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Integers

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Integers

Study Guide

Key Definition

Integers are the set of whole numbers and their opposites, including zero. Represented by $\mathbb{Z}$, integers do not include fractions or decimals.

Important Notes

$0$ is neither positive nor negative.
Integers are represented on a number line as equally spaced points.
Positive integers are greater than $0$.
Negative integers are less than $0$.
The sum, difference, or product of two integers is always an integer.

Mathematical Notation

$\mathbb{Z}$ represents the set of all integers

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Integers are foundational in math because they represent whole quantities without fractions or decimals, allowing for straightforward calculations.

Remember

Integers include negative numbers, positive numbers, and zero, but not fractions or decimals.

Quick Reference

Positive Integers:$1, 2, 3, \ldots$

Negative Integers:$-1, -2, -3, \ldots$

Understanding Integers

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Integers include all whole numbers and their opposites, like $-3, 0, 2$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is an integer?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you have $5$ apples and you give away $3$. How many do you have left?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $\mathbb{Z}$ represents integers, what is the sum of $-6$ and $4$?

Challenge Quiz

Single Choice Quiz

Advanced

What is the product of $-3$ and $4$?

Recap

Watch & Learn

Review key concepts and takeaways