Viral math problems, explained

Every so often an order-of-operations puzzle takes over social media and the comments fill up with people who are certain they are right. Here is what each one comes down to, with every step worked out.

When the notation is ambiguous

These expressions can be read two ways, and both readings are shown side by side.

Left-to-right traps

Only one answer is right here, and the popular wrong answer comes from reading strictly left to right.

When the tool changes the answer

Fractions typed on one line, leading minus signs and basic calculators can all change what you get.

Check any expression yourself

Got one that is not listed? Put it in the solver and it will show every step, and both readings if the notation allows two.

Questions

Why do these puzzles go viral?

They look easy, almost everyone remembers half a rule from school, and the wrong answers are held with great confidence. That mix produces long comment threads.

Is there ever really more than one right answer?

Only when the notation is ambiguous, like 8 ÷ 2(2 + 2). In that case two conventions exist and both are internally consistent. For everything else, such as 7 − 1 × 0 + 3 ÷ 3, there is one answer and the other one is a mistake.