Question

Summarize the mathematical order of operations, as it works in most programming languages.

Short answer

Answer: The order of operations in most programming languages follows the PEMDAS/BODMAS hierarchy: parentheses, exponentiation, multiplication & division (performed from left to right), and addition & subtraction (also performed from left to right). This order is important to ensure consistent and predictable results when evaluating expressions.

Step-by-step solution

1. Parentheses (Brackets)

Parentheses have the highest precedence in the order of operations. Operations inside parentheses are evaluated before anything else. If there are nested parentheses, work from the innermost parentheses outwards. Example: (3 + 5) * 2 evaluates to 8 * 2.

2. Exponentiation

Next in the order of operations is exponentiation (raising to a power). This operation is performed from right to left. Example: 2 ^ (1 + 1) evaluates to 2 ^ 2 which equates to 4.

3. Multiplication and Division

Multiplication and division are performed from left to right, after the exponentiation operation. They have the same precedence level, so they are performed in the order they appear. Example: 6 / 2 * (2 + 1) evaluates to (6 / 2) * 3 which equates to 3 * 3, yielding 9.

4. Addition and Subtraction

Finally, addition and subtraction are performed after all other operations, in order from left to right. They also have the same precedence level. Example: 2 + 4 * 3 - 1 evaluates to 2 + 12 - 1, which results in 14 - 1, giving us the final answer of 13. In summary, the order of operations in most programming languages follows the PEMDAS/BODMAS hierarchy: parentheses, exponentiation, multiplication & division (performed from left to right), and addition & subtraction (also performed from left to right). These rules ensure consistent and predictable results when evaluating expressions.