Google, Graph Calculators, And The Mind Game
Google is the largest search engine on earth. With no academic groups to ensure its many sources of factual assertions, ranging from Wikipedia, which is wrong about many things, to its very own Graph Calculator: there is a very real concern that soon there will be the ability to cause a gigantically delusional view of the world which this corporate entity can accomplish... And this, in spite of evidence that suggests there may be something going on, something unsettling....something now...
6/2(1+2)=1 this answer is wrong.
Because this is Algebra, and it is an exact science.
It is static, and thousands of years old. It connects us to the classical age of Greece, and Euclid, and Pythagoras, among others; Algebra connects us in a living way to those whom first recognized the nature of these numbers in relation to one another.
2(2)+2(2)-[2-2(2)]= in abutted expressions, the negative* sign stays out of the brackets, and the signs change for the set of integers (-2+2), but not for the multiplier (2) as if mutliplication has occured...thus positives inside brackets, except the multiplier, in this case, (2), are negative now.*(if it is a plus sign, then the signs within the brackets remain the same)
...changing the orders integers occur in, as long as we don't assert a change to the sanctity of the expression, doesn't alter the product: f(v)(j)=j(v)f via the commutative property. So, in order to get the wrong answer of 10, we must:
If, for instance we had 2(2)+2(2)-2+2(2) and we simply assess the first values, as 8, we still have abutted to that 8 the product of the difference of two from two, and that difference times two! In every classroom in America, that product is zero.
In my class, I would award half credit for assessing this problem using the Commutative and Distributive Properties properly.