, \(C\). $$-22^{\circ} \mathrm{F}$$

Step-by-Step Solution

Answer

The equivalent Celsius temperature for -22°F is -270°C.

Step 1: Identify the value of Fahrenheit

The temperature given in Fahrenheit is -22 degrees.

Step 2: Substitute F into the formula

The formula for conversion from Fahrenheit to Celsius is \(C = 5(F-32)\). Substitute the value of F (-22) into the formula to get \(C = 5(-22 - 32)\).

Step 3: Perform the operations

Perform the subtraction within the parentheses first to get \(C = 5(-54)\). Then perform the multiplication operation to find the value of C which is -270.

Key Concepts

Fahrenheit to Celsius

Temperature conversion from Fahrenheit to Celsius is a fundamental concept in understanding how different temperature scales relate to one another. Fahrenheit, used mainly in the United States, and Celsius, used worldwide in scientific contexts and most other countries, offer distinct ways to measure temperature. To convert temperatures from Fahrenheit to Celsius, you need to use a special formula. This is because the two scales are offset by different starting points and increments per degree.

To make this conversion, we use the formula:

• The formula is given by: \[ C = 5(F - 32) \] where:
  • \( C \) stands for Celsius
  • \( F \) represents Fahrenheit

This formula effectively re-scales Fahrenheit temperatures into Celsius, making it easy to understand global temperature values in science and day-to-day weather forecasts.

algebraic formula

An algebraic formula is a mathematical statement that expresses a relationship between variables using numbers and symbols. In our case, the formula \( C = 5(F - 32) \) is an example of an algebraic formula used for practical purposes. This formula helps us transform a temperature value in Fahrenheit into Celsius by performing a sequence of arithmetic operations.

The steps involved in using an algebraic formula include:

• Identifying variables and constants: Here, \( F \) is a variable (the input temperature in Fahrenheit), and \( C \) is the variable we want to find (the output temperature in Celsius).
• Substituting values: Substitute the given Fahrenheit value into the formula.
• Perform arithmetic operations: Follow step-by-step arithmetic operations, such as subtraction and multiplication, in a sequence.

Understanding how to manipulate algebraic formulas is crucial in mathematics, as it allows you to solve a wide array of problems by clearly delineating the relationship between different elements involved. This elementary operation skill is not only used in the class but also frequently in scientific work, engineering, and technology.

educational mathematics

Educational mathematics provides the foundational knowledge students need to understand and manipulate numbers and variables using formulas, such as the temperature conversion formula. By comprehending and applying these techniques, students develop problem-solving skills that are beneficial in a wide range of disciplines.

In educational settings, breaking down complex concepts into simpler steps is key:

• Introduce the problem and its context: For instance, how to convert temperatures for local weather forecasts or understanding scientific data.
• Guide through step-by-step solutions: As seen with substituting -22°F into the formula and performing arithmetic operations to find the Celsius equivalent.
• Provide real-world applications: Understanding temperature changes, for example, helps students relate classroom problems to real-life scenarios, like weather forecasting or cooking.

Educational mathematics aligns abstract ideas with practical examples to solidify learning, making it both an essential academic subject and a useful life skill. Through exercises like these, students enhance their logical thinking and analytical skills, which are crucial in academic and everyday decisions.