Order of Operations P E M D A S. Notes: Expressions and Equations (6.EE.1 9) Exponents. Order of Operations x

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1 Parts: Exponents 5 Exponent Base Exponential Form Write the expression using a base and exponent. Expanded Form: Write out what the exponent means. x x x x x Standard Form: Solve the expression *** Any Number to the zero power equals 1.*** Key Points When the exponent is a 2, it is called "squared" or to the second power. When the exponent is a, it is called "cubed" or to the third power. When the exponent is a 0, the answer is always 1. (Ex: 1,82 0 1) When the exponent is 1, the answer is always the base number. (Ex: ) Exponents Exponent Notes Fill in the missing information in the table below. Exponential Form Expanded Form Standard Form x 2 x 2 x 2 x x 6 x x 9 ( 1 / ) 2 1 / x 1 / 1/ x 5 x 5 x (2.2) 2.2 x 2.2 x Exponents on the Calculator Step 1: Enter the base number. Step 2: Hit the button. Step : Enter the exponent. Step : Hit Use the calculator to solve Exponents Practice Exponents in a Calculator (P) E x M/D Order of Operations Please Excuse My Dear Aunt Sally Parenthesis Exponents (Exponent shows how many you have) Multiply and Divide (From Left to Right at the same time) P E M D A S lease xcuse y ear unt ally Order of Operations Parentheses ( ) ( x 1) x 5 Exponents x 5 Multiplication x Division Addition x A/S Add and Subtract (From Left to Right at the same time) Order of Operations Order of Operations Example 1

2 Addition Add, Added to, the sum of, more than, increase by, the total of, plus + Add x to y x + y y added to y The sum of a and b a + b m more than n n + m p increased by 10 p + 10 The total of q and 10 q plus m 9 + m Addition Translations Subtract, subtract from, difference, between, less, less than, decreased by, diminished by, take away, reduced by, exceeds, minus Subtract x from y y x From x, subtract y x y The difference between x and 7 x 7 10 less m 10 m 10 less than m m 10 p decreased by 11 p 11 8 diminished by w 8 w y take away z y z p reduced by 6 p 6 x exceeds y x y r minus s r s Translations Multiplication Multiply, times, the product of,multiplied by, times as much, of 7 times y 7y The product of x and y xy 5 multiplied by y 5y one fifth of p 1/ 5 p x Division Divide, divides, divided by, the quotient of, the ratio of, equal amounts of, per Divide x by 6 x/6 or x 6 7 divided by x 7/x or 7 x The quotient of y and 5 y/5 or y 5 The ratio of u to v u/v or u v u separated into equal parts u/ or u 5 parts per 100 parts 5/100 or Multiplication Translations Division Translations Equals/Multiplication by 2 and 1/2 Is equal to, the same as, is, are, the result of, will be, are, yields x is equal to y x y p is the same as q p q Two, two times, twice, twice as much as, double 2 Twice z 2z y doubled 2y Half of, one half of, half as much as, one half times 1/2 or 1 2 Half of u u/2 one half times m 1/ 2 m Writing Expressions from Word Statements Steps: 1) Label the parts of the sentence. 2) Write the expression. Example: The sum of a number and 7 + x 7 Put the operation where the "and" is. more than the product of and m. x + 7 Equals/Multiplication by 2 and 1/2 Words to Math Example 2

3 Commutative Property a + b b + a a x b b x a Associative Property (a + b) + c a + (b + c) (a x b) x c a x (b x c) Numbers may be added or multiplied together in any order. No matter how the numbers are grouped, the answer will always be the same x 6 6 x 5 ( + ) ( + 5) ( x ) x 5 x ( x 5) Commutative Property Associative Property Additive Inverse Property a + a 0 The sum of a number and its opposite is always zero Reflexive Property a a The sign reflects the same value on both sides of the equation. 12x 12x 15 2x +7 2x Additive Inverse Property Reflexive Property Multiplicative Inverse Property Any number multiplied by its reciprocal is always one. a 1 a a a Distributive Property a(b + c) ab + ac Definition: A property used to find the product of a number and a sum or difference. Distribute what is outside of the parenthesis by what is inside the parenthesis. (x + ) (x) + () x + 12 Multiplicative Inverse Property Distributive Property

4 Distributive Property Notes Different Methods Same Results Box Method Arrow Method ( x + ) ( x + ) x Multiply sides x 12 x + 12 Drop #'s & Operation Multiply (x) + () x + 12 Term The parts of an algebraic expression that are separated by addition or subtraction signs. Example:x 2 + x 6 Terms: x 2, x, 6 Coefficient is a multiplicative factor in some term of an expression. (The number in front of a variable.) Example: x 2 +x 6 Coefficients:, Like Term Terms in an expression that have the same variable raised to the same power. Example: x 2 + x 6x x 2 Like Terms: x 2, x 2 x, 6x 9 Constant Terms a term that has no variable. Example: x 2 + x + 6 Constant Term: 6 Differend Methods Important Vocabulary "Like" terms: all have the same variable, same power: x, x, 12x all are constants (numbers): 1, 2.5, 1½, 5 all have the same variable, same power: 2y 2, 6y 2, y 2 Combining like terms: used to simplify an expression or an equation. circle or box the like terms in each expression or equation use the number in front of the variable (coefficient) and it s sign to combine the term Steps: x 2 + 6x x 5 6x + x 9x +9 5 x 2 + 9x + Circle, box, or underline the like terms in each expression or equation. Group the operation with the term. Use the number in front of the variable (coefficient) and it s sign to combine the term. How to... Example Problem Grouping Method x 2 2x 2 2x 2 a a 1a 2x 2x x 2 + a 2x 2 + 2x a x 2 + a 2x 2 + 2x a Plus/Minus Chart + x 2 x 2 x 2 x 2 aaaa xx x 2 x 2 aaa 2x 2 + a + 2x 2x 2 + a + 2x Simplifying Expressions with Distributive Property and Combining Like Terms Steps: Distribute the term on the outside of to parentheses to all the terms inside the parentheses. Combine Like Terms. (x + 9) 7 8w + (w + 1) x x w + w w + 2 Example Problem Distributive Property with Combining Like Terms

5 Solving Expressions using substitution Solve 6x + 5 if x m + 9 if m 0 6x + 5 6() m Determining if a Solution is Correct Is 5, 8, or 1 a solution to the equation x + 9? Plug in 5 Plug in 8 Plug in 1 x + 9 (5) No x + 9 (8) Yes x + 9 (1) No 8 is the solution to the equation Solving Expressions Using Substitution Determing if a Solution is Correct Perform the inverse operation and then check your solution. Solving One Step Equations Operation Addition Multiplication Division Find the inverse operation to solve Inverse Addition Division Multiplication Solve an addition equation by. Solve a multiplication equation by. Division Solve a subtraction equation by. Addition x + 7 x x 5x x 7 x 1 Solve a division equation by. Multiplcation 7 x 7 7 x 21 Foldable Notes Foldable Examples Solving One Step Inequalities Inequalities Graph the Variable > < Solve the same way you solve an equation. Instead of one solution you will have many. Example: x + < 12 x + < 12 x + < 12 x + < 12 x < 8 Any value less than 8 makes this statement true. x < 8 Any value less than or equal to 8 makes this statement true. > Greater Than or equal to > Greater Than < Less Than or equal to < Less than x is less than or equal to 2 x 2 2 x x is less than 2 x < 2 2 > x x is greater than or equal to 2 x 2 2 x x is greater than 2 x > 2 2 < x Solving One Step Inequalities Foldable 5

6 *Helpful Hints* If your variable is on the left side then your inequality symbol matches the arrow point. x > 2 x < 2 Practice Problems: x < I I I > 1 2 < I I I > 1 2 m < 5 Arrow represents values of the variable. p > 7 Helpful Hints to Graphing Inequalities Graphing Inequalities Practice Problems: y is greater than y > Determine the inequality based on the graph. x < 0 ; 0 > x x is less than or equal to 7 x < 7 x > 0 ; 0 < x m is greater than or equal to m > x < 5 ; 5 > x x > 7 ; 7 < x Writing and Graphing Inequalities Writing Inequalities from a Graph 6