The short answer
Mixed operations follow order of operations (PEMDAS): parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right. For 2 + 3 × 4, multiply first (3 × 4 = 12) then add (2 + 12 = 14) — the answer is 14, not 20.
Key takeaways
- Order of operations changes the answer: 2 + 3 × 4 equals 14, not 20 — multiplication happens before addition even though addition appears first in the expression.
- Division by zero is undefined, not zero or infinity. A correct calculator rejects it with an error rather than returning a number.
- Computer floating-point math can produce tiny rounding artifacts (0.1 + 0.2 stored internally as 0.30000000000000004) — round to the decimal places you actually need, especially for money.
- This calculator's % key means different things in different modes — see the FAQ below before relying on a modulo or percentage result.
Order of operations (PEMDAS)
| Step | Operation | Symbol |
|---|---|---|
| 1 | Parentheses | ( ) |
| 2 | Exponents | ^ |
| 3 | Multiplication & division (left to right) | × ÷ |
| 4 | Addition & subtraction (left to right) | + − |
Worked example: mixed operations
8 + (6 − 2) × 3² ÷ 4
= 8 + 4 × 3² ÷ 4 (parentheses first)
= 8 + 4 × 9 ÷ 4 (exponent next)
= 8 + 36 ÷ 4 (multiply, left to right)
= 8 + 9 (divide, left to right)
= 17 (add last)
Notice multiplication and division are evaluated together, left to right, in the order they appear — multiplication doesn't automatically happen before division. The same rule applies to addition and subtraction in the final step.
Common mistakes to avoid
- Evaluating strictly left to right and ignoring precedence — treating 2 + 3 × 4 as (2 + 3) × 4 = 20 instead of 2 + (3 × 4) = 14.
- Mixing up negation and exponents: −3² equals −9 (square 3, then negate) while (−3)² equals 9 (negate, then square) — the parentheses change the result.
- Rounding intermediate results before the final step, which compounds small errors across a multi-step calculation.
- Assuming % always means the same thing — in this calculator it's percentage in Expression/Keypad mode but true remainder in Operation Selection's Modulo mode.
Related calculators
- Scientific Calculator — add trigonometry, logarithms, and more advanced functions.
- Long Division Calculator — see every step of a division problem worked out by hand.
- Percentage Calculator — handle percentage-of, percentage-change, and reverse-percentage problems directly.
- Rounding Calculator — round results to a specific decimal place or significant figure.