11 – 11 × 11 + 11. At first glance, this calculation looks like a children’s riddle. But in reality, it seriously tests our mathematical logic, which has been well-established since school. This kind of puzzle captivates as much as it disconcerts: because no, it’s not simply an addition and a subtraction… The key is to remember the order of operations. So, ready to take on the challenge without cheating? Come on, let’s get our brains out, not our calculators!
Why does this calculation trap so many people?
When we quickly read an operation like 11 – 11 × 11 + 11, our brain tends to read from left to right, solving each step in the order it appears. This is a common mistake! This reflex often causes us to miss an essential rule of mathematics: multiplications always come before additions and subtractions, unless parentheses change the order.
That’s what makes this kind of challenge so interesting. It’s not about being a « math genius , » but simply about remembering the right method. A welcome refresher—and a pretty cool one !
The order of operations, this discreet hero of our daily lives
Remember: from middle school onwards, we learn the famous rule of priority of operations. It has different names depending on the country (PEMDAS, BODMAS, etc.), but the principle remains the same:
- Parentheses
- Exponents (or powers)
- Multiplication and division, from left to right
- Additions and subtractions, from left to right as well
Don’t panic, here we only have three operations to handle: multiplication, subtraction, and addition. But it’s precisely this false simplicity that makes the exercise misleading.
Let’s solve it together, step by step
Let’s take our time. Here’s the operation:
11 – 11 × 11 + 11
We start with multiplication:
11 × 11 = 121
The operation therefore becomes:
11 – 121 + 11
Then we solve the remaining operations from left to right:
11 – 121 = -110
Then,
-110 + 11 = -99
