Compare the Temperatures Above and Below Zero

Temperature is one of the most relatable real-world uses of integers. Temperatures above zero are positive integers (or zero itself), and temperatures below zero are negative integers. Comparing temperatures above and below zero means comparing positive and negative numbers, a key skill on the GED Math test and in everyday situations like weather reports and science.

What Does “Above and Below Zero” Mean?

On a thermometer, temperatures are measured from a zero reference point (°F uses 32°F as a different reference, but on a number line 0°\(\color{blue}{C = \text{ freezing }}\)):

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• Above zero = positive temperatures (e.g., 15°C, 72°F)
• Zero = the reference point (0°\(\color{blue}{C = 32}\)°F)
• Below zero = negative temperatures (e.g., −8°C, −4°F)

A thermometer is simply a vertical number line: higher numbers mean warmer, lower (more negative) numbers mean colder.

Rules for Comparing Temperatures

On a number line, numbers increase from left to right (bottom to top on a thermometer)

• Any positive temperature > 0 > any negative temperature
• Between two positive temperatures: the larger number is warmer (15° > 8°)
• Between two negative temperatures: the one closer to zero is warmer (−3° > −12°)
• To compare any two temperatures, place them on a number line: the one further right (higher) is warmer

Finding the difference between two temperatures

Subtract the lower temperature from the higher temperature (or use absolute value):

\(\color{blue}{\text{ Difference } = \text{ Higher }}\) \(\color{blue}{\text{ temp } – \text{ Lower }}\) temp

• Difference between 15°F \(\color{blue}{\text{ and } -8}\)°\(\color{blue}{F = 15 – (-8) = 15 + 8}\) = 23°F
• Difference \(\color{blue}{\text{ between } -3}\)°C \(\color{blue}{\text{ and } -10}\)°C = −\(\color{blue}{3 – (-10)}\) = −\(\color{blue}{3 + 10}\) = 7°C

Step-by-Step Summary

1. Plot each temperature on a number line.
2. The number to the right (or higher on the thermometer) is the greater (warmer) temperature.
3. To find the difference, subtract the lower temperature from the higher temperature; remember that subtracting a negative equals adding a positive.
4. Use the correct symbol: > (greater than), < (less than), \(\color{blue}{\text{ or } = (\text{ equal to })}\).

Watch: Comparing and Ordering Integers (Video Lesson)

Math with Mr. J explains how to compare positive and negative integers, including temperature-style examples:

Worked Examples

Example 1: Order from coldest to warmest: 3°C, −12°C, 0°C, −5°C, 8°C.

On a number line: −12 < −5 < 0 < 3 < 8
Coldest to warmest: −12°C, −5°C, 0°C, 3°C, 8°C

Example 2: The temperature \(\color{blue}{\text{ was } -8}\)°C in the morning and rose to 15°C by afternoon. How many degrees did it rise?

\(\color{blue}{\text{ Change } = 15 – (-8) = 15 + 8}\) = 23°C

Example 3: Compare: −3°F ____ −10°F.

−3 is to the right \(\color{blue}{\text{ of } -10}\) on a number line, \(\color{blue}{\text{ so } -3}\) > −10.
−3°F > −10°F (−3° is warmer)

Example 4: The overnight low \(\color{blue}{\text{ was } -20}\)°C and the afternoon high was 5°C. What is the range of temperatures?

\(\color{blue}{\text{ Range } = 5 – (-20) = 5 + 20}\) = 25°C

More Practice: Temperature Word Problems (Video)

Khan Academy solves a real-world temperature word problem using integers and a number line:

Exercises

1. Write >, <, or = : −7°C ____ −2°C
2. Order from coldest to warmest: −15°F, 4°F, −3°F, 0°F, 12°F
3. The temperature dropped from 6°C \(\color{blue}{\text{ to } -9}\)°C. By how many degrees did it drop?
4. Which temperature is warmer: −1°C \(\color{blue}{\text{ or } -20}\)°C?
5. The high was 18°F and the low \(\color{blue}{\text{ was } -5}\)°F. What is the difference?
6. A cold day started \(\color{blue}{\text{ at } -12}\)°C and warmed up by 18 degrees. What was the final temperature?

Answers

1. −7°C < −2°C
2. −15°F, −3°F, 0°F, 4°F, 12°F
3. \(\color{blue}{6 – (-9) = 6 + 9}\) = 15°C
4. −1°C (closer to \(\color{blue}{\text{ zero } = \text{ warmer }}\))
5. \(\color{blue}{18 – (-5) = 18 + 5}\) = 23°F
6. −\(\color{blue}{12 + 18}\) = 6°C

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Frequently Asked Questions

Why \(\color{blue}{\text{ is } -3}\) > −10?

On the number line, −3 is to the right \(\color{blue}{\text{ of } -10}\), meaning it is closer to zero and represents a warmer temperature. The further left (more negative) a number is, the smaller it is.

How do I find how much a temperature changed?

Subtract the starting temperature from the ending temperature: \(\color{blue}{\text{ change } = \text{ end } – \text{ start }}\). If the result is positive, the temperature rose; if negative, it dropped.

Does it matter whether temperatures are in °C or °F for comparing?

For integer comparison purposes, the rules are the same: larger \(\color{blue}{\text{ number } = \text{ warmer }}\). However, you cannot directly compare a Celsius and a Fahrenheit temperature without converting first.

Related Topics

• Converting, Comparing, Adding and Subtracting Mixed Customary Units
• Absolute Value Definition
• Using Number Lines to Represent Integers
• Opposite Integers
• Solve Word Problems of Absolute Value and Integers