LESSON 7: OPERATOR PRECEDENCE

Lesson Outcomes

By the end of this lesson, learners will be able to:

  • Understand what operator precedence is
  • Apply the correct order of operations
  • Use BODMAS correctly in calculations
  • Avoid errors caused by incorrect operation order

Lesson Overview

In mathematics and programming, calculations often involve multiple operations. If these operations are not performed in the correct order, the result will be incorrect.

Operator precedence defines which operations should be performed first when multiple operators are present in an expression.

This concept is critical in:

  • Programming
  • Automation workflows
  • Mathematical calculations
  • Logical expressions

What is Operator Precedence?

Operator precedence determines how expressions are evaluated when more than one operator is present.

Definition

The precedence of an operator specifies how tightly it binds two expressions together.

For example:

1 + 5 × 3 = 16 (not 18)

This is because multiplication has a higher precedence than addition.

Why Operator Precedence is Important

If the order of operations is ignored:

  • Calculations become incorrect
  • Programs produce wrong outputs
  • Automation processes fail

Correct precedence ensures:

  • Accurate results
  • Logical consistency
  • Reliable systems

Order of Operator Precedence

Operations must be performed in the following order:

  1. Exponentiation (powers, roots)
  2. Multiplication and Division
  3. Addition and Subtraction

BODMAS Rule

Operator precedence is commonly remembered using the BODMAS rule:

  • B – Brackets
  • O – Order (powers/roots)
  • D – Division
  • M – Multiplication
  • A – Addition
  • S – Subtraction

How BODMAS Works

When solving expressions:

  1. Solve brackets first
  2. Then powers (orders)
  3. Then division and multiplication (left to right)
  4. Then addition and subtraction (left to right)

Examples

Example 1

5 + 3 × 2

Step 1: Multiply → 3 × 2 = 6
Step 2: Add → 5 + 6 = 11

Example 2

(5 + 3) × 2

Step 1: Brackets → 5 + 3 = 8
Step 2: Multiply → 8 × 2 = 16

Example 3

10 − 2 × 3

Step 1: Multiply → 2 × 3 = 6
Step 2: Subtract → 10 − 6 = 4

Equal Precedence Rules

When operators have the same level of precedence:

  • Solve from left to right

Example:
10 ÷ 2 × 5

Step 1: 10 ÷ 2 = 5
Step 2: 5 × 5 = 25

Use of Parentheses

Parentheses (brackets) can be used to override precedence.

They force certain calculations to be done first.

Example

Without brackets:
2 + 3 × 4 = 14

With brackets:
(2 + 3) × 4 = 20

Operator Precedence in Programming

In programming languages:

  • The same precedence rules apply
  • Incorrect ordering can cause bugs
  • Expressions must be carefully structured

Example in Programming Logic

result = 10 + 5 * 2

Correct result = 20 (not 30)

Lesson Summary

In this lesson, learners explored:

  • The meaning of operator precedence
  • The correct order of operations
  • The BODMAS rule
  • How precedence affects calculations and programming

Understanding operator precedence is essential for accurate calculations and reliable automation systems.

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