Steps

1. Identify types: Check whether operands are integers or floating-point values.
2. Check parentheses: Use parentheses to identify explicitly grouped parts.
3. Apply precedence and associativity: Determine which operands belong to each operator.
4. Calculate valid operations: Use integer or floating-point arithmetic as required.
5. Check the result: Make sure division is valid and values stay within the supported range.

Worked example: integer arithmetic

Evaluate 8 + 12 / 5 * 2. Division and multiplication have higher precedence than addition and group left to right. First, 12 / 5 gives 2 because both operands are integers. Next, 2 * 2 gives 4. Finally, 8 + 4 gives 12. Thus the result is 12.

Worked example: floating-point arithmetic

In 8 + 12.0 / 5 * 2, 12.0 is double. The division gives approximately 2.4, multiplication gives approximately 4.8, and addition gives approximately 12.8. Changing an operand type can therefore change the answer.

Important points

Do not assume that all operands are evaluated from left to right. Short-circuit operators provide particular ordering rules, but many operators do not. An expression such as i++ + ++i has undefined behaviour and no guaranteed numeric result. Divide only by a valid non-zero divisor, and avoid signed overflow.

Reference tables

Diagram or flowchart

Key points

• Integer division happens before a later conversion can preserve a fraction.
• Undefined behaviour is not a puzzle with one portable numerical answer.