Simple math problem proves divisive – and harder than it looks

This one is divisive! Can you solve a ‘simple’ math problem that has stumped the internet?

  • There are two possible solutions – but only one of them is correct
  • The answer you come up with depends on what order you do the calculations 
  • READ MORE: Now try these number puzzles from recent 11+ exam papers 

A basic algebra equation has left people divided over the correct process for solving it, with two methods resulting in two completely different answers.

The debate around the problem hinges on the order of operations people are supposed to use to solve it.

Contemporary equation solving directs people to approach the problem following PEMDAS – meaning they should address what’s in the parenthesis first (P), then do any exponents (E), followed by multiplication or division (MD), addition, and finally subtraction (AS). 

The EM and the MD are considered of equal importance, and when one of those pairs is all that remains in an equation, the problem should be addressed from left to right.

But another order of operations – which dates back to how algebra equations were solved over 100 years ago – creates an entirely different solution to the problem.

Below is the equation, give it a try before reading on:

The equation has left people divided about the proper way to solve it, which affects the answer

Following today’s PEMDAS standards, the correct process for solving the equation is to address what is in the parenthesis first.

So, 1+2 becomes 3, and the equation becomes 6 ÷ 2 (3). The parenthesis around the three indicates it is to be multiplied by what comes before it, so the equation translates to 6 ÷ 2 x 3.

As multiplication and division are of the same precedence, the equation then should be solved left to right: 6 ÷ 2 becomes 3, making the equation 3 x 3, resulting in a correct solution of 9.

Nine is the answer, but following old standards of how equations were written, one could come to a solution of 1.

Following the old route, people would still address the parenthesis first, resulting in 6 ÷ 2 (3).

But old formatting – which Phresh Talwalkar of the puzzle website Mind Your Decisions believes may have been used to work with typesetting and printing formatting from the day – directed people to divide whatever is on the left side of the division sign (the obelus) by the sum of what was to its right. Talwalkar said he saw this approach to the order of operations present in text books from 1917.

By those standards, people would solve 2 x 3 first, resulting in 6, then divide 6 by 6, resulting in an answer of 1.

Another hitch could be following modern PEMDAS, but forgetting to solve left to right when operations of the same precedent remain. Doing so would also result in an answer of 1.

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