THE BOOK OF INTEGERS

RachelAbregana, May 15, 2025

Mastering the Basics of Adding and Subtracting Integers

Table of Contents

  1. INTRODUCTION
    1. Exploring integers on a temperature scale
  2. INTERACTIVE MANIPULATIVES IN ADDING AND SUBTRACTING INTEGERS
    1. Adding and Subtracting Integers with Balloons and Sandbags
  3. ADDING INTEGERS
    1. ADDING AND SUBTRACTING INTEGERS
  4. SUBTRACTING INTEGERS
    1. ADDING AND SUBTRACTING INTEGERS
  5. PRACTICE PROBLEMS
    1. Quiz: Adding Integers
    2. Quiz: Subtracting Integers

1.

INTRODUCTION

[color=#444][color=#b20ea8]Welcome to "[b]Mastering the Basics of Adding and Subtracting Integers.[/b]" Whether you're just starting your math journey or looking to strengthen your understanding, this book is designed to guide you through the essential concepts of working with integers.[/color] Integers are whole numbers that include both positive and negative numbers, and they are fundamental to various mathematical operations and real-life applications. Adding and subtracting integers can sometimes seem tricky, but with the right approach, it becomes an easy and valuable skill. This book aims to break down the process in simple steps, providing clear explanations, useful tips, and plenty of practice problems to help you succeed. By the end of this book, you'll not only be comfortable with adding and subtracting integers but also gain the confidence to tackle more complex mathematical challenges. Let's begin this exciting journey into the world of integers![i][/i][/color]

  • 1. Exploring integers on a temperature scale

1.1.

Exploring integers on a temperature scale

Explore integers using a thermometer model.[br]There are 8 types of problems in this exercise. Click the New task button to get randomly selected 1 of them.[br]You can illustrate each problem on the thermometer model, moving coloured diamond-shaped points on sliders.
– Aleksandra-Maria Vuković

2.

INTERACTIVE MANIPULATIVES IN ADDING AND SUBTRACTING INTEGERS

Drag the sliders (a and b) to change the values. Drag the sign (+ and -) to change the operations.

  • 1. Adding and Subtracting Integers with Balloons and Sandbags

2.1.

Adding and Subtracting Integers with Balloons and Sandbags

Add and subtract integers by building expressions using balloons and sandbags in this interactive activity.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
What direction did the basket move when you added balloons? Sandbags?
What direction did the basket move when you subtracted balloons? Sandbags?
Suppose the basket had a starting position of 35 and you removed 5 sandbags. Where would the basket end up? 
– GeoGebra Content Team

3.

ADDING INTEGERS

When adding integers, we are essentially combining their values. Here are some rules to remember: Adding two positive integers: The result is always positive. Just add their values. Example: (+3)+(+5)=+8. Adding two negative integers: The result is always negative. Add their absolute values and keep the negative s[b][/b]ign. Example: (−2)+(−4)=−6. Adding a positive and a negative integer: Subtract the smaller absolute value from the larger absolute value. The result takes the sign of the integer with the larger absolute value. Example 1: (+7)+(−3)=+4 (7 is larger, so the result is positive). Example 2: (−9)+(+2)=−7 (9 is larger, so the result is negative).

  • 1. ADDING AND SUBTRACTING INTEGERS

3.1.

ADDING AND SUBTRACTING INTEGERS

– RachelAbregana

4.

SUBTRACTING INTEGERS

Subtracting an integer is the same as adding its opposite! The opposite of a number is the number with the same absolute value but the opposite sign. [i]For example, the opposite of +5 is −5, and the opposite of −3 is +3.[/i] To subtract integers, follow these steps: [i][b]Keep[/b][/i] the first integer the same. [i][b]Change[/b][/i] the subtraction sign to an addition sign. [i][b]Change[/b][/i] the second integer to its opposite. Then, follow the rules for adding integers! Examples: 1. (+5)−(+2)=(+5)+(−2)=+3 2. (−3)−(+4)=(−3)+(−4)=−7 3. (+6)−(−1)=(+6)+(+1)=+7 4. (−8)−(−5)=(−8)+(+5)=−3

  • 1. ADDING AND SUBTRACTING INTEGERS

4.1.

– RachelAbregana

5.

PRACTICE PROBLEMS

Solve the following problems: 1.(−12)+(5)= 2. (8)−(−3)= 3. (−7)+(−9)= 4. (15)−(6)= 5. (−4)−(10)= 6. (2)+(−11)= 7. (−6)−(−2)= 8. (11)+(−4)= 9. (-12)-(7)= 10. (8)+(-19)=

  • 1. Quiz: Adding Integers
  • 2. Quiz: Subtracting Integers

5.1.

Quiz: Adding Integers

[b]Students: [/b] [br][br]These problems were intended to be completed WITHOUT the use of a calculator. [br]
– Tim Brzezinski

5.2.

–

Information