Math & logic · ENGLISH
Why does 2 + 2 × 3 equal 8?
Order of operations lets a short expression have a shared interpretation.
A convention that saves brackets
In standard arithmetic notation, multiplication and division are handled before addition and subtraction. Grouping symbols come first, followed by exponents. Operations at the same level are evaluated from left to right. This convention lets writers omit many brackets while retaining a shared reading.
Two expressions, two jobs
In 2 + 2 × 3, first calculate 2 × 3 = 6, then add 2 to obtain 8. In (2 + 2) × 3, the brackets instead group the sum: 4 × 3 = 12.
Imagine two loose counters plus two groups of three counters. You have eight. Four groups of three would be a different arrangement. The brackets tell you which arrangement the symbols describe.
The mnemonic trap
A remembered acronym can mislead if it makes you perform every multiplication before every division. They have equal priority. For 12 ÷ 3 × 2, work left to right: 4 × 2 = 8. Do not silently replace it with 12 ÷ (3 × 2).
Addition and subtraction also share a level. For 10 − 3 + 2, calculate 7 + 2 = 9. Grouping the last two values first changes the expression rather than following it.
In the game
A fair mental-math challenge uses clear symbols and brackets wherever a layout could confuse the intended grouping. It should not rely on notoriously unclear inline fractions to manufacture disagreement.
Before doing arithmetic under pressure, find the groups. A quick glance at brackets and operation signs can save you from calculating a different problem perfectly. Outside the game, the same habit is useful when checking a spreadsheet formula or a shared calculation.
Sources & further reading
Sources support the factual background. The worked examples and game connections are written for 3 SECONDS.