Inverse Operations - Varsity Tutors

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Inverse Operations

Study Guide

Key Definition

Inverse operations are operations that can undo each other. For example, $3 + 5 = 8$ and $8 - 5 = 3$.

Important Notes

  • Inverse means opposite
  • $+$ and $-$ are inverse operations
  • $\times$ and $\div$ are inverse operations
  • Inverse operations are used to solve equations
  • Understanding inverse operations helps in algebra

Mathematical Notation

$+$ represents addition$-$ represents subtraction$\times$ or $*$ represents multiplication$\div$ or $/$ represents divisionRemember to use proper notation when solving problems

Why It Works

Inverse operations allow us to reverse calculations, making it easier to solve equations and verify answers.

Remember

Addition and subtraction are inverses, as well as multiplication and division.

Quick Reference

Addition/Subtraction:$a + b = c$ and $c - b = a$Multiplication/Division:$a \times b = c$ and $c \div b = a$

Understanding Inverse Operations

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Video explanation of this concept

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

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

Inverse operations are like undoing each other. For example, if a + b = c, then c - b = a. For instance, 7 + 2 = 9, and 9 - 2 = 7. To solve for a, subtract b from both sides: a + 2 = 9 → a = 9 − 2 = 7.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the inverse operation of $8 - 3$?

A$8 + 3$B$8 \times 3$C$8 \div 3$D$3 - 8$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

If you buy 5 candies and give away 3, how many do you have left? Use inverse operations to solve.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

If $x \times 4 = 20$, what is $x$? Use inverse operations.

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

Challenge Quiz

Single Choice QuizAdvanced

Solve for $x$ if $x + 3 = 2x - 5$

A$x = 8$B$x = -8$C$x = 5$D$x = -5$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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