Ambiguous Math Problem: The Results


Courtesy of Julia Lin ’22

About a year ago, a simple math question took the internet by storm, dividing the r/CasualMath SubReddit in half. Just for fun, the Circle Voice wanted to see what the general consensus was at Groton. So we sent a form to the entire student body on October 1st to get some results. 

Problem: 8 ÷ 2(2 + 2) = ?

Upon finalizing the data, I was utterly baffled and disappointed. As students who go to one of the most prestigious boarding schools in the United States, we should be ashamed of ourselves. In total we received 251 responses, which would be over 65% of the student body (assuming that no faculty filled out the form). Overall, 143 (57%) students believed the answer to be 16 while 108 (43%) students claimed it to be 1. 

The answer is . . . *drum-roll please*: 16

So why 16? we wanted to get a definitive answer from the math department, so the CV conducted an interview with Mrs. LeRoy, the Math Department Head. The mistake most people make is that they will group the 2(2+2) together first before dividing by 8. By following the order of operations, you should first do operations in parentheses, and then multiply or divide before you add or subtract. So here’s how it should be done written out:

8 ÷ 2(2 + 2) = ?

8 ÷ 2 x (2 + 2) = ?

8 ÷ 2 x 4 = ?

4 x 4 = 16

Mrs. LeRoy mentioned that you may also type this equation into Wolfram Alpha or your calculator to confirm this answer. “While not surprised by the school-wide result, I do think this means that math teachers need to focus more on PEMDAS and the order of operations,” said Mrs. LeRoy. If you enjoyed this, leave a comment below of other types of articles you would like to see!