Arithmetic operators in Java - Step-by-Step Execution

Concept Flow - Arithmetic operators

Start

↓

Initialize variables

↓

Apply +, -, *, /, %

↓

Store results

↓

Print results

↓

End

This flow shows how arithmetic operators take values, perform calculations, and store or display the results.

Execution Sample

Java

int a = 10;
int b = 3;
int sum = a + b;
int diff = a - b;
int prod = a * b;
int quot = a / b;
int mod = a % b;
System.out.println(sum + ", " + diff + ", " + prod + ", " + quot + ", " + mod);

This code calculates sum, difference, product, quotient, and remainder of two numbers and prints them.

Execution Table

Step	Operation	Expression	Result	Explanation
1	Addition	sum = a + b	13	10 + 3 = 13
2	Subtraction	diff = a - b	7	10 - 3 = 7
3	Multiplication	prod = a * b	30	10 * 3 = 30
4	Division	quot = a / b	3	Integer division 10 / 3 = 3
5	Modulo	mod = a % b	1	Remainder of 10 / 3 is 1
6	Print	System.out.println(...)	13, 7, 30, 3, 1	Outputs all results
7	End	-	-	Program ends

💡 All arithmetic operations done and results printed, program ends.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	Final
a	10	10	10	10	10	10	10
b	3	3	3	3	3	3	3
sum	undefined	13	13	13	13	13	13
diff	undefined	undefined	7	7	7	7	7
prod	undefined	undefined	undefined	30	30	30	30
quot	undefined	undefined	undefined	undefined	3	3	3
mod	undefined	undefined	undefined	undefined	undefined	1	1

Key Moments - 3 Insights

Why does division 10 / 3 give 3 instead of 3.333?

Because both a and b are integers, Java does integer division which discards the decimal part. See execution_table step 4.

What does the % operator do?

It gives the remainder after division. For 10 % 3, the remainder is 1 as shown in execution_table step 5.

Are the original variables a and b changed by the operations?

No, a and b keep their original values throughout. The results are stored in new variables like sum, diff, etc. See variable_tracker.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the value of prod?

A 7

B 13

C 30

D 3

💡 Hint

Check the 'Result' column at step 3 in execution_table.

At which step does the modulo operation happen?

A Step 5

B Step 2

C Step 4

D Step 1

💡 Hint

Look for '%' operator in the 'Operation' column in execution_table.

If variable b was 4 instead of 3, what would be the new value of quot at step 4?

A 4

B 2

C 3

D 1

💡 Hint

Integer division 10 / 4 equals 2, check how quot is calculated in execution_table step 4.

Concept Snapshot

Arithmetic operators in Java:
+ (add), - (subtract), * (multiply), / (divide), % (modulo)
Operate on numbers and produce results.
Integer division discards decimals.
Modulo gives remainder.
Store results in variables.

Full Transcript

This example shows how Java uses arithmetic operators to calculate sum, difference, product, quotient, and remainder of two integers. Variables a and b start with 10 and 3. Each operator is applied step-by-step: addition gives 13, subtraction 7, multiplication 30, division 3 (integer division), and modulo 1 (remainder). Results are stored in separate variables. The program prints all results. Important points: integer division truncates decimals, modulo returns remainder, and original variables remain unchanged.

Practice

1. Which of the following is the correct symbol for the modulus operator in Java, which gives the remainder of a division?

easy

A. *

B. /

C. -

D. %

Solution

1. Step 1: Understand the modulus operator

   The modulus operator returns the remainder after division of two numbers.

2. Step 2: Identify the correct symbol in Java

   In Java, the symbol for modulus is %.

3. Final Answer:

   % -> Option D

4. Quick Check:

   Modulus operator = % [OK]

Hint: Modulus operator is always % in Java math [OK]

Common Mistakes:

• Confusing modulus % with division /
• Using * or - instead of %
• Thinking modulus returns quotient

2. Which of the following Java statements correctly calculates the product of two integers a and b?

easy

A. int result = a / b;

B. int result = a + b;

C. int result = a * b;

D. int result = a % b;

Solution

1. Step 1: Identify the multiplication operator

   In Java, the multiplication operator is *.

2. Step 2: Check the statement that uses multiplication

   The statement int result = a * b; correctly multiplies a and b.

3. Final Answer:

   int result = a * b; -> Option C

4. Quick Check:

   Multiplication operator = * [OK]

Hint: Use * for multiplication in Java expressions [OK]

Common Mistakes:

• Using + instead of * for multiplication
• Confusing division / with multiplication
• Using % which is remainder, not product

3. What is the output of the following Java code?

int x = 10;
int y = 3;
System.out.println(x / y);

medium

A. 3

B. 3.3333333

C. 3.0

D. 4

Solution

1. Step 1: Understand integer division in Java

   Both x and y are integers, so division drops the decimal part.

2. Step 2: Calculate integer division result

   10 divided by 3 is 3.333..., but integer division returns 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Integer division drops decimals = 3 [OK]

Hint: Integer division drops decimals, result is integer [OK]

Common Mistakes:

• Expecting decimal output with int division
• Confusing / with % operator
• Assuming automatic float conversion

4. Identify the error in the following Java code snippet:

int a = 5;
int b = 0;
int c = a / b;
System.out.println(c);

medium

A. Division by zero causes runtime error

B. Variable c is not declared

C. Missing semicolon after declaration

D. Incorrect use of modulus operator

Solution

1. Step 1: Analyze the division operation

   The code divides a by b, where b is zero.

2. Step 2: Understand division by zero in Java

   Dividing an integer by zero causes a runtime ArithmeticException error.

3. Final Answer:

   Division by zero causes runtime error -> Option A

4. Quick Check:

   Division by zero throws error [OK]

Hint: Never divide by zero; it crashes the program [OK]

Common Mistakes:

• Ignoring division by zero error
• Thinking it returns zero or infinity
• Confusing syntax error with runtime error

5. Given the code below, what will be the value of result after execution?

int a = 15;
int b = 4;
int result = a / b + a % b * 2;

hard

A. 11

B. 9

C. 8

D. 7

Solution

1. Step 1: Calculate integer division and modulus

   15 / 4 = 3 (integer division), 15 % 4 = 3 (remainder).

2. Step 2: Apply operator precedence and compute expression

   Expression is 3 + 3 * 2. Multiplication first: 3 * 2 = 6. Then addition: 3 + 6 = 9.

3. Step 3: Re-check calculation

   Wait, re-check: 15 / 4 = 3, 15 % 4 = 3, 3 * 2 = 6, 3 + 6 = 9.

4. Final Answer:

   9 -> Option B

5. Quick Check:

   Division + (modulus * 2) = 9 [OK]

Hint: Remember * before + in mixed expressions [OK]

Common Mistakes:

• Adding before multiplying
• Confusing division and modulus results
• Forgetting integer division truncates decimals