Use order of operations to evaluate expressions.

SECTION 1

Why We Need Order of Operations

Imagine playing a game where everyone follows different rules. That would be confusing! Long ago, mathematicians faced the same problem with expressions like 2 + 3 × 4. Without clear rules, one person might get 20, and another 14. The order of operations fixes this by giving steps to follow. It started in the 1600s when people like Descartes wrote math books.

1637

Descartes' Book

René Descartes uses fractions and powers in geometry, hinting at order rules.

1800s

Math Textbooks

Books agree: do multiplications before additions for consistency.

1900s

PEMDAS Mnemonic

Schools teach PEMDAS (Parentheses, Exponents, Multiply/Divide, Add/Subtract) like a fun acronym.

Today

SSAT Tests

Every test like SSAT uses these rules so everyone gets the same answer.

These rules solve the big question: How do we agree on expression values? Now you can too!

SECTION 2

Core Principles of Order of Operations

The order of operations is a set of rules. It tells you the right sequence for math. Think of it like steps in a video game level.

Parentheses First

Do inside () or [] before anything else. Like opening a gift box first.

Exponents Next

Powers like 2² = 4. Do these after parentheses.

Multiply & Divide

From left to right, × or ÷ before + or −.

Add & Subtract Last

Finally, + and − from left to right.

PEMDAS Mnemonic

**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally.

🚀 KEY TAKEAWAY

Order of operations is like a recipe for cookies. Skip steps, and it tastes wrong! Follow PEMDAS to bake perfect math answers. You got this!

SECTION 3

Visualizing the Order

This pyramid shows PEMDAS steps. Arrows point the order, like levels in a game.

See the pyramid above? It shows how to climb from top to bottom. Parentheses are always first. This visual makes PEMDAS easy to remember!

SECTION 4

How It Works: The Rules in Action

Use PEMDAS every time. Start with parentheses, then exponents, and so on. Let's see examples.

PEMDAS RULE

Parentheses → Exponents → MD (left→right) → AS (left→right)

MD means multiply or divide. AS means add or subtract.

EXAMPLE

5 + 3 × 2² = 5 + 3 × 4 = 5 + 12 = 17

Exponents first (2²=4), then × (3×4=12), then +.

Always go left to right for same-level steps. You are building math superpowers!

SECTION 5

Step-by-Step Breakdown

Tree branches show each step. Parentheses first, then exponent, multiply, add/subtract.

The tree above breaks down 2 + 5 × (3 + 1)² − 4. Each branch is one step. Follow it like a treasure map!

SECTION 6

Worked Example

Evaluate 10 − 2 × 3 + 4²

Step 1: ParenthesesNo parentheses. Go to exponents.

10 − 2 × 3 + 4²

Step 2: Exponents4² = 16.

10 − 2 × 3 + 16

Step 3: Multiply/Divide left to right2 × 3 = 6.

10 − 6 + 16

Step 4: Add/Subtract left to right10 − 6 = 4, then 4 + 16 = 20.

💡 Tip

Rewrite the expression after each step. It keeps you from getting lost!

SECTION 7

Strengths and Common Errors

Order of operations makes math fair. But watch for traps like forgetting left-to-right.

Avoid these to score high on SSAT!

Correct Way	Common Mistake	Why Wrong?
3 + 2 × 4 = 11	Do + first = 20	× before +!
12 ÷ 3 × 2 = 8	÷ first only = 4	Left to right for same level.

✦ KEY TAKEAWAY

Strength: Same answer everywhere. Like team sports rules. Practice beats mistakes!

SECTION 8

To Algebra and Beyond

PEMDAS works with variables too, like x + 2y. It leads to harder SSAT problems.

Basic PEMDAS	Advanced Version
Numbers only	Variables, fractions
5 + 3 × 2	(x + 1)² / 2 − y

Master this now for algebra later. You're on the path to acing upper levels!

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

What does the P in PEMDAS mean? A) Powers B) Parentheses C) Plus D) Product E) Please

PROBLEM 2 — BASIC CALCULATION

Evaluate 4 + 3 × 2. A) 14 B) 11 C) 7 D) 9 E) 12

PROBLEM 3 — INTERMEDIATE

Evaluate 12 ÷ 3 × 2 − 1. A) 7 B) 23 C) 1 D) 9 E) 8

PROBLEM 4 — APPLIED

A game score is 5 × (2 + 3) − 4². What is it? A) 5 B) 21 C) 1 D) 9 E) −11

PROBLEM 5 — CRITICAL THINKING

Simplify ⅘ × (10 − 2) + 3 ÷ 3. A) 32 B) 9 C) 6 D) 12.8 E) 8

SUMMARY

Lesson Summary

Master PEMDAS: Parentheses, Exponents, Mult/Div left-right, Add/Sub left-right. Use diagrams and steps.

Practice makes you fast for SSAT. Believe in yourself—you just leveled up math skills!