Order of Operations - PEMDAS Rule - Grade 6 Arithmetic Simplification Guide

Oct 13, 2026

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Arithmetic order of operations establishes the correct sequence for simplifying expressions, preventing mistakes like applying operations left to right. The document explains and motivates the PEMDAS rule (parentheses, exponents, multiplication/division, then addition/subtraction) and highlights left-to-right evaluation within the same precedence level. Worked examples simplify divisions, multiplications, nested parentheses, and exponent terms, demonstrating how to reduce expressions step by step, including multi-term problems and final subtraction or addition to reach the correct result.

LanguageEnglish

CategoryPaper Templates

FormatPDF

Pages2

Reading Time1 min

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Order of Operations Fundamentals

PEMDAS Priority and Left-to-Right Rule

Step-by-Step Simplification Examples

Parentheses and Exponents

Multiplication/Division then Addition/Subtraction

Applying Order of Operations to Multi-Term Problems

Order of operations chart Order of operations anchor chart printable. Order of operations anchor chart 6th grade. Order of operations chart pdf. Order of operations chart printable. Order of operations flow chart. Order of operations chart free printable. Order of operations anchor chart 5th grade. Order of operations anchor chart gemdas. Financial order of operations chart. Order of operations anchor chart 3rd grade. Order of operations chart free. Order of operations anchor chart. Order of operations anchor chart 4th grade. Order of operations anchor chart pdf. Order of operations chart 5th grade. The order of operations is a fundamental concept in arithmetic that dictates the correct sequence for performing mathematical operations. Let's examine how Rob and Patty simplified numerical expressions using this rule. What was Rob's mistake? He carelessly applied operations from left to right, whereas Patty got it right by following the rules. Patty correctly applied the PEMDAS Rule (Please Excuse My Dear Aunt Sally), a set of rules prioritizing operations from most important to least. The steps are: simplify expressions inside parentheses, then exponential numbers, and finally perform multiplication and division before addition and subtraction. Let's apply these steps to some examples. Example 1: Simplify the expression [latex]5 \div 5 + 6 \times 2-3[/latex] . First, divide [latex]5 \div 5 = 1[/latex], then multiply [latex]6 \times 2 = 12[/latex], and finally add [latex]1 + 12 = 13[/latex] before subtracting [latex]13-3 = 10[/latex] . Example 2: Simplify the expression inside parentheses first, such as [latex](5 + 3) \times 4[/latex] . Evaluate expressions inside the parentheses, then multiply [latex]8 \times 4 = 32[/latex] . Example 3: Simplify the expression [latex]10- (7-2) \times 5 + 4[/latex] . First, evaluate expressions inside the parentheses, then subtract [latex]7-2 = 5[/latex], multiply [latex]5 \times 5 = 25[/latex], and finally add [latex]10-25 + 4 = -11[/latex] . Example 4: Simplify the expression [latex](3 + 2) \div (5-1) + 9[/latex] . Evaluate expressions inside parentheses, multiply [latex]3 + 2 = 5[/latex], divide [latex]5 \div 4 = 1.25[/latex], and finally add [latex]1.25 + 9 = 10.25[/latex] . These examples demonstrate the correct application of the order of operations to simplify numerical expressions. The last operation left is subtraction therefore that’s what we’re going to do. The final examples will involve exponents so be careful with each step because they are so many things going on. As long as you remain focus in following the rules governing the order of operations, it shouldn’t be that difficult! Here we go… Example 5: Simplify numerical expression below using the rules of Order of Operations. We first need to simplify the expressions inside the parentheses. But more specifically, simplify the numbers with exponents. There are two parentheses to simplify. We will simplify the second one which is (30 – 27) because it is much simpler. Here, the difference of 30 and 27 is 3 . Now we turn our attention to the other parenthesis. The Order of Operations tells us to divide before we subtract. Finally we can get rid of the parenthesis by performing subtraction as there is no other thing to do. Looking at what we have left, simplifying exponential numbers takes precedence over the operations of multiplication, addition, and subtraction. Scanning from left to right, it’s obvious that we must multiply before adding and/or subtracting. Based on the Order of Operations, addition and subtraction are of equal importance. We must subtract first because the operation of subtraction comes before addition when viewed from left to right. The last step is to add because there is no other operations left. Example 6: Simplify the expression below using the Order of Operations. Focus our attention on the single grouping symbol which is the parenthesis. Notice that there is a number with an exponent. Let’s simplify

FAQs

What is the correct order of operations for simplifying arithmetic expressions?

Use PEMDAS: evaluate parentheses first, then exponents, then multiplication and division (left to right), and finally addition and subtraction (left to right).

What mistake did Rob make compared with Patty?

Rob applied operations carelessly from left to right, while Patty followed the rule-based precedence order in PEMDAS.

How do you handle multiplication vs. addition when simplifying an expression?

Multiplication and division have higher precedence than addition and subtraction, so you complete all multiplication/division steps before any addition/subtraction steps.

Oct 13, 2026

Upload by SANS