Wednesday, 12 February 2014

Old time maths question. What is 7+7/7+7*7-7 ?




This is a bit of a trick question. For the modern age the question would have been better phrased as either "What answer should your calculator give you when you push these keys ?" or "If this was an Excel formula, what would be the answer ?"

For extra credit this is how to get the various answers: Work out the bits in the innermost  ( brackets ) first. (second bit ( first bit )) 

0=(7+7)/(7+7)*(7-7)
8=(7+(7/(7+(7*(7-7)))))
50=7+7/7+7*7-7
50=7+(7/7)+(7*7)-7
56==((((7+7)/7)+7)*7)-7

The highlighted answers give the "correct" method to work out the answer.  When a sum has both + and -  as well as * and / but no brackets then the * and / should be worked out first.  Parts of a sum in ( ) should be worked out first followed by any * and / only then can the + and - be evaluated.  Breaking this down

From
7+7/7+7*7-7
First work out the * and /
7+ 1 + 49 - 7
becomes
8 + 42
= 50

Some calculators, will incorrectly give the answer 56 because they jump to the partial answers after each time any of the + - * /  keys are pushed.

7+7 = 14
 / 7 = 2
+ 7 = 9
* 7 = 63
- 7 = 56

The answer to why is this wrong comes from the basic rule that the order that a sum is written should not make a difference to the answer.

2 + 1 / 2  must be the same as  1 / 2  + 2  read this as
Two plus a half is equal to two plus a half.
Two plus a half is equal to a half plus two.

A "bad" calculator would read 2 + 1 / 2  as
Two plus one is three, divided by two equals one and a half.

There are more ways to get the wrong answer. We also we have
44=(7+7)/7+(7*7)-7
2=(7+7)/7+7*(7-7)
0.2857=(7+7)/(7+7*7-7)
-6.75=(7+7)/(7+7*7)-7

With such possible choices for a simple sum there has to be agreement on how to calculate any written sum. Having two people work out the same sum in different ways is the road to math madness.  Google "Bodmas" or see order of operations more explanations.

As career advice, just for fun, here is how various professions would tackle this question. What is closest to your way of thinking ?

  • Mathematician – There are at least 8 possible answers depending on …..
  • Scientist – I asked 500 people the same question and they said …..
  • Engineering – The answer has been calculated in Excel, on a Calculator, with a slide-rule, on paper and in my head as …
  • Teacher – We can find the answer by following this method  ….
  • Lawyer – What do the books say the answer is ?
  • Philosopher – First we must understand how we relate to the concept of 7 in this context.
  • Graphics designer – The spacing between the symbols is inconsistent, and the font does not match, resulting in ambiguity and confusion.
  • PR consultant – Whatever the client wants is The Answer.
  • Media Guru – Call 0907834348*  to get the answer. *( 75p/Min + call charges apply )


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3 comments:

Clint Reno said...

A "bad" calculator would still give 2 1/2 or 2.5
2 + 0.5 = 2.5 whichever way round you write it.

James Pearce said...

2 + 1 / 2 versus 1 / 2 + 2 will give a different answers on non-scientific calculators.

sarah lee said...

I really enjoyed reading your article. I found this as an informative and interesting post, so i think it is very useful and knowledgeable. I would like to thank you for the effort you have made in writing this article.


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