Please explain with an example and a memory trick like a mnemonic the order of operations in mathematics.
The order of operations in evaluating mathematical expressions is given by the mnemonic PEMDAS. Here P represents the parenthesis or brackets, E represents exponentiation, M represents multiplication, D represents division, A represents addition and S represents subtraction.
It has to be remembered that multiplication and division have the same weight as do addition and subtraction. You just need to carry out the operations from left to right.
For example using the rule to solve the expression: (3 + 5)(3*5)(3^5 + 4/8*7) we get:
First solve each expression within the parenthesis
=> 8*15*(4 + 3^5 + 4/8*7)
Within the third set of brackets solve the parenthesis first followed by multiplication/division and then addition/subtraction
=> 8*15*(4 + 243 + 3.5)
The order of operations can be easily recollected with the mnemonic PEMDAS.
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.
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.