And now something completely different. Since I was always bad at math I need the advice of the engineers, math teachers and economists here :-))
This is from math test my 11 year old son had:
600-200-200-200=800
Wanted: put BRACKETS in a way that the result is correct.
This is what Marjan (my son) did:
600-(200-200)-200=800
Result: 0 points: ("Germany zero points ;-)))
This is what the math teacher wanted: 600-(200-200-200)=800
I understand that this is correct, but isn’t Marjan’s solution correct too?
I only have doubts because a MATH student (helping my kids) said that my son’s version is correct too. Which is hard to believe …
… but isn’t Marjan’s solution correct too?
No. Because 600 -(200-200) -200 is equivalent to 600 -0 -200 = 400 (but I am not am math student, ph.d. aersopace engineering is all I can offer.)
No.
The part in brackets should be calculated first.
So
600-(200-200)-200=
becomes
600-0-200= 400
What he could have done wasadd a second set of brackets:
600-((200-200)-200)=
Colm
I don’t have kids or much knowledge left from my maths studies now, but subtracting a negative number (so a double negative) becomes a positive so the ultimate answer really will be 600+200=800. This is one reason I am glad I don’t have kids – I couldn’t bear to go through homework style questions again :-)
So, Peter, how would you solve it?
Sorry – I deleted my reply. I was going to suggest sending the teacher to the UK where he/she would win a prize for modern and relevant educational methods 
I think to get 800 it requires a trick like
-(-200) = +200.
The order of precedence, as taught to my 10 years old son, is BODMAS: Brackets, Orders, Division, Multiplication, Addition, Substractions. Orders means powers (squares, square roots etc).
Frankly if your child’s tutor thinks his answer is correct, you need to hire another one.
What? Can you please write the whole thing with the brackets the way you would set them?
That’s why I think the question was a little tough for that age.
It’s not easy, but the focus has shifted since our days at school. At his age, we would have been kept busy doing the actual calculation. Number by number. Now they rather teach the rules and logic, because they know that nobody will ever do a complicated calculation on paper in his life. He will use a computer instead. But that computer obeys simple rules and logic. And if I don’t have a clear understanding of that logic myself, I will get wrong results all the time. Without even noticing.
There are three simple rules in your example:
1. Every number carries it’s own sign, immediately left of it. (Signs of other numbers belong to those number alone and are unaffected by all other signs)
2. Numbers inside brackets can be seen as one single number.
3. Evaluate the contents of backets first, then evaluate the results.
For verifying the correctness of a calculation (numeric or symbolic) or for doing the calculation proper, the “ultimate tool” available online is Wofram Alpha: http://www.wolframalpha.com/input/?i=600-%28200-200%29-200
NB: My son (now 14) was given a “CAS” calculator (Ti Nspire) at school at age 12. They don’t work with paper at all any more, they solve problems like yours directly with their little gadgets.
