# Lesson 3: Comparing Positive and Negative Numbers

Let’s compare numbers on the number line.

## 3.1: Which One Doesn’t Belong: Inequalities

Which inequality doesn’t belong?

$\frac{5}{4} < 2$

$8.5 > 0.95$

$8.5 < 7$

$10.00 < 100$

## 3.2: Comparing Temperatures

Here are the low temperatures, in degrees Celsius, for a week in Anchorage, Alaska.

day Mon Tues Weds Thurs Fri Sat Sun
temperature 5 -1 -5.5 -2 3 4 0
1. Plot the temperatures on a number line. Which day of the week had the lowest low temperature?
2. The lowest temperature ever recorded in the United States was -62 degrees Celsius, in Prospect Creek Camp, Alaska. The average temperature on Mars is about -55 degrees Celsius.

1. Which is warmer, the coldest temperature recorded in the USA, or the average temperature on Mars? Explain how you know.
3. On a winter day the low temperature in Anchorage, Alaska was -21 degrees Celsius and the low temperature in Minneapolis, Minnesota was -14 degrees Celsius.

Jada said: “I know that 14 is less than 21, so -14 is also less than -21. This means that it was colder in Minneapolis than in Anchorage.”

Do you agree? Explain your reasoning.

## 3.3: Rational Numbers on a Number Line

1. Plot the numbers -2, 4, -7, and 10 on the number line. Label each point with its numeric value.
1. Decide whether each inequality statement is true or false. Be prepared to explain your reasoning.

$\text-2 < 4$

$\text-2 < \text-7$

$4 > \text-7$

$\text-7 > 10$

Drag each point to its proper place on the number line. Use your observations to help answer the questions that follow.

GeoGebra Applet wh5qyme4

1. Andre says that $\frac14$ is less than $\text{-}\frac {3}{4}$ because, of the two numbers, $\frac14$ is closer to 0. Do you agree? Explain your reasoning.

2. Answer each question. Be prepared to explain how you know.
1. Which number is greater: $\frac14$ or $\frac54$?

2. Which number is farther from 0: $\frac14$ or $\frac54$?

3. Which number is greater: $\text{-}\frac {3}{4}$ or $\frac58$?

4. Which number is farther from 0: $\text{-}\frac {3}{4}$ or $\frac58$?

5. Is the number that is farther from 0 always the greater number? Explain your reasoning.

## Summary

We use the words greater than and less than to compare numbers on the number line. For example, the numbers -2.7, 0.8, and -1.3, are shown on the number line.

Because -2.7 is to the left of -1.3, we say that -2.7 is less than -1.3. We write: $$\text-2.7 <\text -1.3$$ In general, any number that is to the left of a number $n$ is less than $n$.

We can see that -1.3 is greater than -2.7 because -1.3 is to the right of -2.7. We write $$\text-1.3 >\text -2.7$$ In general, any number that is to the right of a number $n$ is greater than $n$

We can also see that $0.8 > \text-1.3$ and $0.8 > \text-2.7$. In general, any positive number is greater than any negative number.

## Glossary

sign

#### sign

The sign of a nonzero number is either positive or negative.