Showing posts with label order of operations. Show all posts
Showing posts with label order of operations. Show all posts

Order of Operations

When several operations are to be applied within a calculation, we must follow a specific order to ensure a single correct result.

Order of Operations:
  1. Perform all calculations within the innermost Parentheses first.
  2. Evaluate Exponent expressions.
  3. Apply the Multiplication and Division operations from left to right.
  4. Lastly, work all Addition and Subtraction operations from left to right.
Caution:  Please do not dismiss the fact that multiplication and division should be worked from left to right.  Many standardized exams will test you on this fact.  The following example illustrates the problem.

Instructional Video: Order of Operations - The Basics

Simplify.
Order of operation problems get a bit more tedious when fractions are involved. Remember that when adding or subtracting fractions you need to first find the equivalent fractions with a common denominator. Multiplication does not require a common denominator.

Simplify.


We will see that some of the problems have different looking parentheses { [ ( ) ] }, treat them the same and just remember to perform the innermost parentheses first.  Some problems may involve an absolute value, in which case you will need to apply the innermost absolute value first as you would if it were a parentheses.
To avoid these unnecessary mistakes, work one operation at a time and for each step rewrite everything.  This may seem like a lot of work but it really helps avoid errors.

Simplify.

Video Examples on YouTube:










Adding and Subtracting Radical Expressions

To add or subtract radical expressions, simplify first and then add like terms if there are any.  The radical parts of the terms must be exactly the same before we can add them. (Assume all variables are positive.)

Perform the operations.
Be sure to follow the correct order of operations.
  
Simplify.
Unsimplified rational expressions may look as if they have no like terms, but first try simplifying and then check for like terms.
Simplifying is a challenge for many students. In particular, the numerical part is the source of confusion.  It is much easier to deal with the prime factors of the number in a radical than it is with the number itself. Create a factor tree and determine the prime factorization of all numbers before simplifying radical expressions.

Simplify: 
Begin by determining the prime factorizations of 108 and 864.
Substitute the prime factorization in and then simplify.


Instructional Video: Adding and Subtracting Radicals

Simplify.
Video Examples on YouTube: