The Number Line - Varsity Tutors

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The Number Line

Study Guide

Key Definition

A number line offers a visual representation of real numbers on a straight line. It helps to compare and order numbers where positive numbers are on the right and negative numbers are on the left of $0$.

Important Notes

  • The point $0$ is called the origin.
  • Numbers to the right of $0$ are positive.
  • Numbers to the left of $0$ are negative.
  • Opposites are the same distance from $0$ in opposite directions.
  • Arrows indicate the line continues indefinitely.

Mathematical Notation

$+$ represents addition$-$ represents subtraction$\times$ or $*$ represents multiplication$\div$ or $/$ represents division$|a|$ represents absolute valueRemember to use proper notation when solving problems

Why It Works

The number line visually represents the concept of positive and negative values, making it easier to understand operations like addition and subtraction of integers.

Remember

Numbers get larger as you move right and smaller as you move left.

Quick Reference

Origin:$0$Positive Direction:Right of $0$Negative Direction:Left of $0$

Understanding The Number Line

Choose your learning level

Watch & Learn

Video explanation of this concept

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

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

Imagine a ruler with numbers extending infinitely in both directions; this is the number line with $0$ as the origin.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the opposite of $5$ on the number line?

A$-5$B$5$C$0$D$-10$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're tracking temperature changes over a day. At noon, the temperature is $5^\circ C$, while at midnight, it drops to $-5^\circ C$. How many degrees does the temperature change?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

If $x$ is twice the distance from $0$ as $-4$, what is $x$?

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

Challenge Quiz

Single Choice QuizAdvanced

Which number is twice as far from $0$ as $-3$ on the same side of $0$?

A$-6$B$6$C$-9$D$9$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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