Learn on PengiOpenstax Prealgebre 2EChapter 3: Integers

Lesson 1: Introduction to Integers

In this lesson from OpenStax Prealgebra 2E, Chapter 3, students are introduced to integers by learning to locate positive and negative numbers on the number line, order and compare integers, and find opposites. The lesson also covers simplifying expressions with absolute value and translating word phrases into integer expressions. Real-world contexts like temperature, elevation, and bank balances are used to build conceptual understanding of negative numbers.

Section 1

📘 Introduction to Integers

New Concept

This lesson introduces integers: positive numbers, negative numbers, and zero. You'll learn to place them on a number line, order them, find opposites, and use absolute value to describe real-world quantities like temperature and elevation.

What’s next

You’ve got the basics. Next, work through practice cards and interactive examples to master locating numbers, finding opposites, and simplifying absolute value expressions.

Section 2

Integers

Property

Integers are counting numbers, their opposites, and zero.

\ldots -3, -2, -1, 0, 1, 2, 3 \ldots

Examples

To plot the number 4 on a number line, we move 4 units to the right of 0.

To plot the number -5, we start at 0 and move 5 units to the left into the negative side.

Section 3

Order positive and negative numbers

Property

On a number line, numbers increase in value from left to right. We use inequality symbols to show ordering:

$a < b$ (read $a$ is less than $b$ ) when $a$ is to the left of $b$ .
$a > b$ (read $a$ is greater than $b$ ) when $a$ is to the right of $b$ .

Examples

To compare 15 and 8, we see 15 is to the right of 8 on the number line, so $15 > 8$ .

Section 4

Opposites

Property

The opposite of a number is the number that is the same distance from zero on the number line, but on the opposite side of zero.

Opposite Notation: $-a$ means the opposite of the number $a$ . The notation $-a$ is read as "the opposite of $a$ ."

Examples

The opposite of 2 is $-2$ because it is the same distance from 0 but on the opposite side.

Section 5

Absolute value

Property

The absolute value of a number is its distance from 0 on the number line. The absolute value of a number $n$ is written as $|n|$ .

|n| \ge 0 \text{ for all numbers}

Examples

The absolute value of -25 is 25, because -25 is 25 units away from 0. We write $|-25| = 25$ .

To simplify $5|-3|$ , first find the absolute value of -3, which is 3. Then multiply: $5 \cdot 3 = 15$ .

Section 6

Translate word phrases to expressions

Property

To translate word phrases into expressions with integers, look for words that indicate a negative sign. Other key words include "below," "loss," and "overdrawn."

Examples

The phrase "a loss of 5 yards" in football translates to the integer $-5$ yards, because a loss is a negative change.

The phrase "the opposite of positive ten" is a direct instruction to find the opposite of 10, which is $-10$ .

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Chapter 3: Integers

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Lesson 3: Subtract Integers
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Lesson 4: Multiply and Divide Integers
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Lesson 5
Lesson 5: Solve Equations Using Integers; The Division Property of Equality
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Lesson overview

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Section 1

📘 Introduction to Integers

New Concept

What’s next

You’ve got the basics. Next, work through practice cards and interactive examples to master locating numbers, finding opposites, and simplifying absolute value expressions.

Section 2

Integers

Property

Integers are counting numbers, their opposites, and zero.

\ldots -3, -2, -1, 0, 1, 2, 3 \ldots

Examples

To plot the number 4 on a number line, we move 4 units to the right of 0.

To plot the number -5, we start at 0 and move 5 units to the left into the negative side.

Section 3

Order positive and negative numbers

Property

On a number line, numbers increase in value from left to right. We use inequality symbols to show ordering:

$a < b$ (read $a$ is less than $b$ ) when $a$ is to the left of $b$ .
$a > b$ (read $a$ is greater than $b$ ) when $a$ is to the right of $b$ .

Examples

To compare 15 and 8, we see 15 is to the right of 8 on the number line, so $15 > 8$ .

Section 4

Opposites

Property

The opposite of a number is the number that is the same distance from zero on the number line, but on the opposite side of zero.

Opposite Notation: $-a$ means the opposite of the number $a$ . The notation $-a$ is read as "the opposite of $a$ ."

Examples

The opposite of 2 is $-2$ because it is the same distance from 0 but on the opposite side.

Section 5

Absolute value

Property

The absolute value of a number is its distance from 0 on the number line. The absolute value of a number $n$ is written as $|n|$ .

|n| \ge 0 \text{ for all numbers}

Examples

The absolute value of -25 is 25, because -25 is 25 units away from 0. We write $|-25| = 25$ .

To simplify $5|-3|$ , first find the absolute value of -3, which is 3. Then multiply: $5 \cdot 3 = 15$ .

Section 6

Translate word phrases to expressions

Property

To translate word phrases into expressions with integers, look for words that indicate a negative sign. Other key words include "below," "loss," and "overdrawn."

Examples

The phrase "a loss of 5 yards" in football translates to the integer $-5$ yards, because a loss is a negative change.

The phrase "the opposite of positive ten" is a direct instruction to find the opposite of 10, which is $-10$ .

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 3: Integers

Back to Openstax Prealgebre 2E

Lesson 1Current
Lesson 1: Introduction to Integers
Learn Practice
Lesson 2
Lesson 2: Add Integers
Learn Practice
Lesson 3
Lesson 3: Subtract Integers
Learn Practice
Lesson 4
Lesson 4: Multiply and Divide Integers
Learn Practice
Lesson 5
Lesson 5: Solve Equations Using Integers; The Division Property of Equality
Learn Practice

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

📘 Introduction to Integers

New Concept

What’s next

You’ve got the basics. Next, work through practice cards and interactive examples to master locating numbers, finding opposites, and simplifying absolute value expressions.

Section 2

Integers

Property

Integers are counting numbers, their opposites, and zero.

\ldots -3, -2, -1, 0, 1, 2, 3 \ldots

Examples

To plot the number 4 on a number line, we move 4 units to the right of 0.

To plot the number -5, we start at 0 and move 5 units to the left into the negative side.

Section 3

Order positive and negative numbers

Property

On a number line, numbers increase in value from left to right. We use inequality symbols to show ordering:

$a < b$ (read $a$ is less than $b$ ) when $a$ is to the left of $b$ .
$a > b$ (read $a$ is greater than $b$ ) when $a$ is to the right of $b$ .

Examples

To compare 15 and 8, we see 15 is to the right of 8 on the number line, so $15 > 8$ .

Section 4

Opposites

Property

The opposite of a number is the number that is the same distance from zero on the number line, but on the opposite side of zero.

Opposite Notation: $-a$ means the opposite of the number $a$ . The notation $-a$ is read as "the opposite of $a$ ."

Examples

The opposite of 2 is $-2$ because it is the same distance from 0 but on the opposite side.

Section 5

Absolute value

Property

The absolute value of a number is its distance from 0 on the number line. The absolute value of a number $n$ is written as $|n|$ .

|n| \ge 0 \text{ for all numbers}

Examples

The absolute value of -25 is 25, because -25 is 25 units away from 0. We write $|-25| = 25$ .

To simplify $5|-3|$ , first find the absolute value of -3, which is 3. Then multiply: $5 \cdot 3 = 15$ .

Section 6

Translate word phrases to expressions

Property

To translate word phrases into expressions with integers, look for words that indicate a negative sign. Other key words include "below," "loss," and "overdrawn."

Examples

The phrase "a loss of 5 yards" in football translates to the integer $-5$ yards, because a loss is a negative change.

The phrase "the opposite of positive ten" is a direct instruction to find the opposite of 10, which is $-10$ .

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 3: Integers

Back to Openstax Prealgebre 2E

Lesson 1Current
Lesson 1: Introduction to Integers
Learn Practice
Lesson 2
Lesson 2: Add Integers
Learn Practice
Lesson 3
Lesson 3: Subtract Integers
Learn Practice
Lesson 4
Lesson 4: Multiply and Divide Integers
Learn Practice
Lesson 5
Lesson 5: Solve Equations Using Integers; The Division Property of Equality
Learn Practice

Lesson 1: Introduction to Integers

New Concept

What’s next

Property

Examples

Property

Examples

Property

Examples

Property

Examples

Property

Examples

Chapter 3: Integers

Lesson 1: Introduction to Integers

Lesson 2: Add Integers

Lesson 3: Subtract Integers

Lesson 4: Multiply and Divide Integers

Lesson 5: Solve Equations Using Integers; The Division Property of Equality

Lesson overview

New Concept

What’s next

Property

Examples

Property

Examples

Property

Examples

Property

Examples

Property

Examples

Chapter 3: Integers

Lesson 1: Introduction to Integers

Lesson 2: Add Integers

Lesson 3: Subtract Integers

Lesson 4: Multiply and Divide Integers

Lesson 5: Solve Equations Using Integers; The Division Property of Equality

Lesson 1: Introduction to Integers

Lesson 2: Add Integers

Lesson 3: Subtract Integers

Lesson 4: Multiply and Divide Integers

Lesson 5: Solve Equations Using Integers; The Division Property of Equality