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Order of Operations

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Order of Operations

Study Guide

Key Definition

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to correctly solve expressions. Follow $PEMDAS$: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Important Notes

Always start with $parentheses$ in expressions.
Handle $exponents$ next after parentheses.
Perform $multiplication$ and $division$ from left to right.
$Addition$ and $subtraction$ are last, also from left to right.
PEMDAS helps remember the order: $Parentheses, Exponents, Multiplication, Division, Addition, Subtraction$.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$\sqrt{x}$ represents the square root of $x$

Remember to use proper notation when solving problems

Why It Works

The order of operations ensures that everyone solves expressions the same way and gets the same result. It prevents ambiguity and errors in calculations, using $PEMDAS$ as the guideline.

Remember

Use the mnemonic 'Please Excuse My Dear Aunt Sally' to recall the order: $Parentheses, Exponents, Multiplication, Division, Addition, Subtraction$.

Quick Reference

Order:$PEMDAS$

First Step:$Parentheses$

Second Step:$Exponents$

Understanding Order of Operations

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

To solve expressions with multiple operations, follow PEMDAS: do Parentheses first, then Exponents, then Multiplication and Division from left to right, and finally Addition and Subtraction from left to right. For example, in $2 + 3 \times 4$, multiply $3 \times 4$ first to get 12, then add 2 to get 14.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the result of $5 + 3 \times (8 - 9)\times 2$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you have $2$ stacks of video games, each stack containing $8$ games plus $3$ additional games. How many games do you have in total?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If you have an expression $4 \times (6 + 2^2) - 3$, what result do you get?

Challenge Quiz

Single Choice Quiz

Advanced

Solve the expression $(2^3 - 4) \times (5 + 3) \div 2$

Recap

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Review key concepts and takeaways