The Last Word: Only for genius ?? 3 – 3 x 6 + 2 = ??


David Meego - Click for blog homepageWow, I cannot believe the responses, comments and arguments that this simple mathematical equation is generating. If you have not seen my earlier posts, have a read (and answer the poll in the first article):

I had planned not to post again on this topic, but I feel that I have some further points and examples to share.

The question posed on the internet as an image was:

Maths_Question

I should point out that I did not add the wording “Only for genius ??” and that being able to correctly solve this equation is not necessarily a measure of genius or a person’s IQ (Intelligence Quotient).

In fact, I believe that anyone who remembers their primary/elementary school maths lessons should be able to solve this correctly.

There are still two incorrect answers that people are swearing by and so I would like to address them.

Incorrect Answer of 2

Calculating left to right with no rules:

  • 3 – 3 x 6 + 2
  • 0 x 6 + 2
  • 0 + 2
  • 2

The mistake here is not performing the multiplication first. But this gives me a perfect way to demonstrate why the order of operations rules are important….

Do you agree that the order of the equation should not make a difference to the result?

e.g.:

  • 3 + 2 – 1 = 4
  • 2 – 1 + 3 = 4

and

  • 3 x 4 / 2 = 6
  • 4 / 2 x 3 = 6

OK, so let’s reorder the equation from this challenge. Now we calculate left to right ignoring the order of operations rules and we get four different answers.

  • 3 – 3 x 6 + 2 = 2
  • 2 + 3 – 3 x 6 = 12
  • 2 – 3 x 6 + 3 = -3
  • -3 x 6 + 2 + 3 = -13

However, if we follow the order of operation rules and perform the multiplication first, we will get the correct answer of -13 for all four equations shown. Q.E.D.

N.B.: The last answer is actually correct as it did the multiplication first.

Incorrect Answer of -17

Calculating using order of operation rules, but not handling negative numbers correctly:

  • 3 – 3 x 6 + 2
  • 3 – 18 + 2
  • 3 – 20
  • -17

The mistake here is that -18 + 2 is not -20, it is -16. If you remember the concept of number lines from school, you will remember that adding a positive number to a negative number makes the result less negative (i.e. moves the result to the right).

If you think of it as adding a negative number rather than subtracting a positive number it is easier to see.

  • 3 – 3 x 6 + 2
  • 3 + -3 x 6 + 2
  • 3 + -18 + 2  or  3 + -18 + 2
  • 3 + -16  or  -15 + 2
  • -13  or  -13

Also the order of operations rules specify that multiplication and division are executed first but at the same time. Then addition and subtraction are done together. So there is no reason to perform -18 + 2 before 3 + -18, as shown in the alternative solution path above.

Problem solving

One of the issues raised in the comments was that understanding a real world problem and translating that to a maths problem is part of what makes you “a genius”. So to that end, here is a real world problem which you can solve:

  • You are an apple farmer. You can sell apples individually or in a box of 6 apples.
  • You have 3 individual apples in stock when a shop asks for 3 boxes to be supplied.
  • You give the individual apples you have to the shop and promise to supply the rest.
  • 2 more apples are now ready for picking and so you also supply those to the shop.
  • How many apples do you still owe to the shop? What is your stock level?

You should know the answer to this problem…..

Hint: How many did the shop ask for subtract how many supplied already.

Online Solutions

Don’t just take my word for it …. for more proof of the correct answers to the recent maths challenges, try these links:

3 – 3 x 6 + 2 = -13

7 + 7 ÷ 7 + 7 x 7 – 7 = 50

Hopefully we are finished now.

Have a look at the other posts in the series:

Enjoy

David

PS: Answer for real world problem here: [ Farmer owes shop 18 – 5 = 13 apples, so stock level is -13 ] Just highlight between square brackets with cursor to read.

PPS: Please forgive the use of Latin abbreviations, e.g., Q.E.D., N.B., i.e., P.S.. 🙂

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

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