What is rules governing operations on real numbers?

Answer 1

there's a phrase you can use to remember the order of operations: Please Excuse My Dear Aunt Sally.

it breaks down like this:

P stands for Parenthesis, complete any operations that are in parenthesis (includes brackets, braces and absolute value).

E stands for Exponents, clear any exponents next (includes square roots).

M stands for Multiplication, complete any multiplication problems (from left to right) in the problem.

D stands for Division, complete any division problems (from left to right) in the problem.

A stands for Addition, complete any addition problems (from left to right) in the problem.

S stands for Subtraction, complete any subtraction problems (from left to right) in the problem.

This order of operations must be followed because if it's not then you can come up with all sorts of wrong answers.

For Example: 5+6*2=? or 5 plus 6 times 2

first: Multiply 6*2=12

now you have: 5+12=?

second: Add 5+12=17

Therefore your final answer for 5+6*2=17