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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 divisionRemember 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

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

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BeginnerIntermediateAdvanced

Beginner Explanation

Integers include all whole numbers and their opposites, like $-3, 0, 2$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Which of the following is an integer?

A$2.5$B$-1$C$\frac{3}{4}$D$0.75$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

Imagine you have $5$ apples and you give away $3$. How many do you have left?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

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

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

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

A$-12$B$12$C$-7$D$7$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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