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➗ Operators & Expressions · Beginner

Integer division & remainder in Java

int / int truncates toward zero; % keeps the sign of the dividend.

🧩 The mysteryThe average of 3 and 4? Java says 3.0. And isOdd(-3) returns false. Two bugs, one cause: integer division.

int / int = int

When both operands are integers, / throws away the fractional part, truncating toward zero. Make one operand a double to keep the decimals.

7 / 2      // 3
-7 / 2     // -3 (toward zero, not -4)
7 / 2.0    // 3.5
🔮 Predict it

Your turn

What does this print?

System.out.println(9 / 4);
System.out.println(-9 / 4);
  1. 2 -2
  2. 2.25 -2.25
  3. 2 -3
Show the answer

Both are int divisions, truncated toward zero: 2.25 → 2 and -2.25 → -2.

The remainder's sign

a % b always takes the sign of the left operand (the dividend). The divisor's sign doesn't matter. The rule a == (a / b) * b + a % b always holds.

-7 % 2    // -1   (-7 = -3*2 + -1)
7 % -3    // 1    (7 = -2*-3 + 1)
🔮 Predict it

Your turn

What does this print?

System.out.println(-10 % 3);
System.out.println(10 % -3);
  1. -1 1
  2. 2 -2
  3. 1 1
Show the answer

The result follows the dividend: -10 gives -1, and 10 gives 1, whatever the divisor's sign.

⚠️ The trap

The isOdd bug

For negative odd numbers, n % 2 is -1, not 1, so this returns false for -3. Test n % 2 != 0 instead.

boolean isOdd(int n) {
    return n % 2 == 1;  // fails for -3
}

Averages

✗ 3.0
int a = 3, b = 4;
double avg = (a + b) / 2;

(a + b) / 2 is int division: 7 / 2 = 3, widened to 3.0 too late.

✓ 3.5
int a = 3, b = 4;
double avg = (a + b) / 2.0;

2.0 is a double, so the division itself is floating-point.

🤔 Think first

Why not cast it?

Why doesn't double avg = (double) ((a + b) / 2); fix it?

Think about it, then reveal the answer

The int division has already thrown away the .5 before the cast runs: you're casting 3 into 3.0. An operand must be a double before dividing.

💼 In the real world

In real projects

Progress bars stuck at 0% are a classic: done / total * 100 with ints is 0 until the job finishes. Multiply first (done * 100 / total) or use doubles.

Key takeaways

  1. 7 / 2 is 3, and -7 / 2 is -3 (toward zero)
  2. -7 % 2 is -1: sign follows the dividend
  3. Make one operand a double to get decimals: 7 / 2.0
  4. Test odd numbers with n % 2 != 0
🤯 Did you know?

Languages disagree: Python's -7 // 2 is -4 (it rounds down), while Java's -7 / 2 is -3 (it truncates toward zero). Same numbers, different answers.

Practice questions

What does this print?

System.out.println(-7 / 2);
System.out.println(-7 % 2);
  1. -4 1
  2. -3 1
  3. -4 -1
  4. -3 -1
Check your answer

-3 -1. Integer division truncates toward zero, so -3.5 becomes -3. The remainder takes the dividend's sign: -7 = -3 × 2 + (-1).

What does this print?

System.out.println(7 % -3);
  1. -1
  2. -2
  3. 2
  4. 1
Check your answer

1. The sign of the divisor doesn't matter; the result follows the dividend 7, which is positive. 7 = -2 × -3 + 1.

Next: divide by zero. Java throws an exception... unless you're using doubles, where you get Infinity instead. Wait, what?