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Chapter 2: Problem 5

Tell which temperature is warmer. \(5^{\circ} \mathrm{F}\) or \(-15^{\circ} \mathrm{F}\)

Short Answer

Expert verified
5掳F is warmer than -15掳F.

Step by step solution

01

Understand the Significance of Positive and Negative Temperatures

A positive temperature indicates warmth compared to a negative temperature, which indicates cold. Therefore, recognizing which number is positive or negative will help determine which is warmer.
02

Compare the Values Directly

Identify the given temperatures: \(5^{\circ} \mathrm{F}\) and \(-15^{\circ} \mathrm{F}\). Since 5 is a positive number and -15 is a negative number, we can already infer that 5 is warmer. Generally, a positive temperature is always warmer than a negative one as it lies to the right on the number line.
03

Conclusion

Based on the number line comparison, \(5^{\circ} \mathrm{F}\) is warmer than \(-15^{\circ} \mathrm{F}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Positive and Negative Numbers
Understanding the difference between positive and negative numbers is crucial when comparing temperatures. Positive numbers are greater than zero and indicate a higher, warmer value. Negative numbers, on the other hand, are less than zero and represent a lower, colder value. When you compare a positive number to a negative one, the positive number is always higher. For example:
  • 5 is a positive number, signifying warmth.
  • -15 is a negative number, indicating cold.
Therefore, in temperature terms, 5掳F is warmer than -15掳F.
Number Line
A number line is a handy tool for comparing values, including temperatures. It is a straight line where numbers are placed in their respective order.
Positive numbers appear to the right of zero, and negative numbers to the left. For instance, consider 5 and -15:
  • 5 is positioned to the right of 0.
  • -15 is positioned to the left of 0.
Since numbers increase as you move to the right of the line, 5 is to the right of -15, making it a higher value. Consequently, a temperature of 5掳F is warmer than -15掳F.
Temperature Comparison
When comparing temperatures, it is essential to look at the values' signs. Positive temperatures are always warmer than negative temperatures. This is because a positive temperature (above zero) indicates more warmth than a negative temperature (below zero). Let's consider the given values again:
  • 5掳F is a positive temperature.
  • -15掳F is a negative temperature.
Since positive numbers are higher than negative ones, 5掳F is warmer than -15掳F. This means any temperature above zero will always be warmer than any temperature below zero. Remember, looking at the sign of the temperature is the first step in determining which one is warmer.

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