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Introduction to Positive and Negative Numbers
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Introduction

In this lesson, you will learn the importance of negative numbers.

Critical Thinking Question

Think of an example of a negative number. When have you used a negative number in your own life?

This video illustrates the lesson material below. Watching the video is optional.

Negative Numbers

Why are there negative numbers?

In history, people have not always had negative numbers. Ancient Greek mathematicians didn’t believe in negative numbers. In AD 620, Indian mathematicians developed the first rules for negative numbers.

Negative numbers are very useful. They are used in finances to express debt. They can also be used to express a payment.

Negative numbers are also used in temperatures. In Celsius, zero represents the freezing point for water. As it gets warmer, the numbers increase in the positive direction. When the temperature is below freezing, the numbers are negative.

Below is a number line. In the middle is the number 0. All numbers to the right of 0 are positive. Each number is bigger than the last. For example, 5 is bigger than 4, and 4 is bigger than 3, etc. All numbers to the left of 0 are negative. Notice the small minus or negative sign (-) in front of each of the negative numbers; this is an indicator that these are negative numbers. The larger the negative number, the farther it is from zero. Notice -4 is greater than -5 because -4 is farther to the right than -5.

A number line with zero in the middle, negative numbers to the left, and positive numbers to the right. It shows numbers from -6 to 0 and 0 to 6, and it is implied that the number line extends onward in both directions.

Figure 1

Another way to think about negative numbers is the numbers on a thermometer. On the Celsius scale, zero is the temperature at which water freezes. Temperatures that are colder than zero are represented by negative numbers. Temperatures that are warmer than zero are represented by positive numbers. For the Fahrenheit temperature scale, 32 degrees is the temperature at which water freezes. Negative temperatures on the Fahrenheit scale are far below the point of freezing.

A celsius thermometer shown as a vertical number line, with 40 degrees at the top and negative 40 at the bottom with increments of 10 shown in between.

Figure 2

Note: Zero is neither positive or negative.

Things to Remember


  • Negative numbers are easily identifiable by the minus or negative sign (-) in front of them.

Practice Problems

Look at the number line. Some of the numbers have been replaced with a letter. Match the letter with the correct number.

This picture is of a long horizontal line with short vertical lines spaced evenly representing the whole numbers on a number line. We will call these vertical lines hash marks. The center most hash mark has a zero below it. The other hash marks going to the left and right of this center mark also have either numbers or letters below them. The first hash mark to the right of zero has a one. The second hash mark to the right has a B. The third hash mark has a three. These are followed by D, E, and six going to the right. The hash mark to the left of zero has A under it. The second hash mark to the left has negative two under it. This pattern continues with C, negative four, F, and negative six going further and further to the left.
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Video Solution
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Solution: A = -1, B = 2, C = -3, D = 4, E = 5, F = -5
Details:

| Transcript)
    Whole Numbers, Integers, and Real Numbers
    Introduction to Place Values