Table Of Contents

What Is the Order of Operations in Math?

When to Use PEMDAS?

Common Mistakes and How to Avoid Them in PEMDAS

Real-world applications of PEMDAS

Solved Examples of PEMDAS

FAQs on PEMDAS

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Last updated on July 22nd, 2025

PEMDAS

Q: What does PEMDAS stand for?

The acronym PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. According to PEMDAS, we first solve the terms in parentheses or brackets, followed by exponents, then multiplication and division (left to right), and addition and subtraction (left to right)

Q: Are PEMDAS and BODMAS the same?

Yes, PEMDAS and BODMAS are similar acronyms that represent the order of operations.

Q: What does the P stand for in PEMDAS?

The P in PEMDAS stands for parentheses.

Q: What is 30 ÷ (8 – 1 × 2)?

According to PEMDAS, first we have to solve the parentheses, that is 1 × 2 = 2; 8 - 2 = 6. Then division, 30 ÷ 6 = 5. So, the value of 30 ÷ (8 - 1 × 2) = 5

Q: What are the applications of PEMDAS?

PEMDAS is a key rule widely used in different fields, such as computer programming, scientific calculations, mathematical calculations, financial calculations, and more.

Q: How can children in Australia use numbers in everyday life to understand PEMDAS?

Numbers appear everywhere—from counting money to measuring ingredients. Kids in Australia see how PEMDAS helps solve real problems, making numbers meaningful beyond the classroom.

Q: What are some fun ways kids in Australia can practice PEMDAS with numbers?

Games like board games, sports scoring, or even cooking help children in Australia use numbers naturally. These activities make practicing PEMDAS enjoyable and connected to their world.

Q: What role do numbers and PEMDAS play in helping children in Australia develop problem-solving skills?

Working with numbers through PEMDAS sharpens reasoning and critical thinking, preparing kids in Australia for challenges inside and outside the classroom.

Q: How can families in Australia create number-rich environments to improve PEMDAS skills?

Families can include counting chores, measuring recipes, or budgeting allowances, helping children connect numbers and PEMDAS with everyday activities.

Professor Greenline Explaining Math Concepts

Mathematical expressions with multiple operations can be confusing. PEMDAS is a rule that defines the correct order of operations in mathematical expressions. In this topic, we will learn about PEMDAS, its order, and how it is used.

PEMDAS for Australian Students

What is PEMDAS

The order in which the expression can be solved is given by the PEMDAS rule, which defines the order of operations. Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are denoted by the letters P, E, M, D, A, S, respectively. According to PEMDAS, we solve the terms enclosed in parentheses or brackets first, then the exponents, and finally addition, subtraction, multiplication, and division.

For example, to solve 6 + 2 × (3² - 1), first solve the parentheses, that is 32 - 1 = 9 - 1 = 8. Next multiplication, 2 × 8 = 16, next addition, 6 + 16 = 22.

BODMAS vs. PEMDAS

BODMAS and PEMDAS are two important rules in solving complex expressions involving different arithmetic operations. Here, we will discuss the key differences between BODMAS and PEMDAS:

PEMDAS	BODMAS
Used when solving expressions involving mathematical operations such as division, multiplication, addition, and subtraction.	Used to simplify expressions involving operations like division, multiplication, addition, and subtraction.
In PEMDAS, P stands for parentheses, E for exponents, M for multiplication, D for division, A for addition, and S for subtraction.	BODMAS stands for B — Brackets, O — Order (exponents), D — Division, M — Multiplication, A — Addition, and S — Subtraction

What Is the Order of Operations in Math?

In mathematical expressions where there are different operations, like addition, subtraction, multiplication, and division, we follow a set of rules. PEMDAS defines the rules for the order of operations, which tells us the sequence for solving expressions.

When to Use PEMDAS?

Now, let’s learn when to use PEMDAS. It is used to solve expressions that contain more than one operation.

We use PEMDAS in math to provide a structured approach to finding the correct answer. When applying PEMDAS, we first solve the operations within the parentheses or brackets, and next, we solve the exponential expression. Moving from left to right, we solve the multiplication, division, addition, and subtraction.

Common Mistakes and How to Avoid Them in PEMDAS

PEMDAS helps students solve complex expressions. However, students make mistakes when applying for it. These are some typical errors and how to avoid them:

Mistake 1

Prioritizing Multiplication Over Division

When solving mathematical expressions, students often consider that multiplication has higher priority than division, as it comes first in the order of PEMDAS. However, multiplication and division have equal precedence, so calculations should be performed from left to right.

For example, in 16 ÷ 4 × 3, since both operations are of equal precedence, evaluate them from left to right; we divide first, 16 ÷ 4 = 4, then multiply 4 × 3 = 12.

Mistake 2

Performing Addition Over Subtraction

The order of operations, addition and subtraction, have equal precedence, so evaluate them from left to right. For example, 3 - 5 + 2 should be calculated in this order (3 - 5) + 2, not 3 - (5 + 2).

Mistake 3

Misapplying Negative Signs with Exponents

Students mistakenly think that -(3)² as 9 by considering -(3)² as (-3) × (-3) = 9 instead of applying the exponent first -(3)² = -(3 × 3) = -9. So it is important to check whether the exponents have parentheses or not. This means with parentheses, (-3)² is considered as (-3) × (-3) = 9, whereas without parentheses, -3² is considered as -(3 × 3) = -9.

Mistake 4

Neglecting the Left-to-Right Rule

PEMDAS follows a certain order, but for operations with equal precedence, follow the left-to-right order for operations with the same priority, such as multiplication and division, or addition and subtraction. For example, 5 - 3 +2 is treated as (5 - 3) + 2 = 4.

Mistake 5

Confusing Subtraction with Addition of Negatives

Students sometimes incorrectly group addition and subtraction with parentheses, changing the intended order of operations: for example, 10 - 3 + 2 = 10 - (3 + 2) = 5 instead of 10 - 3 + 2 = 10 + (-3) + 2 = 9. So, make sure the calculation is in left-to-right order.

Real-world applications of PEMDAS

In daily life, there are many situations where we need to solve the sequence of operations in math. Now let’s learn how PEMDAS is used in various sectors.

In construction, to calculate the loads and stresses for designing structures, we use PEMDAS.
In computer science, to ensure algorithms follow correct logic in calculation, we use PEMDAS.
To calculate accurate medication dosages, pharmacists use PEMDAS
PEMDAS is essential for solving multi-step mathematical problems..

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Solved Examples of PEMDAS

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Simplify the expression: 36 ÷ (12 – 4 × 2)

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Okay, lets begin

36 ÷ (12 – 4 × 2) = 9

Explanation

Step 1: Inside the parentheses, solve the multiplication, 4 × 2 = 8

Step 2: Subtract inside the parentheses: 12 - 8 = 4

Step 3: Division, 36 ÷ 4 = 9

So, 36 ÷ (12 – 4 × 2) = 9

Max from BrightChamps Praising Clear Math Explanations

Well explained 👍

Problem 2

Simplify the expression: 20 ÷ (5 – 1 × 3)

Okay, lets begin

20 ÷ (5 - 1 × 3) = 10

Explanation

Step 1: Inside the parentheses, solve the multiplication, 1 × 3 = 3

Step 2: Subtract inside the parentheses: 5 - 3 = 2

Step 3: Division, 20 ÷ 2 = 10

Well explained 👍

Problem 3

Simplify: (9² ÷ 3) – 5 × 2

Okay, lets begin

(9² ÷ 3) - 5 × 2 = 17

Explanation

Step 1: Evaluate the exponents: 9²= 9 × 9 = 81

Step 2: Divide: 81 ÷ 3 = 27

Step 3: Multiply: 5 × 2 = 10

Step 4: Subtraction: 27 - 10 = 17

Well explained 👍

Problem 4

Simplify the expression: 98 ÷ (49 – 7 × 6)

Okay, lets begin

98 ÷ (49 – 7 × 6) = 14

Explanation

Step 1: Inside the parentheses, solve the multiplication, 7 × 6 = 42

Step 2: Subtract inside the parentheses: 49 - 42 = 7

Step 3: Division, 98 ÷ 7 = 14

Well explained 👍

Problem 5

Simplify: (2^4 ÷ 4) + 6 × (5 – 3)

Okay, lets begin

(2⁴ ÷ 4) + 6 × (5 – 3) = 16

Explanation

Step 1: Evaluating the exponents: 2⁴= 2 × 2 × 2 × 2 = 16

Step 2: Divide: 16 ÷ 4 = 4

Step 3: Evaluate the second exponents: 5 - 3 = 2

Step 4: Multiply: 6 × 2 = 12

Step 5: Adding the results: 4 + 12 = 16