Few math problems have started more arguments than this one:
8 ÷ 2(2 + 2) = ?
Half the internet swears the answer is 16. The other half swears it is 1 – and both sides are completely certain the other side failed basic math. Comment sections explode. Friendships wobble. So who is actually right?
Under the standard order of operations taught in schools today, the answer is 16. Here is the full step-by-step solution, and – just as important – an honest explanation of why smart people get 1, and why this problem is sneakier than it looks.
Step by Step: The Standard Solution
The order of operations (PEMDAS / BODMAS) says: Parentheses first, then Exponents, then Multiplication and Division left to right, then Addition and Subtraction left to right. The part everyone forgets is in bold, and it decides this entire fight.
Step 1 – Parentheses. Solve inside the brackets first: (2 + 2) = 4. The problem is now:
8 ÷ 2(4)
Step 2 – Division and multiplication, left to right. The expression reads 8 ÷ 2 x 4 (the “2(4)” is multiplication, written without a sign). Multiplication and division have equal priority, so you work from the left: 8 ÷ 2 = 4. Then:
4 x 4 = 16
That is it. 8 ÷ 2(2+2) = 16. Google, WolframAlpha, and every modern calculator agree.
Where Does 1 Come From?
The 1 camp reads 2(2+2) as a single glued-together unit. In algebra, a number written directly against parentheses – 2(x) – often feels like one term, as if the problem were 8 ÷ [2(2+2)]. Following that instinct:
- 2(2 + 2) = 2 x 4 = 8
- 8 ÷ 8 = 1
This is not random ignorance. In some older textbooks and in professional typesetting, multiplication by juxtaposition (numbers touching, no x sign) is given priority over regular division. If you were taught that convention, 1 is the answer your rules produce. The two camps are literally playing by different rulebooks.
The Real Culprit: The Division Sign
Here is what mathematicians actually say about this problem: it is badly written. The ÷ symbol is almost never used in real mathematics beyond elementary school, precisely because it creates this ambiguity. A professional would write the problem as a fraction, where the layout removes all doubt:
- 8 / 2 x (2 + 2) – written on one line with a slash – is conventionally read left to right: 16
- 8 over a horizontal bar, with 2(2+2) under the bar – is unambiguously 1
The viral version uses ÷ plus a missing multiplication sign, the two most ambiguous choices available. That is not an accident – ambiguity is exactly what makes it viral. A clear problem gets solved once. An ambiguous one gets argued about forever.
How to Never Get Caught by This
Three habits protect you from every problem in this family:
1. Equal priority means left to right. Multiplication and division are partners, not rivals. Neither goes first – position decides. Same for addition and subtraction.
2. Parentheses are not glue. (2+2) becomes 4, and 2(4) becomes ordinary multiplication with ordinary priority. Unless brackets [ ] actually group it, do not group it yourself.
3. When you write math, remove the ambiguity. Use extra parentheses or fractions. 8 ÷ (2(2+2)) and (8 ÷ 2)(2+2) are two different problems with two different answers – write which one you mean.
<
Enjoyed this? Try these next: If x^x = 49, Then x = ? (Solved Step by Step) and NYT Pips: How to Solve the Domino Logic Puzzle (Strategy Guide).