Order of operations

You buy two pretzels at 2 € each and three rolls at 1 € each. In your head you naturally work out what each kind costs first (4 € and 3 €) and then add up. That exact order is a fixed rule in mathematics, and once you know it, calculations like 3 + 4 × 2 will never trip you up again.

Multiplication and division come first

Multiplying (×) and dividing (÷) come before adding (+) and subtracting (−). In 3 + 4 × 2 you therefore calculate 4 × 2 = 8 first and then 3 + 8 = 11. If you stubbornly work left to right you get 14, and that is wrong. The rule makes sure everyone in the world gets the same result from the same expression.

Brackets beat everything

Sometimes you want to set the order yourself. That is what brackets are for: whatever is inside brackets is always calculated first. (3 + 4) × 2 gives 7 × 2 = 14, without breaking any rule. The full ranking is: brackets first, then multiplication and division, then addition and subtraction.

Common traps

Two traps come up especially often. First: several multiplications or divisions in the same expression. In 6 × 3 − 4 × 2 you work out both products first (18 and 8) and subtract afterwards. Second: operations of equal rank. When only additions and subtractions, or only multiplications and divisions, stand side by side, you work through them from left to right. That is why 10 − 3 + 2 is 9 and not 5. The safest approach is to do exactly one operation per step and copy the rest unchanged.