MENSA IQ Test and rules of maths
Solution 1:
In response to edit of initial post, then answer is clearly $30$. Basic calculators are assumed to evaluate in order from left to right.
Original post I responded to
In a Mensa calander, IQ dialy challenge I got this and put a challenge up at work.
Using +,-,time and divide only once. Use the math operator only once to get the highest answer.
5 ? 4 ? 7 ? 3 ? 2 =
We all worked out
5 + 4 x 7 - 3 / 2 = 30
Except that my result answer was 31.5 and not 30, like in the answers of the MENSA calendar.
Why was I the only one that applied the rules of maths on this? ANd when I asked why nobody else applied the rule of maths, I got the weirdest looks. Nobody knew about multiplication before division, subtraction before adding? I thought that was why the question was marked as the most difficutl to test if you knew this.
Response to original post
Sadly, many people forget the basic rules of arithmetic as they (a) don't view them as affecting their lives, (b) didn't like maths, and/or (c) know technology can handle the problem for them. The issue with the last point is that different technologies handle things differently. The Google calculator (much like most graphing calculators) will handle order of operations for you correctly. The standard Windows calculator appears to be operating like an old 4 function calculator which evaluates after every operation is completed as opposed to correct order of operations. Though this can also happen when users hit enter after every operation is finished as opposed to when the whole expression is finished. (Don't have access to a Windows calculator right now so can't tell which is the reason for the wrong answer.)
Solution 2:
You are indeed correct in that we apply multiplication and division before addition and subtraction.
However, multiplication and division have the same precedence, as does addition and subtraction. When multiplication and division (or addition and subtraction) are both part of an expression, we evaluate which ever appears first (when reading from left to right).
"When do I apply what?"
The good old "order of operations, once again:
Parentheses or brackets. Perform the part of the expression enclosed in parentheses or brackets, first, working from innermost to outermost. $$50/[5 \times (2 + 3)] = 2$$
Exponents. Then take powers of a term. $(2+3)^2 / 3 = (5)^2/3 = \frac{25}{3}$.
multiplication and division (performed from left to right).
$8/4 \times 3 = 2\times 3$, $8\times 4/3 = \frac{32}{3}$addition and subtraction (performed from left to right)