Chapter 10: Problem 7
Evaluate \(\frac{9}{5} C+32\) for \(C=-40\) A. -72 B. -40 C. 0 D. 40
Short Answer
Expert verified
B. -40
Step by step solution
01
Understand the Formula
The formula given is \(\frac{9}{5}C + 32\). It is used to convert a temperature from Celsius to Fahrenheit.
02
Substitute the Value of C
We need to substitute \(-40\) for \(C\) in the formula. So, it becomes \(\frac{9}{5} \times (-40) + 32\).
03
Multiply the Fraction and the Value
Calculate \(\frac{9}{5} \times (-40)\). This is equal to \(\frac{9 \times -40}{5} = -72\).
04
Add the Constant
Now, add 32 to \(-72\). \(-72 + 32 = -40\).
05
Choose the Correct Answer
The final result is \(-40\), which corresponds to option B.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Celsius to Fahrenheit
To convert a temperature from Celsius to Fahrenheit, you use the formula: \(\frac{9}{5}C + 32\).
This formula helps you quickly convert any temperature measured in Celsius to its Fahrenheit equivalent.
The formula can be broken down into two main parts:
This conversion formula is essential in many scientific fields and everyday situations since different countries use different temperature scales. To solidify your understanding of this concept, try converting a few temperatures on your own by following the two steps above.
This formula helps you quickly convert any temperature measured in Celsius to its Fahrenheit equivalent.
The formula can be broken down into two main parts:
- First, multiplying the Celsius temperature by \( \frac{9}{5} \).
- Then, adding 32 to the result.
This conversion formula is essential in many scientific fields and everyday situations since different countries use different temperature scales. To solidify your understanding of this concept, try converting a few temperatures on your own by following the two steps above.
Fraction Multiplication
Multiplying fractions is a fundamental concept in math that often appears in various problems, including temperature conversions.
The general rule is to multiply the numerators together and the denominators together. For example: \[ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \]
When you apply this to our problem: \[ \frac{9}{5} \times (-40) \], you multiply the numerators: 9 and -40, and the denominator 5 remains as it is. So, it becomes: \[ \frac{9 \times -40}{5} \]
This gives you: \[ \frac{-360}{5} = -72 \]
Whether dealing with whole numbers or fractions, understanding fraction multiplication is key!
The general rule is to multiply the numerators together and the denominators together. For example: \[ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \]
When you apply this to our problem: \[ \frac{9}{5} \times (-40) \], you multiply the numerators: 9 and -40, and the denominator 5 remains as it is. So, it becomes: \[ \frac{9 \times -40}{5} \]
This gives you: \[ \frac{-360}{5} = -72 \]
Whether dealing with whole numbers or fractions, understanding fraction multiplication is key!
Order of Operations
Order of operations is crucial for solving math problems correctly and avoiding mistakes. The order of operations dictates the sequence in which you should execute mathematical operations within an expression.
The most common acronym to remember is PEMDAS:
You should first handle the multiplication: \[ \frac{9}{5} \times (-40) = -72 \], and then perform the addition: \[ -72 + 32 = -40 \]
Keeping the correct order of operations in mind ensures that you arrive at the correct solution.
The most common acronym to remember is PEMDAS:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
You should first handle the multiplication: \[ \frac{9}{5} \times (-40) = -72 \], and then perform the addition: \[ -72 + 32 = -40 \]
Keeping the correct order of operations in mind ensures that you arrive at the correct solution.
Substitution in Formulas
Substitution is the process of replacing a variable with a given value in a mathematical formula.
It involves identifying the variable you need to replace and then precisely inserting the specified value into the location of the variable.
For example, in the temperature conversion formula: \[ \frac{9}{5} C + 32 \]
When told to evaluate for \( C = -40 \), the process is to substitute \( -40 \) wherever \( C \) appears in the formula, resulting in: \[ \frac{9}{5} \times (-40) + 32 \]
After substitution, you can carry on with the rest of the operations, such as multiplication and addition, to find the final result. Mastering substitution skills is crucial for solving more complex algebraic expressions and equations efficiently.
It involves identifying the variable you need to replace and then precisely inserting the specified value into the location of the variable.
For example, in the temperature conversion formula: \[ \frac{9}{5} C + 32 \]
When told to evaluate for \( C = -40 \), the process is to substitute \( -40 \) wherever \( C \) appears in the formula, resulting in: \[ \frac{9}{5} \times (-40) + 32 \]
After substitution, you can carry on with the rest of the operations, such as multiplication and addition, to find the final result. Mastering substitution skills is crucial for solving more complex algebraic expressions and equations efficiently.
