📘 Order of Operations

PEMDAS vs. Java Operator Precedence

🎯 Why This Matters

Computers do exactly what you tell them to do — not what you meant. If you misunderstand order of operations, your program can run without errors but give the wrong answer.

🔢 Part 1: PEMDAS (What You Learned in Math)

PEMDAS tells us the order to solve math expressions:

  1. P – Parentheses ( )
  2. E – Exponents
  3. M – Multiplication
  4. D – Division
  5. A – Addition
  6. S – Subtraction

Important:

✏️ Example

8 + 4 × 2

Steps:

✅ Answer: 16

💻 Part 2: Java Order of Operations (Operator Precedence)

Java follows rules similar to PEMDAS, but with more operators. This is called operator precedence.

🔝 Common Java Operator Precedence (High → Low)

  1. Parentheses ( )
  2. Unary operators ++ -- + - !
  3. Multiplication / Division / Modulus * / %
  4. Addition / Subtraction + -
  5. Relational operators < > <= >=
  6. Equality operators == !=
  7. Logical AND &&
  8. Logical OR ||
  9. Assignment =

Note: Java has more operators than this list, but these are the ones you’ll use most often.

🧠 Key Difference: Java is NOT Just Math

Java evaluates expressions using precedence rules, one step at a time.

Example 1

int result = 10 + 6 / 2;

Steps:

✅ result = 13

Example 2 (Using Parentheses)

int result = (10 + 6) / 2;

Steps:

✅ result = 8

⚠️ Modulus (%) in Java

Java includes modulus, which finds the remainder.

int x = 10 % 3;

✅ x = 1

⚠️ Integer Division Gotcha

If both numbers are integers, Java cuts off decimals. (This is called integer division.) 

int x = 5 / 2;

✅ x = 2

To fix:

double x = 5.0 / 2;

✅ x = 2.5

🔄 Left-to-Right Rule Still Applies

When operators have the same precedence, Java evaluates left to right.

int x = 20 / 5 * 2;

Steps:

✅ x = 8

🧩 Comparison Example (Very Common Bug)

boolean answer = 10 > 5 + 3;

Steps:

✅ answer = true

⭐ Best Practice Rule

When in doubt, use parentheses.

📝 Quick Summary

Concept Math (PEMDAS) Java
Parentheses ✔ ✔
Multiplication / Division ✔ ✔
Addition / Subtraction ✔ ✔
Modulus (%) ❌ ✔
Logical operators ❌ ✔
Integer division ❌ ✔

🧪 Practice Check

What is the output?

System.out.println(8 + 12 / 4 * 2);

Steps:

✅ Output: 14