Question

Frank hears that the average temperature at a science station in Antarctica one winter is \(-40^{\circ} \mathrm{C}\). He knows he can change the Celsius temperature into Fahrenheit by multiplying the given temperature by 9 , adding 160 , and then dividing by 5 . What temperature should Frank come up with? A. \(-104^{\circ} \mathrm{F}\) B. \(-40^{\circ} \mathrm{F}\) C. \(40^{\circ} \mathrm{F}\) D. \(104^{\circ} \mathrm{F}\)

Short answer

-40^{\bullet} F. So, the correct answer is B.

Step-by-step solution

Understand the Formula

The formula to convert Celsius to Fahrenheit is given as: Multiply the Celsius temperature by 9, add 160, and then divide by 5.

Apply the Formula

Start by inserting the given temperature, \(-40^{\bullet} C\), into the formula: \[ F = \frac{9 \times C + 160}{5} \text {Where } C = -40\]

Perform the Multiplication

Multiply \(-40\) by 9. \[9 \times -40 = -360 \]

Add 160 to the Result

Add 160 to \(-360\). \[-360 + 160 = -200 \]

Divide by 5

Divide the result by 5. \[ \frac{-200}{5} = -40 \]

Find the Answer

The temperature in Fahrenheit is \( -40^{\bullet} F\). So, the correct answer is \(B. -40^{\bullet} F\).

Key concepts

Celsius to Fahrenheit Conversion

Temperature conversion is an essential skill in science.
One of the most common conversions is between Celsius and Fahrenheit.
To convert a temperature from Celsius to Fahrenheit, follow a specific formula.
The formula is: Multiply the Celsius temperature by 9, add 160, then divide by 5.
For example, let's convert \(-40^{\bullet} C\) to Fahrenheit.
We input \(-40\) into the formula, perform the operations, and find the result. Following these steps will always give you the Fahrenheit equivalent of a given Celsius temperature.

Mathematical Formulas

Mathematical formulas are tools that help us solve specific types of problems.
The formula for converting Celsius to Fahrenheit can be written as:
\[ F = \frac{9 \times C + 160}{5} \text {, where } C \text{ is the temperature in Celsius} \text { and } F \text{ is the temperature in Fahrenheit}\]
This formula is precise and can be used for any Celsius temperature.
By understanding and using this formula, one can easily change temperatures from one unit to another.
Formulas like this one are crucial in math and science because they provide clear methods to find solutions.

Arithmetic Operations

Understanding arithmetic operations is key to solving math problems.
In our example, we use three operations: multiplication, addition, and division.
Let's look at each step:

- **Step 1: Multiplication**: We multiply \(-40\) by 9, giving us \-360\.

- **Step 2: Addition**: We add 160 to \(-360\), resulting in \-200\.

- **Step 3: Division**: Finally, we divide \text{-200}\ by 5, getting back \text{-40}\.

These operations must be done in order so the correct result is obtained. Practicing these steps with different numbers can help improve skills in arithmetic operations.