PEMDAS, Explained: Why 8 2(2+2) = 16, Not 1

Every few years, the expression 8 ÷ 2(2+2) goes viral and splits the internet into two camps: the 16s and the 1s. Both camps include engineers. Both camps are furious. And both camps, remarkably, are following a rule — just not the same one.

I build small free math tools at Calcrio, and this expression is the most-requested thing I have ever added to an order of operations calculator. So here is the definitive breakdown: the answer is 16, the reasoning is boring, and the reason people disagree is a single false assumption.

TL;DR for the impatient: Parentheses first (2+2=4), then division and multiplication are the same priority level, so you go left to right: 8 ÷ 2 = 4, 4 × 4 = 16. The answer 1 requires believing 2(4) outranks ÷ — it does not.

The boring, correct solution

PEMDAS — Parentheses, Exponents, Multiplication, Division, Addition, Subtraction — is the order of operations taught in every US curriculum. Here it is applied mechanically:

Step 1 — Parentheses. 2 + 2 = 4. The expression is now:

8 ÷ 2 × 4

Note: 2(4) is just 2 × 4. Implied multiplication is multiplication.

Step 2 — Exponents. None. Moving on.

Step 3 — Multiplication and division, LEFT TO RIGHT. This is the step that matters. × and ÷ are one priority level. You do not do all the multiplication first. You read left to right:

8 ÷ 2 = 4
4 × 4 = 16

Answer: 16.

Where the 1 comes from

The 1 camp reasons like this:

8 ÷ 2(2+2) → 8 ÷ 2(4) → 8 ÷ 8 → 1

They solve the parentheses correctly (4), then treat 2(4) as a single glued unit — doing the implied multiplication before the division. That move has a name: privileged implied multiplication. It is not part of the standard order of operations.

Why does it feel right? Because in algebra, 2x ÷ 2x does read as 1. But that works because the variable binds to its coefficient by notation convention. With pure numbers, there is nothing to bind: 2(4) is exactly 2 × 4, with exactly multiplication's priority.

The empirical evidence agrees. Google's calculator, the iPhone calculator, Casio scientifics, WolframAlpha — all return 16. The rare calculators returning 1 were programmed with non-standard precedence for implied multiplication. A design choice, not a math law.

The same mistake, smaller numbers

The viral puzzle has quieter cousins that show up on actual exams:

• 6 + 2 × 3 = 12, not 20. Multiplication outranks addition: 2 × 3 = 6, then 6 + 6 = 12.
• (6 + 2) × 3 = 24. Parentheses outrank everything — they literally change the expression's meaning.
• 6 ÷ 2(1+2) = 9. Parentheses give 3, then 6 ÷ 2 × 3 left to right: 3 × 3 = 9.
• 33 − 12 + 4² = 37. Exponent first (16), then left to right: 33 − 12 = 21, 21 + 16 = 37.

And the trap BODMAS students fall into too: in 33 − 12 + 16, do NOT add first. Left to right. 21 + 16 = 37, not 5.

The two sentences that replace the acronym

PEMDAS and BODMAS are the same rule in different clothes (Brackets = Parentheses, Orders = Exponents). The acronym misleads in exactly one place: it looks like a strict sequence. It is not. The whole rule is:

× and ÷ are one level — left to right. + and − are one level — left to right.

Memorize those two sentences and the mnemonics become interchangeable.

Try it yourself

I added a step-by-step solver to Calcrio's free pemdas calculator: type any expression, and it shows every step — which operation it evaluates and why — plus the two most common wrong answers with the exact point where each one breaks the rule. Paste 8 ÷ 2(2+2) into a group chat and watch the 1 camp go quiet.