Question

A scientist working during the summer at the South Pole station notes that the temperature is about \(-21^{\circ} \mathrm{F} .\) During the winter, she can expect the temperature to be as much as \(57^{\circ} \mathrm{F}\) colder. What temperature might she expect during the winter?

Short answer

Answer: The expected winter temperature at the South Pole station is -78°F.

Step-by-step solution

Identify the given values

The given values are: - Current summer temperature: \(-21^{\circ} \mathrm{F}\) - Temperature drop during winter: \(57^{\circ} \mathrm{F}\)

Subtract the temperature drop from the current temperature

To find the expected winter temperature, subtract the temperature drop (57 degrees Fahrenheit) from the current summer temperature (-21 degrees Fahrenheit): \(-21^{\circ} \mathrm{F} - 57^{\circ} \mathrm{F}\)

Perform the calculation

Calculate the result of the subtraction: \(-21^{\circ} \mathrm{F} - 57^{\circ} \mathrm{F} = -78^{\circ} \mathrm{F}\)

Write the final answer

The expected winter temperature at the South Pole station is \(-78^{\circ} \mathrm{F}\).

Key concepts

Understanding Temperature Subtraction

When dealing with temperature changes, subtraction is a key concept. In this context, the task was to determine how much colder the South Pole gets from summer to winter. Subtraction helps us find this difference in temperature. Here, you want to take the known summer temperature and adjust it by subtracting the expected drop in temperature.

It’s like tracking how much the weather changes over time. If you’re at \(-21^{\circ} \mathrm{F}\) and it's expected to get 57 degrees colder, you're simply finding the result of going from a known temperature to an even lower one. This action is represented mathematically as subtraction: \(-21 - 57\).

The solution shows that this straightforward arithmetic gives us a way to predict conditions in different seasons.

The Role of Negative Numbers

Negative numbers are essential when dealing with temperatures, especially in cold environments. Understanding them will help you in this type of arithmetic. In mathematics, numbers to the left of zero on the number line are negative, and they reflect temperatures below freezing.

In the exercise, \(-21^{\circ} \mathrm{F}\) is already a negative. When we subtract another positive number (57), it means we are moving further into the negatives. This can be visualized by thinking of a thermometer: as the temperature drops, the mercury or digital reading moves down the scale.

Subtracting 57 from \(-21\) involves adding a greater negative value, which results in \(-78^{\circ} \mathrm{F}\). Understanding the interplay of positive and negative values is crucial in accurately reading and calculating temperature differences.

Real-Life Application of Math Concepts

Math is not just about numbers and formulas; it’s a tool to understand the world. Temperature calculation is just one of many ways math is applied in real life. Think about scientists studying climate patterns. They use math to predict weather changes, much like finding the expected winter temperature at the South Pole.

In this scenario, a simple subtraction helped anticipate seasonal temperatures. Such predictions can be vital for planning research activities, ensuring safety, and even for designing equipment and structures that can withstand extreme cold.

Beyond science, math aids in everyday decisions, like budgeting or planning travel itineraries based on seasonal changes. Learning how to apply mathematical concepts in various real-world contexts develops critical thinking and analytical skills.