Order of Operations

Lesson Objectives

Understand the correct sequence of operations in solving expressions.
Apply the BODMAS/PEMDAS rule to simplify expressions accurately.
Identify and correct errors in the order of operations.
Solve real-life problems involving multiple operations.

Lesson Introduction

Order of operations is a fundamental concept in mathematics that ensures consistency when solving expressions involving multiple operations. Without a standard rule, a single expression could have many interpretations and results. That is why we use a set rule — BODMAS or PEMDAS.

Lesson Content

What is BODMAS/PEMDAS?

BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It tells you the sequence in which to perform operations.

PEMDAS (used in some countries) stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

Brackets or Parentheses

Always start with simplifying the expressions inside brackets or parentheses first.

Example: Simplify $(4 + 3) \times 2$

$7 \times 2 = 14$

Orders or Exponents

Next, handle exponents (powers and roots).

Example: Simplify $3^2 + 4$

$9 + 4 = 13$

Multiplication and Division (from left to right)

Perform multiplication and division as they appear from left to right in the expression.

Example: Simplify $12 \div 3 \times 2$

$4 \times 2 = 8$

Addition and Subtraction (from left to right)

Lastly, perform addition and subtraction as they appear from left to right.

Example: Simplify $10 - 4 + 2$

$6 + 2 = 8$

Combined Expressions

Use all parts of BODMAS together when expressions include multiple operation types.

Example: Simplify $6 + (2 \times 3)^2 - 4$

$6 + (6)^2 - 4 = 6 + 36 - 4 = 38$

Further Examples

Example 1:

5 + 2 \times (3 + 1) = 5 + 2 \times 4 = 5 + 8 = 13

Example 2:

(8 - 3)^2 + 6 = 5^2 + 6 = 25 + 6 = 31

Example 3:

18 \div 3 \times (2 + 1) = 18 \div 3 \times 3 = 6 \times 3 = 18

Example 4:

(7 + 5) - 4^2 = 12 - 16 = -4

Example 5:

3 \times (4 + 5) - 6 \div 2 = 3 \times 9 - 3 = 27 - 3 = 24

Interactive Graph

Exercises

Simplify $4 + 2 \times 3$
[NECO] Evaluate $(5 + 3)^2 - 7$ (Past Question)
Simplify $18 \div 2 + 6$
[WAEC] Simplify $(6 - 2)^2 + 5$ (Past Question)
Evaluate $4^2 + 2 \times 5$
Simplify $30 - (3 \times 4)$
[JAMB] Evaluate $6 + 2 \times (7 - 4)$ (Past Question)
Find the result of $20 \div 4 + 3 \times 2$
[NABTEB] Simplify $2 \times 3 + (5 - 1)^2$ (Past Question)
Simplify $9 - 3 \times 2 + 4$

Conclusion/Recap

In this lesson, we studied the correct order of operations using the BODMAS rule. By following the correct sequence — brackets, orders, division and multiplication (left to right), addition and subtraction (left to right) — you can solve even the most complex expressions with confidence and accuracy.