Algebra Tutorials!  
Monday 24th of June
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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Order of Operations

(Priority Rules for Arithmetic)

One way to remember the operation priority rules is to use the acronym BEDMAS, meaning

B (rackets) first

E (xponents) next

M (ultiply) and D (ivide) next


A (dd) and S (ubtract) last of all.

Here are a few more examples:


Example 1:

35 × 16 - 96 + 14 = 560 - 96 + 14 Do the single multiply first – it has the highest priority present.
  = 464 + 14 Do the left-most of the two add/subtract operations. They have the same level of priority, so the left-most one is done first
  = 478 Finally, do the remaining addition, to get the correct final result of 478.


Example 2:

3 – 5(4 – 6 x 2 – 5 + 7) + 8 × 3

= 3 – 5(4 – 12 – 5 + 7) + 8 × 3 We need to start with the expression inside the brackets, which has the highest priority. Inside the brackets, the multiply operation has the highest priority.
= 3 – 5(-8 – 5 + 7) + 8 × 3 Now, do the leftmost subtract inside the brackets, since the two subtracts and one add otherwise are at the same priority level.
= 3 – 5(-13+7) + 8 × 3 Again, leftmost subtract inside the brackets.
= 3 – 5(-6) + 8 × 3 And, the last add in the brackets.
= 3 +30 + 24 Both of the multiplies are at the same priority level – here they don’t interfere with each other, so we can do both at the same step. We can regard the first one as being -5 times -6, giving the positive result +30.
= 33 + 24 Now the remaining two adds can be done to get the final answer.
= 57  

We’ve shown the steps above in a little more detail than one might normally employ, just to show the application of the priority rules very precisely.


Example 3:

2 – 5(6 – 9) 3 = 2 – 5(-3) 3 Evaluation of the bracketed expression takes priority over every other operation present.
  = 2 – 5 × (-27) The exponentiation is done next, since it is the highest priority of the remaining operations. The power 3 is applied to the entire contents of the brackets: (-3) × (-3) × (-3)
  = 2 + 135 The multiplication has the next highest priority.
  = 137  



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