Home -> Solved problems -> 6÷2(1+2) = ?

\(6\div2(1+2) = ?\)

Solution

The expression
\(6 \div 2(1 + 2)\) has sparked debate across the internet, raising questions about the order of operations, implied multiplication, and historical notation.
In this explanation, we will analyse the problem step‑by‑step, clarify which rules apply under modern conventions, and show how the correct answer
\(9\) is obtained.

At first, the expression contains a parenthetical expression which we must evaluate first

6÷2(1+2)=6÷2(3)

Now, we continue the order of operations

6÷2(1+2)=6÷2(3)

=6÷2×3

The expression 6÷2×3 contains only a division and a multiplication, these operators have an equal precedence. So, we evaluate the operators from left to right

6÷2×3=3×3=9

This is the correct answer : 6÷2(1+2)=9

Some historical justifications tell that the answer is 1, but today we interpret that differently.

By applying the standard interpretation of division and multiplication with equal precedence (evaluated left to right), we see that:

\[
6 \div 2(1 + 2) = 6 \div 2 \times 3 = 3 \times 3 = 9
\]

This case highlights the importance of clear notation in mathematics and shows that ambiguity in expression can lead to different results.
Use parentheses explicitly when needed, and remember that modern textbooks and calculators follow the left‑to‑right rule for multiplication and division.

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\(6\div2(1+2) = ?\)

Solution

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The Beauty of Mathematics : It Can Never Lie to You

Carl Friedrich Gauss

Leonhard Euler

Pythagoras

Nikola Tesla