Definition

The absolute value of a number a is denoted as |a|

|a| = a, if a is positive

|a| = a, if a is negative

|0| = 0

Absolute value of a number is the distance of the number on the number line from 0. The absolute value of a number is never negative.

For example, the absolute value of both 5 and 5 is 5. The absolute value of 0 is 0.

Finding absolute value of a number is like removing any negative sign in front of a number, and considering all numbers as positive.

In this lesson, we solve problems involving operations with absolute values.

Example 1

Evaluate the following

|13 19| |11|

Solution

Step 1:

Simplifying

|13 19| |11| = |6| 11 = 6 11

Step 2:

It is a subtraction of integers problem

The signs are different. So, we take the difference of absolute values

|11| |6| = 11 6 = 5

Step 3:

The sign of the numbers with larger absolute value (11) is .

We keep this sign with the difference obtained in above step

So, |13 19| |11| = 5

Example 2

Evaluate the following

|7 23| |6|

Solution

Step 1:

Simplifying

|7 23| |6| = |16| 6 = 16 6

Step 2:

It is a subtraction of integers problem

The signs are different. So, we take the difference of absolute values

|16| |6| = 16 6 = 10

Step 3:

The sign of the numbers with larger absolute value (16) is +.

We keep this sign with the difference obtained in above step

So, |7 23| |6| = + 10

Introduction

Integers are whole numbers and their opposites taken together. They dont have decimal or fractional parts.

For example, the following set of numbers are integers

Z = {3, 2, 1, 0, 1, 2, 3}

In this lesson, we solve problems involving addition of integers

In this addition of two integers, there are two cases.

• When the integers have a common or same sign.
• When the integers have different signs, i.e., one integer is positive while the other is negative.

Rules of Integer Addition

In case, the signs of the integers are common or same (either both positive or both negative)

• We add the absolute values of the integers, i.e., add the integers after ignoring their signs.
• Then we attach the common sign to the sum from above step.

In case, the signs of the integers are different (one positive and another negative)

• We first take the absolute values of the integers by ignoring their signs.
• We subtract the smaller number from the larger.
• Then we attach the sign of the integer with larger absolute value to the difference obtained in above step.

Formula

If the signs of integers are same, we add and keep the sign.

If the signs of integers are different, we subtract and keep the sign of larger number.

Example 1

Add

3 + (7)

Solution

Step 1:

The signs of the numbers are different. So, we subtract the absolute values of the integers.

|7| |3| = 7 3 = 4

Step 2:

The sign of the number with larger absolute value (7) is .

We keep this sign with the difference obtained in above step

So, 3 + (7) = 4

Example 2

Add

5 + (8)

Solution

Step 1:

The signs of the numbers are same. So, we add the absolute values of the integers.

|5| +| 8| = 5 + 8 = 13

Step 2:

The common sign of both numbers is .

We keep this sign with the sum obtained in above step

So, 5 + (8) = 13

This tutorial provides comprehensive coverage of operations with integers based on Common Core (CCSS) and State Standards and its prerequisites. Students can navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs. This simple tutorial uses appropriate examples to help you understand operations with integers in a general and quick way.

Audience

This tutorial has been prepared for beginners to help them understand the basics of operations with integers. After completing this tutorial, you will find yourself at a moderate level of expertise in operations with integers, from where you can advance further.

Prerequisites

Before proceeding with this tutorial, you need a basic knowledge of elementary math concepts such as number sense, addition, subtraction, multiplication, division, whole numbers, comparing and ordering whole numbers, opposite numbers, number line, absolute value and so on.