Viral: Only for genius ?? 3 – 3 x 6 + 2 = ??

Back in February of this year I posted a simple maths puzzle that I had seen on a Facebook post; Trending: Only for genius ?? 3 – 3 x 6 + 2 = ?? to challenge my readers.

Little did I know that the follow up post; Answer: Only for genius ?? 3 – 3 x 6 + 2 = ?? would go viral and cause my blog to reach the number 1 ranking on Worldmaps.

All this activity for a fun post that is not actually related to Winthrop Development Consultants’ products or services or even interesting stuff that I am doing.

The puzzle question was posed in the image below:

The correct answer is as follows:

• Question: 3 – 3 x 6 + 2
• Multiplication first: 3 – 18 + 2
• Addition and Subtraction together (left to right): -15 + 2 = -13
• Or Addition first, then Subtraction: 3 – 16 = -13

Regardless of how you apply the order of operations rules (BODMAS, BOMDAS, PEDMAS, PEMDAS, etc.), the answer is always -13 if you do the calculations correctly.

It seems that there are two main errors that people are making:

Not following the order of operations, like a simple calculator:

• Question: 3 – 3 x 6 + 2
• Subtraction: 0 x 6 + 2
• Multiplication: 0 + 2
• Addition: 2 …. is the wrong answer

Following the order of operations, but ignoring the negative value:

• Question: 3 – 3 x 6 + 2
• Multiplication: 3 – 18 + 2
• Addition: 3 – 20  …. this is wrong …. -18 + 2 = -16
• Subtraction: -17 …. is the wrong answer

From the vast number of comments I have received, it looks like many students were taught the order of operations without actually understanding them. They should be written as BO[MD][AS] or PE[MD][AS] because the multiplication and division steps can be performed at the same time as long as they are before the addition and subtraction steps (which can also be performed at the same time).

The order multiplication and division are performed does not change the result of a calculation, for example: 3 x 6 / 2 = 9 and 6 / 2 x 3 = 9.

The order addition and subtraction are performed does not change the result of a calculation, for example: 3 + 4 – 2 = 5 and 4 – 2 + 3 = 5.

A final point is that subtracting a number is the same as adding a negative number of the same value, for example: 4 – 3 = 1 and 4 + -3 = 1.

If you type the equation 3 – 3 x 6 + 2 into Google or Bing, you will see they add brackets/parenthesis to the formula to make it 3 – (3 x 6) + 2 or even (3 – (3 x 6)) + 2. This forces the order of operations for a simple calculator, but should not be needed. Either way, both websites calculate the answer as -13.

Maybe if the question was asked in the form below, then more people would get it right:

• 3 + -3 x 6 + 2

Have a look at the other posts in the series:

• Trending: Only for genius ?? 3 – 3 x 6 + 2 = ?? With Poll and Order of Operations
• Answer: Only for genius ?? 3 – 3 x 6 + 2 = ?? Provides Answer and common errors
• Conclusion: Only for genius ?? 3 – 3 x 6 + 2 = ?? Breaks down solution into steps
• The Last Word: Only for genius ?? 3 – 3 x 6 + 2 = ?? Explains ordering of DM and AS
• Viral: Only for genius ?? 3 – 3 x 6 + 2 = ?? This article

Enjoy

David

This article was originally posted on http://www.winthropdc.com/blog.