Sunday, July 14, 2013

What is the Order of Arithmetic Operations ( PEDMAS ) ?

2:34 AM
The order of operations is a convention that guides us in what order arithmetic operations need to be carried out in order to evaluate an expression. For example consider the following expression:
$\usepackage{color} \definecolor{Myblue}{rgb}{0.27,0.38,0.5} \color{Myblue} 3 \times 2 + 8 \div 2$
How do you evaluate such an expression? In the absence of a convention, you could:
1. Add 2 and 8, multiply the sum by 3 and then divide the product by 2 to get 15 as the answer
OR
2. Multiply 3 and 2 and add the product to the result of dividing 8 by 2 to get 10 as the answer
OR
3. Divide 8 by 2, add 2 to the quotient and multiply the sum by 3 to get 18 as the answer
As you can see, there are many ways you can evaluate the expression and you end up with different values depending upon how you choose to perform the operations. The order of operation convention resolves this issue. This ensures that that regardless of who evaluates the expression, you get the same result. In the above example, the correct answer is 10. In order to arrive at this correct answer, it is essential that you perform the operations using the "Order of Operation" convention.
The Order of Operations convention is as follows:
1. All calculations are done left to right.
2. If there are parenthesis, the expression inside them must be evaluated first, starting from the innermost parenthesis moving outward.
3. If there are exponents, they must evaluated next.
4. Next step is to perform multiplications and divisions.
5. Finally, perform additions and subtractions.
Are you finding that tough to remember? Enter PEDMAS , a simple mnemonic to remember the order of operations:
 Letter Stands For What it means? P Parenthesis Evaluate expression inside parenthesis first E Exponents Then evaluate exponents D Division Perform division and multiplication operations M Multiplication A Addition In the end perform addition or subtraction operations S Subtraction
Let’s use the PEDMAS principle to evaluate an expression.
Example:

Evaluate the expression $\usepackage{color} \definecolor{Myblue}{rgb}{0.27,0.38,0.5} \color{Myblue} 10 + (5 - 3)^ 2 \times 2 - \frac{16}{4}$
A) -28
B) -2
C) 2
D) 14
E) 24
Solution:

First, solve the expression inside the parenthesis: $\usepackage{color} \definecolor{Myblue}{rgb}{0.27,0.38,0.5} \color{Myblue} 5-3 = 2$
Next evaluate the exponent: $\usepackage{color} \definecolor{Myblue}{rgb}{0.27,0.38,0.5} \color{Myblue} 2^2 = 4$
Multiplication and division follows: $\usepackage{color} \definecolor{Myblue}{rgb}{0.27,0.38,0.5} \color{Myblue} 4 \times 2 = 8, \frac{16}{4} = 4$
Finally, complete the addition, subtraction operations: $\usepackage{color} \definecolor{Myblue}{rgb}{0.27,0.38,0.5} \color{Myblue} 10 + 8 - 4 = 14$