Equation: 60 ÷ 3(3 + 1)
Can You Solve This Faster Than Most People?
At first glance, this equation looks simple—just a division and some parentheses. But don’t be fooled. The way it’s written creates confusion about the order of operations and how to handle the implicit multiplication next to the parentheses.
This puzzle has gone viral many times because different people follow different mental shortcuts, and those shortcuts often lead to wrong answers. Let’s break it down carefully.
Why This Problem Is Confusing
- The parentheses (3 + 1) make people instinctively want to deal with them first—which is correct.
- But after that, many forget that division and multiplication are equal in priority. They’re handled from left to right, not by choosing one first.
- The “3(3+1)” looks like it might carry special weight because the multiplication is “implied,” but mathematically it doesn’t outrank division.
This is where most people slip.
Common Wrong Answers (and Why People Get Them)
❌ Wrong Answer: 5
- How people get it: They first simplify the parentheses → (3 + 1) = 4.
Then they treat 3 × 4 = 12 as a “unit” and divide: 60÷12=560 ÷ 12 = 560÷12=5. - Why it’s wrong: Division and multiplication must be solved left to right. You can’t give the multiplication priority just because it touches parentheses.
❌ Wrong Answer: 20
- How people get it: They stop halfway.
60÷3=2060 ÷ 3 = 2060÷3=20 and then forget about the × (3 + 1). - Why it’s wrong: The expression isn’t complete—multiplication with the 4 still needs to be done.
❌ Wrong Answer: 24
- How people get it: After calculating 60÷3=2060 ÷ 3 = 2060÷3=20, some mistakenly add the parentheses result instead of multiplying:
20+4=2420 + 4 = 2420+4=24. - Why it’s wrong: This mixes operations incorrectly. The problem clearly states multiplication, not addition.
❌ Wrong Answer: 5 (Fraction Misread)
- How people get it: Some rewrite it mentally as a single fraction:
603(3+1)=6012=5\frac{60}{3(3+1)} = \frac{60}{12} = 53(3+1)60=1260=5. - Why it’s wrong: If that’s what was intended, it should be written as:
60÷[3(3+1)]60 ÷ [3(3+1)]60÷[3(3+1)]. As written, the expression is solved step by step, left to right.
The Step-by-Step Correct Answer
Now let’s solve it properly using order of operations (PEMDAS/BODMAS):
- Parentheses first:
3+1=43 + 1 = 43+1=4 Expression becomes:
60÷3×460 ÷ 3 × 460÷3×4 - Division and multiplication are equal priority. Work left to right:
- First: 60÷3=2060 ÷ 3 = 2060÷3=20
- Then: 20×4=8020 × 4 = 8020×4=80
✅ Correct Answer: 80
Final Takeaway
This puzzle proves how much small details matter in math. The tricky part is not the arithmetic itself—it’s knowing that multiplication and division must be handled in order, from left to right, not based on how the equation “looks.”
That’s why so many people end up with 5, 20, or 24. But the only mathematically correct result is:
👉 80
