Why do we need the order of operations?
What is the order of operations?
What is the only order of operations that does NOT proceed from the left to the right
The order of operations refers to a set of rules that dictate the order in which mathematical operations should be performed in an expression involving multiple operations. These rules ensure that everyone arrives at the correct answer when solving mathematical problems.
The order of operations is represented by the acronym "PEMDAS," which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It emphasizes the sequence in which operations must be performed.
We need the order of operations because it prevents ambiguity in mathematical expressions and guarantees a consistent and standardized approach to solving math problems. Without these rules, different people may interpret expressions differently, leading to inconsistent and incorrect answers.
Let me explain how the order of operations works through an example:
Consider the expression 8 + 3 * 2. Without the order of operations, one might assume that we add 8 and 3 first and then multiply the sum by 2. However, according to the order of operations, we must perform the multiplication before the addition.
Following the order of operations, we multiply 3 and 2 to get 6, and then add 8 to the result. So, the correct answer is 14.
In summary, the order of operations is necessary to ensure a consistent and universal approach to solving mathematical expressions, preventing ambiguity and ensuring that everyone arrives at the correct answer.
http://www.mathsisfun.com/operation-order-pemdas.html
many webpages give the reason why, and show how to follow the correct sequence.
Here is one ...
http://www.purplemath.com/modules/orderops.htm