Arithmetic Operators, Integer Division and Remainder

New words in this topic, in plain English. Come back here whenever one feels fuzzy.

Operator

A symbol that does something to values, like + (add) or % (remainder).

Operand

A value an operator works on. In 7 / 2, the operands are 7 and 2.

Expression

Any piece of code that produces a value, like price * qty + 5.

Integer division

Dividing two whole numbers and keeping only the whole part of the answer.

Remainder (modulo)

What's left over after integer division. % gives it: 7 % 2 is 1.

Precedence

The rule for which operators run first when there are no brackets, like multiplication before addition.

Associativity

The direction operators of equal precedence run in. Arithmetic runs left to right.

Increment

Increasing a variable by one, written ++.

Side effect

A change to a variable caused while an expression is being evaluated, like the ++ inside a[i++].

1. 1

   Predict the signs

   Write down the values of -9 / 4, -9 % 4, 9 % -4 and Math.floorMod(-9, 4), then add them to the first example and check. (Answers: -2, -1, 1, 3.)

2. 2

   Convert minutes

   Change totalSeconds to 100000 in the third example. Predict the hours, minutes and seconds (27h 46m 40s), then add a days calculation with / 86400.

3. 3

   Divide by zero two ways

   Add System.out.println(10.0 / 0); and then System.out.println(10 / 0);. The first prints Infinity; the second compiles (the compiler doesn't reject it) but throws ArithmeticException when it runs.

Errors are the best teachers. Make each change, read the error, guess what went wrong, then reveal the answer.

public class Main {
    public static void main(String[] args) {
        int apples = 10;
        int kids = 0;
        System.out.println(apples / kids);
    }
}

1. 1

   Integer division (/ with two integer operands) truncates toward zero: 7 / 2 is 3 and -7 / 2 is -3. If either operand is a double, you get decimal division: 7 / 2.0 is 3.5.

2. 2

   Remainder % satisfies (a / b) * b + (a % b) == a, so its sign follows the left operand: -7 % 3 is -1 and 7 % -3 is 1. When you need a result that's never negative (for example wrapping around a circular array), use Math.floorMod(-7, 3), which gives 2.

3. 3

   Division by zero: with integers, / and % throw ArithmeticException: / by zero. With double, 1.0 / 0 is Infinity and 0.0 / 0 is NaN (Topic 1.4).

4. 4

   Precedence: *, /, % happen before + and -; operators of equal precedence run left to right. 2 + 3 * 4 is 14 and 10 - 4 - 3 is 3. Use parentheses whenever the order isn't obvious to a reader.

5. 5

   Increment and decrement: ++i adds one and gives the new value; i++ adds one but gives the old value. On a line of its own they behave identically. Inside a bigger expression they differ, and i = i++; famously leaves i unchanged.

6. 6

   ^ is not power in Java; it's bitwise XOR (Topic 1.9), so 2 ^ 10 is 8. Use Math.pow(2, 10) (returns double 1024.0) or, for powers of 2, 1 << 10. The Math class also has abs, max, min, sqrt, floorDiv and floorMod.

• ↔

  Integer division is fast and exact for whole quantities, but silently drops fractions; decide deliberately whether you want truncation, floor, or a decimal result.

• ↔

  % is cheap and familiar but its negative results surprise people; Math.floorMod is clearer for wrap-around logic at a tiny cost.

• ↔

  ++ inside expressions saves a line but makes code harder to read and review; most style guides allow it only as a standalone statement or in loop headers.

• I can predict / and % for any mix of positive and negative integers.

• I know when Java does integer versus decimal division and how to force decimal division.

• I know integer division by zero throws and decimal division doesn't.

• I can explain prefix vs postfix ++ and the i = i++ puzzle.

• I use Math.pow, not ^, for powers and know operator precedence.