A basic algebraic equation has divided people about the correct procedure for solving it, with two approaches leading to two entirely different answers.
The debate around this problem depends on the order of operations one should use to solve it.
Contemporary equation solving instructs people to approach problems according to PEMDAS – meaning they should first solve what is in parentheses (P), then any exponents (E), then multiplication or division (MD), addition, and finally subtraction ( AS).
EM and MD are considered equally important, and when one pair is all that remains in the equation, the problem should be solved from left to right.
But another order of operations — dating back more than 100 years to how algebraic equations were solved — creates an entirely different solution to the problem.
Here’s the equation, try it out before reading on:
By today’s PEMDAS standards, the correct procedure to solve the equation is to first solve what’s in the brackets.
So, 1+2 becomes 3 and the equation becomes 6 ÷ 2 (3). The parentheses around the three indicate that it is multiplied by the value preceding it, so the equation translates to 6 ÷ 2 x 3.
Since multiplication and division have the same priority, the equation should be solved from left to right: 6 ÷ 2 becomes 3, making the equation 3 x 3, which leads to the correct solution of 9.
9 is the answer, but by the old standard of how the equations are written, a solution to 1 can be found.
Going the old route, one would still process the parentheses first, resulting in 6 ÷ 2 (3).
But the old format—which, according to puzzle site Mind Your Decisions’ Phresh Talwalkar, may have been used in typography and typography since that day—instructs people to divide whatever is to the left of the division sign (obelus) by the sum to its right. Talwalkar said he saw this approach to order of operations in a 1917 textbook.
Following these criteria, one would first solve for 2 x 3, which yields 6, and then divide 6 by 6, which yields 1.
Another hurdle might be following modern PEMDAS, but forgetting to solve left-to-right when operations of the same precedent still exist. Doing so also results in an answer of 1.