Please explain with an example and a memory trick like a mnemonic the order of operations in mathematics.

There are some rules that has to be respected, with regard
of order of operations:

1) Solve all calculations within
the bracklets;

2) Then, starting from left and going to the
right, same with writting a sentence in english language, compute all multiplications
and divisions;

3) The last operations are additions and
subtractions, also performed from left to
right.

Example:

E = 2 +
5*(3+1)/2 - 6

1) We'll perform the addition inside
brackets: 3 + 1 = 4

2) We'll perform multiplication above
the fraction bar: 5*4 = 20

3) Since below fraction bar
there is nothing to evaluate, we'll perform the division: 20/2 =
10

4) We'll start from the left and we'll perform the
addition; 2 + 10 = 12

5) We'll evaluate the subtraction: 12
- 6 = 6

The result of the given expression is
E = 6, evaluated with respect to order of operations
rules.