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The PEMDAS Controversy

OMG! The PEMDAS controversy has gone viral! Hammered into our brains is the fact that each math calculation has a single result, yet multiple answers for the same calculation are being vigorously debated online. Check it out.

Today’s blog will explore why two people might interpret PEMDAS differently leading to different results.

The mnemonics PEMDAS and Please Excuse my dear Aunt Sally are used by millions to recall the correct order for doing calculations.

P = parenthesis E = exponents M = multiplication D = division A = addition S = subtraction

The controversy is because PEMDAS at face value oversimplifies the actual rule. This can be illustrated with one example. 40 ÷ 5 x 8 = ?

Should you Divide then Multiply? or Should you Multiply then Divide?

Dividing first: 40 ÷ 5 x 8 = 8 x 8 = 64 or Multiplying first: 40 ÷ 5 x 8 = 40 ÷ 40 = 1

Even though M is clearly before D in PEMDAS the correct answer is 64. SO what’s the problem.

After taking care of calculations within parenthesis and exponents, the actual rule calls for doing multiplication and division from left to right in the order that they appear. The same applies to the order in which you decide to add or subtract.

I conveyed this to my students by adjusting the acronym to PE - MD(L to R) - AS(L to R)

Now try this: 6 ÷ 2(1 + 2) First work the problem in parenthesis 1 + 2 = 3.

Rewriting the problem clarifies the question, which operation is done next; 6 ÷ 2 or 2 x 3?

The rule makes clear that you divide because it comes first when looking from left to right.

The correct answer is 6 ÷ 2(1 + 2) = 9.


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