Posted by unknown on Saturday, July 25, 2009 at 8:38pm.
In evaluating an algebraic expression, it is necessary to observe the rules of priorities of operators, namely
1. parentheses (from inside out)
2. exponents (from right to left)
3. multiplications and divisions (left to right), and
4. additions and divisions (left to right).
For example, we would evaluate as follows
3*(4+2*3^{2*²}-2)
= 3+(4+2*3^{4}-2)
= 3+(4+2*81-2)
= 3+(4+162-2)
= 3+(166-2)
= 3+(164)
= 167
Which means that the location and number of parentheses are very important.
In the given expression, evaluation as is will give
11-6/7-7
= 11 - (6/7) - 7
= 10 1/7 - 7
= 3 1/7
The evaluation you have posted seems to assume the following expression:
(11-6)/(7-7)
=5/0
which as you said is indefinite.
So it is important to examine the question and reproduce ALL parentheses, if there are any, and DO NOT ASSUME parentheses if they are not present.
In summary, the expression evaluated as is is not indefinite. But if the parentheses are present, it would be indefinite.