Problem 119 - Introductory Algebra for College Students

Question

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I found the variation in U.S. temperature by subtracting the record low temperature, a negative number, from the record high temperature, a positive number.

Step-by-Step Solution

Answer

The statement 'makes sense'. The process of subtracting a negative temperature (record low) from a positive temperature (record high) gives the correct variation as it adds the magnitude of the negative number to the positive one, reflecting the real temperature range.

Step 1: Understanding the Statement

First, let's look at the statement more closely. It says, 'I found the variation in U.S. temperature by subtracting the record low temperature (a negative number) from the record high temperature (a positive number).' Without doing the math, we need to understand if this process makes sense.

Step 2: Analyzing the Process

Considering the term 'variation', it refers to the difference between two numbers. Here, those numbers are the record high and low temperatures. When you subtract a negative number from a positive number, you are essentially adding the absolute value of the negative number to the positive number. This operation will widen the gap between the two temperatures, therefore, it does correctly represent the variation between the two temperatures.

Step 3: Concluding the Analysis

Given the process and the definition of 'variation', the method of calculating the variation in temperatures by subtracting the record low temperature from the record high temperature indeed makes sense. This is because subtracting a negative number from a positive one actually results in adding the magnitude of the negative number to the positive one, which increases the temperature range, capturing the variation correctly.