# For Maths Stalwarts

Discussion in 'Interesting Shares' started by jayasala42, Aug 4, 2019.

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This math equation tried to stump the internet

8 ÷ 2(2+2) = ?

SUMMED UP: While math is seen as objective, many on the internet are divided over this math problem

Mathematical Twitter is normally a quiet, well-ordered place. 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: 8 ÷ 2(2+2) = ?

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.

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, 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. 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.

To help students in the United States remember this order of operations, teachers drill the acronym PEMDAS into them: parentheses, exponents, multiplication, division, addition, subtraction. Other teachers use an equivalent acronym, BODMAS: brackets, orders, division and multiplication, and addition and subtraction.

This math problem isn’t the first time the internet has stood divided. Remember Yanny and Laurel? How about the color of this dress?

This method is purely a matter of convention. In that sense, PEMDAS is arbitrary. Furthermore, in my experience as a mathematician, expressions like 8÷2×4 look absurdly contrived. No professional mathematician would ever write something so obviously ambiguous. We would insert parentheses to indicate our meaning and to signal whether the division should be carried out first, or the multiplication.

The last time this came up on Twitter, I reacted with indignation. But now, having been enlightened by some of my computer-oriented friends on Twitter, I’ve come to appreciate that conventions are important, and lives can depend on them. We know this whenever we take to the highway. If everyone else is driving on the right side of the road (as in the U.S.), you would be wise to follow suit.

Ultimately, 8 ÷ 2(2+2) is less a statement than a brickbat; it’s like writing the phrase “Eats shoots and leaves” and concluding that language is capricious. Well, yes, in the absence of punctuation, it is; that’s why we invented the stuff. NYT NEWS SERVICE (Times of India – 4-8-2019)

ramasala

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