Problem 50 - Elementary Algebra

Question

Convert the following temperatures to degrees Celsius given \(C=59(F-32),\) where F represents degrees Fahrenheit. $$ 0^{\circ} \mathrm{F} $$

Step-by-Step Solution

Answer

0°F is approximately -17.78°C.

Step 1: Identify the Formula

The formula to convert Fahrenheit to Celsius is \( C = \frac{5}{9}(F - 32) \). We'll use this formula to perform the conversion.

Step 2: Substitute the Fahrenheit Value

Substitute the given Fahrenheit value into the formula. Here, \( F = 0 \). Substitute this value into the formula: \( C = \frac{5}{9}(0 - 32) \).

Step 3: Simplify the Expression

Perform the subtraction inside the parenthesis: \( 0 - 32 = -32 \). The expression becomes \( C = \frac{5}{9}(-32) \).

Step 4: Calculate Celsius Temperature

Multiply \( -32 \) by \( \frac{5}{9} \) to find the equivalent Celsius temperature. This is \( C = \frac{5}{9} \times (-32) = -\frac{160}{9} \approx -17.78 \).

Step 5: Round the Result

Round \(-17.78\) to two decimal places, which gives approximately \(-17.78\).

Key Concepts

Fahrenheit to Celsius

Converting temperatures from Fahrenheit to Celsius is quite straightforward, once you understand the formula. The formula for this conversion, \( C = \frac{5}{9}(F - 32) \), allows us to translate a temperature expressed in degrees Fahrenheit into one in degrees Celsius. This formula is derived from the relationship between the two scales:

• The Celsius scale is based on 0 for the freezing point of water and 100 for the boiling point.
• The Fahrenheit scale is based on 32 for the freezing point and 212 for the boiling point of water.

By using the conversion formula, you subtract 32 from the Fahrenheit temperature to adjust for the zero mark difference.
Then, multiply by \( \frac{5}{9} \) to convert the size of the Fahrenheit degree increment to that of a Celsius degree.

Math Formulas

Math formulas are equations that express relationships between different quantities. They are essential tools for solving mathematical problems and making calculations smoother. In our case, the formula \( C = \frac{5}{9}(F - 32) \) is used for converting Fahrenheit to Celsius temperatures.

• The fraction \( \frac{5}{9} \) signifies the proportional relationship between the temperature units on the Celsius and Fahrenheit scales.
• The subtraction of 32 accounts for the different starting points of the two scales.

Understanding math formulas involves recognizing their components and the logical order of operations. Remember to handle the parenthesis first, which tells us to perform subtraction before multiplication.
This structured approach simplifies complex mathematical tasks, making them approachable and solvable.

Algebraic Expressions

An algebraic expression represents a combination of numbers, variables, and mathematical operations. In the temperature conversion formula, \( C = \frac{5}{9}(F - 32) \), "C" and "F" represent specific variables: the Celsius and Fahrenheit temperatures, respectively.
The expression consists of:

• The variable \( F \), which gives us flexibility to plug in any Fahrenheit temperature we need to convert.
• The operations inside the parenthesis, \( F - 32 \), which need to be calculated first.
• The multiplication by the fraction \( \frac{5}{9} \), which adjusts the difference to the size of degrees on the Celsius scale.

Breaking down algebraic expressions into steps, as done here, helps in solving the equation accurately. These expressions are the building blocks of algebra and are used widely across various fields of science and mathematics.