Question

The record January temperatures (in degrees Fahrenheit) for a city are given. Find the distance between the numbers to determine the range of temperatures for January.McGrath, Alaska: lowest: \(-75^{\circ} \mathrm{F}\) highest: \(54^{\circ} \mathrm{F}\)

Short answer

The range of temperatures for January in McGrath, Alaska is \(129^{\circ} \mathrm{F}\).

Step-by-step solution

- Identify the Lowest and Highest Temperatures

Identify the lowest and highest temperatures in January for McGrath, Alaska. The lowest is \(-75^{\circ} \mathrm{F}\) and the highest is \(54^{\circ} \mathrm{F}\).

- Apply the formula for calculating the range

The range is calculated by subtracting the lowest value from the highest. So let's subtract the lowest temperature from the highest temperature to calculate the range. This would mean subtracting \(-75^{\circ} \mathrm{F}\) from \(54^{\circ} \mathrm{F}\). The range becomes \(54 - (-75) = 129^{\circ} \mathrm{F}\). The negative sign before the 75 becomes positive when you subtract, because subtracting a negative number is the equivalent of adding a positive number.

Key concepts

Understanding the Range of Temperatures

When we talk about the range of temperatures, we refer to the difference between the highest and lowest temperatures observed over a given period. It's a simple but effective way to gauge how extreme weather conditions can get. The larger the range, the more varied the climatic conditions are likely to be.

In our example with McGrath, Alaska, the range must be calculated by identifying the highest and lowest temperatures on record for January and then finding the difference between these two values. Expressing the range numerically gives us a clear idea of temperature variability, which might impact everything from clothing choices to survival strategies in such extreme climates.

It's worth noting that in different areas and seasons, the calculated range can vary significantly, hence why understanding the method to determine this range is critical for students studying geography or climate science.

Working with Negative Numbers in Calculations

Dealing with negative numbers can sometimes get confusing, but it's crucial in many real-world situations, like calculating temperature ranges. Negative numbers represent values less than zero, which are commonly encountered in temperatures, debts, or below sea-level elevations, to name a few examples.

Subtracting a negative number—which you might come across while calculating a temperature range—is the same as adding its positive counterpart. This is because two negatives make a positive. Hence, asking what is the difference between -75 and 54 degrees, requires us to subtract -75 from 54, which translates to adding 75 to 54. The result is a positive 129 degrees Fahrenheit, which signifies the vast range of temperatures experienced in McGrath, Alaska.

This concept is fundamental not just in mathematics but in science, finance, and more, making it a valuable part of any curriculum.

Applying Formulas in Algebra

Algebra serves as the language through which we express and solve a wide array of mathematical problems. Applying formulas is a significant aspect of algebra that helps us to systematically approach and solve problems using established relationships between quantities. In the context of our temperature range problem, the formula is simple: subtract the lowest temperature from the highest.

It might look straightforward, but the process of applying such formulas often requires careful consideration of mathematical rules, particularly when negative numbers are involved. By using algebraic formulas, we can turn real-world problems into solvable equations, and mastering this skill is a turning point in any student's mathematical education. Algebra is not just about finding unknowns, but also about applying structured methods to interpret and resolve practical issues.