Operator precedence

Introduction

Operator precedence tells the computer which math or logic steps to do first when there are many in one line.

When you write math calculations with multiple operators like +, -, *, / in one line.

When you combine different types of operations like adding and multiplying in the same expression.

When you use logical operators like && and || together in a condition.

When you want to make sure your code does things in the right order without extra parentheses.

When you want to avoid mistakes in complex expressions by understanding which parts run first.

Syntax

C

expression with multiple operators, e.g., a + b * c - d / e

Operators with higher precedence run before operators with lower precedence.

Use parentheses () to change the order if needed.

Examples

Multiplication (*) happens before addition (+), so 3*4=12 first, then 2+12=14.

C

int result = 2 + 3 * 4;

Parentheses force addition first: 2+3=5, then multiply by 4 = 20.

C

int result = (2 + 3) * 4;

Division (/) happens before addition (+), so 10/2=5, then 5+3=8.

C

int result = 10 / 2 + 3;

Parentheses change order: 2+3=5, then 10/5=2.

C

int result = 10 / (2 + 3);

Sample Program

This program shows how operator precedence works with multiplication, division, addition, and parentheses.

C

#include <stdio.h>

int main() {
    int a = 5, b = 10, c = 2;
    int result1 = a + b * c;  // multiplication first
    int result2 = (a + b) * c; // parentheses change order
    int result3 = b / c - a;   // division then subtraction
    int result4 = b / (c - a); // parentheses first

    printf("result1 = %d\n", result1);
    printf("result2 = %d\n", result2);
    printf("result3 = %d\n", result3);
    printf("result4 = %d\n", result4);

    return 0;
}

Important Notes

Remember that multiplication (*) and division (/) have higher precedence than addition (+) and subtraction (-).

Use parentheses to make your code clear and avoid mistakes.

Operator precedence applies to all operators, including logical and bitwise ones, but start with math operators first.

Summary

Operator precedence decides which part of an expression runs first.

Multiplication and division happen before addition and subtraction.

Use parentheses to control the order and make your code easier to read.

Practice

1. Which operator has the highest precedence in the expression 3 + 4 * 5?

easy

A. Division (/)

B. Addition (+)

C. Subtraction (-)

D. Multiplication (*)

Solution

1. Step 1: Recall operator precedence rules

   Multiplication and division have higher precedence than addition and subtraction in C.

2. Step 2: Identify operators in the expression

   The expression has addition (+) and multiplication (*). Multiplication runs first.

3. Final Answer:

   Multiplication (*) -> Option D

4. Quick Check:

   Multiplication > Addition [OK]

Hint: Multiplication and division run before addition and subtraction [OK]

Common Mistakes:

• Thinking addition runs before multiplication
• Ignoring operator precedence
• Assuming left to right always applies

2. Which of the following expressions is correctly written to add 2 and 3, then multiply the result by 4?

easy

A. (2 + 3) * 4

B. 2 + (3 * 4)

C. 2 + 3 * 4

D. 2 * 3 + 4

Solution

1. Step 1: Understand the desired calculation

   Add 2 and 3 first, then multiply by 4.

2. Step 2: Check parentheses usage

   Only (2 + 3) * 4 uses parentheses to add 2 and 3 first, then multiply by 4.

3. Final Answer:

   (2 + 3) * 4 -> Option A

4. Quick Check:

   Parentheses change order to add first [OK]

Hint: Use parentheses to force addition before multiplication [OK]

Common Mistakes:

• Ignoring parentheses and trusting default precedence
• Misreading the expression order
• Assuming left to right overrides precedence

3. What is the output of this C code?

int x = 5 + 3 * 2 - 4 / 2;
printf("%d", x);

medium

A. 10

B. 9

C. 11

D. 8

Solution

1. Step 1: Apply operator precedence

   Multiplication and division first: 3 * 2 = 6, 4 / 2 = 2.

2. Step 2: Calculate the expression left to right

   Expression becomes 5 + 6 - 2 = 9.

3. Final Answer:

   9 -> Option B

4. Quick Check:

   5 + 6 - 2 = 9 [OK]

Hint: Calculate * and / before + and - [OK]

Common Mistakes:

• Adding before multiplying
• Dividing after subtraction
• Calculating left to right ignoring precedence

4. Identify the error in this expression:

int result = 10 / 2 * 3 + 4 - 5;

medium

A. Multiplication and division have the same precedence and are left to right

B. Subtraction should be done before multiplication

C. Addition has higher precedence than multiplication

D. Division should be done after addition

Solution

1. Step 1: Check operator precedence and associativity

   Multiplication (*) and division (/) have the same precedence and are evaluated left to right.

2. Step 2: Verify the expression evaluation order

   Expression evaluates as ((10 / 2) * 3) + 4 - 5, which is correct.

3. Final Answer:

   Multiplication and division have the same precedence and are left to right -> Option A

4. Quick Check:

   * and / same precedence, left to right [OK]

Hint: Remember * and / are equal precedence, evaluated left to right [OK]

Common Mistakes:

• Thinking division happens after addition
• Assuming addition has higher precedence
• Ignoring left-to-right rule for same precedence

5. Given the expression int y = 8 - 3 + 2 * 4 / 2;, which parentheses placement changes the result to 14?

hard

A. 8 - 3 + (2 * 4) / 2

B. 8 - (3 + 2) * 4 / 2

C. (8 - 3 + 2) * 4 / 2

D. (8 - (3 + 2)) * 4 / 2

Solution

1. Step 1: Calculate original expression

   * and / first left-to-right: 2 * 4 = 8, 8 / 2 = 4; then 8 - 3 + 4 = 9.

2. Step 2: Evaluate (8 - 3 + 2) * 4 / 2

   (8 - 3 + 2) = 7, 7 * 4 = 28, 28 / 2 = 14.

3. Step 3: Confirm others

   8 - (3 + 2) * 4 / 2 = 8 - 20 / 2 = 8 - 10 = -2; 8 - 3 + (2 * 4) / 2 = 9; (8 - (3 + 2)) * 4 / 2 = 3 * 4 / 2 = 6.

4. Final Answer:

   (8 - 3 + 2) * 4 / 2 -> Option C

5. Quick Check:

   Parentheses force addition before multiplication [OK]

Hint: Try parentheses around addition to change multiplication order [OK]

Common Mistakes:

• Assuming original order always applies
• Not recalculating expression after adding parentheses
• Misplacing parentheses without recalculating