8 ÷ 2(2 + 2): is the answer 16 or 1?
It is 16 if you work strictly left to right, which is how most classrooms teach PEMDAS and BODMAS. It is 1 if you treat 2(2 + 2) as a single tightly bound unit, as some textbooks, journals and calculators do. Both answers come from consistent rules, which is exactly why this one keeps starting arguments.
See it worked out
Left to right
A number touching a bracket counts as ordinary ×.
= 16
Written out: 8 ÷ 2 × (2 + 2)
Implicit multiplication first
A number touching a bracket is glued to it as one factor.
= 1
Written out: 8 ÷ (2 × (2 + 2))
Where the two answers come from
Everyone starts the same way. The brackets go first, so 2 + 2 becomes 4 and the expression turns into 8 ÷ 2(4). The disagreement is about what 2(4) means.
Left to right. In the classroom reading, a number written right next to a bracket is just multiplication with the × sign left out. Multiplication and division share a rank, so you go left to right: 8 ÷ 2 = 4, then 4 × 4 = 16.
Implicit multiplication first. In the other reading, a number pressed against a bracket is glued to it as a single factor. So 2(4) is worked out as 8 before the division happens: 8 ÷ 8 = 1.
So which one is right?
Neither reading breaks arithmetic. The trouble is the notation. A one-line expression that mixes ÷ with multiplication that has no sign has no single universal standard, and style guides that care about this tell writers to add brackets rather than rely on the reader's habits.
If you meet this in a class, use the convention your teacher or textbook uses. If you are writing it, add the brackets.
Answers people give
| Answer | How you get there |
|---|---|
| 16 | Working left to right after the brackets: 8 ÷ 2 × 4. |
| 1 | Doing the implicit multiplication first: 8 ÷ (2 × 4). |
| 10 | Ignoring the brackets: 8 ÷ 2 × 2 + 2. This is wrong under either convention. |
How to write it so nobody argues
- 8 ÷ 2 × (2 + 2) for 16.
- 8 ÷ (2(2 + 2)) for 1.
- Or set it as a stacked fraction, so the layout shows which parts belong together.
The two readings of this pattern always differ by a fixed factor: the square of the bracket's value. Here the bracket is worth 4, and 4² = 16, which is why 16 and 1 are the two answers. The implicit multiplication guide explains why.
Try your own expression
Type anything, including brackets, fractions and exponents, and get the steps.
Questions
Is 8 ÷ 2(2 + 2) equal to 16?
It is under the most common classroom convention: work out the bracket, treat 2(2 + 2) as 2 × (2 + 2), and go left to right. Under the implicit-multiplication-first convention it equals 1. The notation does not settle it, so add brackets when you write it.
Why do some calculators say 1?
Calculators and software differ in how they read multiplication with no sign. Some treat it as tighter than division, which gives 1. Others treat it like ×, which gives 16. Checking your manual or adding brackets removes the doubt.
Is PEMDAS wrong or incomplete?
PEMDAS is a memory aid, and it does not say where unsigned multiplication like 2(4) sits. The part people forget is that multiplication and division share a rank, and so do addition and subtraction. The daily puzzle drills exactly that.