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. Parts of a sum in ( ) must be worked out first, followed by all * and / only then can the + and - be evaluated. Breaking this down we get
7+7/7+7*7-7
There are not brackets so we first work out the 7/7 and 7*7
7+ 1 + 49 - 7
which becomes
8 + 42
= 50
Some "bad" 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 the "bad" calculator method is 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 wrong answers from the sum above if the order of execution is adjusted. Work out the parts in brackets first :
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 so many 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 written sum in different ways is the road to math madness. Luckily this has been mostly resolved. See Google "Bodmas" or order of operations more detailed explanations.
How did "bad" calculators come about ? Back in history when calculators were mechanical they only had a single "running total" displayed. Each operation immediately changed the running total without reference to the previous operations. Such calculator users were expected to reorder the operations before using the calculator. The early electronic calculator followed this methodology.
An easy explanation why * and / comes before + and -
Q : How many soccer players are there on the team ?
A: 11 and let's break that down .... Here is a picture of a typical team but there is also a referee and team mascot that may be on the pitch but don't count as team members.
Adding up the people on the pitch goes as :
1 Keeper - grey
4 Backs - blue
2 Half Backs - yellow
2 Wingers - red
2 Forwards - also red
1 Referee
1 Banana based team mascot.
We said that the Referee and the mascot don't count so lets set those to 0 giving
1 Keeper
4 Backs
2 Half Backs
2 Wingers
2 Forwards
0 Referee
0 Banana based team mascot.
Turning that into a long sum as each person counts as 1 * the number we have of them.
1 * 1 {Keeper} +
1 * 4 {Backs } +
1 * 2 {Half Backs} +
1 * 2 {Wingers} +
1 * 2 {Forwards} +
1 * 0 {Referees} +
1 * 0 {Mascots} = total number of players.
taking out the {words} gives us this sum ...
1 * 1 + 1 * 4 + 1 * 2 + 1 * 2 + 1 * 2 + 1 * 0 + 1 * 0 = 11 because we already know the answer,
One of a thing is the thing so we can work out the 1 * parts of the sum to get ....
1 + 4 + 2 + 2 + 2 + 0 + 0 = 11 that must equal 11 and it does.
If the sum is done on an old style calculator that accumulates a partial result as it goes along, when the last bit of + 1 * 0 is entered, the running total becomes 0 which ruins the whole calculation. If the sum is worked out strictly left to right it also fails on {total so far } + 1 * 0
The second line of the calculation above gives the correct total 11.
To prove this method is correct if the team came out in reverse order there would be the same number of folks on the pitch and the sums would be .....
{Referees} * 0 + {Mascots} * 0 + {Forwards} * 2 + {Wingers} * 2 + { Half Backs} * 2 + { Backs } * 4 + {Keeper} * 1
that's
1 * 0 + 1 * 0 + 1 * 2 + 1 * 2 + 1 * 2 + 1 * 4 + 1 * 1 = 11 which must equal 11 and it does ...
0 + 0 + 2 + 2 + 2 + 4 + 1 = 11
Both lines also happen to give the correct answer on an old style calculator because the 1 * 0 parts are at the start.
A modern calculator app that shows the sum before calculation gives the correct answer both way round.
In general terms, given a long sum the calculation must be performed according to the rules of what parts to do first.
Brackets. <<<< some times used to change the order of the parts.
"Orders" <<<<< Raised the power of like squares and square roots,
multiplications and divisions <<<<<. after all these parts are done go onto
additions and subtractions.
Old style calculators
Try these "half plus one" on your calculator :
1 + 1 / 2
and then
1 / 2 + 1
If you get the answer 1 for the first line then your calculator is breaking the math rules and you will need to adjust the calculation order to get the right answers. This is why folks using a calculator sometimes gives the wrong answer. "I used a calculator." does not make the answer correct unless you load the calculations according to what parts have to be done first.
We used to write calculation differently that made this more obvious:
1 + 1
-
2
must give the same answer as :
1 + 1
-
2
being 1.5
The answer the "incorrect" calculator is giving is for this sum where the divider line extends across both parts.
1 + 1
_____
2
which is not the answer we are after.
See also Expanded explanation here
Fun
Just for fun, here is how various professions would tackle the original 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 )
**Update April 2025 **
Find out how to solve Sudoku and Giant Sudoku variants using a logic solver here
See also :
