The Math Equation That Tried to Stump the Internet
Sometimes BODMAS is just PEMDAS by another name. And no, the answer is not 100.
CreditCredit By Steven Strogatz Aug. 2, 2019
807 Mathematical Twitter is normally a quiet, well-ordered place, a refuge from the aggravations of the internet. But on July 28, someone who must have been a troll off-duty decided to upset the stillness, and did so with a surefire provocation.
It has to do with something that high school teachers call “the order of operations.” The latest blowup concerned this seemingly simple question:
Many respondents were certain the answer was 16. Others heard Yanny, not Laurel, and insisted the right answer was 1. That’s when the trash talking began. “Some of y’all failed math and it shows,” said one. Another posted a photo showing that even two different electronic calculators disagreed. The normally reassuring world of math, where right and wrong exist, and logic must prevail, started to seem troublingly, perhaps tantalizingly, fluid.
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The question above has a clear and definite answer, provided we all agree to play by the same rules governing “the order of operations.” When, as in this case, we are faced with several mathematical operations to perform ― to evaluate expressions in parentheses, carry out multiplications or divisions, or do additions or subtractions ― the order in which we do them can make a huge difference.
When confronted with 8 ÷ 2(2+2), everyone on Twitter agreed that the 2+2 in parentheses should be evaluated first. That’s what our teachers told us: Deal with whatever is in parentheses first. Of course, 2+2 = 4. So the question boils down to 8÷2×4.
And there’s the rub. Now that we’re faced with a division and a multiplication, which one takes priority? If we carry out the division first, we get 4×4 = 16; if we carry out the multiplication first, we get 8÷8 = 1.
Which way is correct? The standard convention holds that multiplication and division have equal priority. To break the tie, we work from left to right. So the division goes first, followed by the multiplication. Thus, the right answer is 16.
More generally, the conventional order of operations is to evaluate expressions in parentheses first. Then you deal with any exponents. Next come multiplication and division, which, as I said, are considered to have equal priority, with ambiguities dispelled by working from left to right. Finally come addition and subtraction, which are also of equal priority, with ambiguities broken again by working from left to right. （リンク先に続きあり)