Last updated on July 4th, 2025
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.
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 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 |
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.
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.
PEMDAS helps students solve complex expressions. However, students make mistakes when applying for it. These are some typical errors and how to avoid them:
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.
Simplify the expression: 36 ÷ (12 – 4 × 2)
36 ÷ (12 – 4 × 2) = 9
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
Simplify the expression: 20 ÷ (5 – 1 × 3)
20 ÷ (5 - 1 × 3) = 10
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
Simplify: (9² ÷ 3) – 5 × 2
(92 ÷ 3) - 5 × 2 = 17
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
Simplify the expression: 98 ÷ (49 – 7 × 6)
98 ÷ (49 – 7 × 6) = 14
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
Simplify: (2^4 ÷ 4) + 6 × (5 – 3)
(24 ÷ 4) + 6 × (5 – 3) = 16
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