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Here’s one that I found floating around the internet a couple of days ago from an account that seems to re-share a lot of existing content in the hope of going viral. The tweet reads (in true viral bait style) “Please don’t use a Calculator, use your BRAIN: 50+50 – 25 x 0 + 2 + 2 = ??”.
Now, the equation is sufficiently ambiguous in its design that, depending on how you tackle it, it produces a number of different answers. In this instance, users concluded that the answer was definitely 0, 4, 79 or 104. The subsequent chat often breaks out into some discussion about how Order of Operations work and how stupid the other people are. Between argument, counter-argument, and people smugly retweeting about how other people didn’t pay attention to high school math, the original poster has succeeded in getting their engagement.
But there is a solution, and a neat way of arriving at the correct answer both for this problem and for any others you see online. And I’ve enlisted the help of a mathematician to help explain it so that this sort of viral bait never trips you up ever again. Especially if you don’t recall your PEMDAS (or BODMAS, if you were raised on the other side of the pond) from high school math.
Dr. Helen Crowley is lecturer in mathematics at the University of East Anglia, and took issue with how I’d described the equation. “The problem shared [above] is not actually ambiguous at all,” she said, “maths is a very well-behaved subject and there are fixed rules that all problems like this follow.” Dr. Crowley is, of course, referring to the Order of Operations, which explains how a multi-part equation like the one above is meant to be broken down and worked out.
In the US and UK, Order of Operations is expressed under the acronyms PEMDAS (US) or BODMAS (UK). The terms may differ, but the order in which you calculate each component part of the equation remains the same. You start with anything in Parentheses / Brackets, and then move on to anything using Exponents / Orders, which are figures including square-roots and powers. The equation above, uses neither.
Third in the list is Multiplication and Division, which is the first function that we actually need to do. “For this problem, we [first] do 25 x 0 = 0,” said Dr. Crowley. That 0 then inserts itself into the sum, which now looks like 50 + 50 – 0 + 2 + 2. “The last two operations to consider are Addition and Subtraction,” said Dr. Crowley, making the final sum 50 + 50 – 0 + 2 + 2 = 104. “This is exactly what your calculator does, as it is programmed to ‘know’ the order,” said Dr. Crowley, “the above problem certainly isn’t ambiguous, we are just forgetting the rules.”
Now, you may be wondering who was in charge of establishing this order, and when that may have happened. According to the UEA’s Dr. Mark Cooker, the current Order of Operations was probably first laid down in their current form in the middle of the 16th century. Before that point, “manuscripts were wholly wordy, and free from operational symbols, except abbreviations,” said Dr. Cooker. But from the mid-16th century onwards, math texts “were first printed in large numbers for education.”
Cooker then believes that it was the wide-ranging influence of the Philosophical Transactions of the Royal Society of London that “set new high standards to reduce ambiguity in handling powers, brackets and multiplications or additions, in the correct order.” He said that the journal, as it would now be described, “spread higher standards of maths typography as far afield as St. Petersburg, where Leonard Euler was working.” Euler was one of the most pioneering mathematicians of the 18th century, who “published so many papers and influential textbooks,” along with “clear explanations of BODMAS rules in his elementary texts must have made everyone agree on the current order of operations.”
Now that you know how to solve those crappy equations people post on social media, don’t forget to share a link to this story to serve as a bulwark against folks cynically trying to juice their engagement.
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