Ch 1.6 Commutative & Associative Properties

Slides:

Advertisements

Similar presentations

Commutative and Associative Properties

Advertisements

Properties of Real Numbers. Closure Property Commutative Property.

EXAMPLE 3 Identify properties of real numbers

Properties of Real Numbers

PROPERTIES REVIEW!. MULTIPLICATION PROPERTY OF EQUALITY.

PO D basicadvanced 4b + 6 b= 5, c= 3, d=7 (10c ÷b) 2 + d 4(5) (10(3) ÷5) (30 ÷5) (6)

Algebra 1 Chapter 1 Section Properties of Real Numbers The commutative and associate properties of addition and multiplication allow you to rearrange.

Chapter 1-4: Properties Commutative Property: the order in which you add or multiply numbers does not change the sum or product Ex = * 8.

1.7 Logical Reasoning Conditional statements – written in the form If A, then B. Statements in this form are called if-then statements. – Ex. If the popcorn.

1. 3 x = x 3 2. K + 0 = K (3 + r) = (12 + 3) + r 4. 7 (3 + n) = n Name the Property Commutative of Multiplication Identity of Addition.

Properties and Numbers 1.4. Deductive Reasoning Using facts, properties or rules to reach a valid conclusion Conjecture: statement that could be true.

Commutative Properties The Commutative Property is when a change in the order of the numbers does not change the answer. For example, addition would be:

Ch 2.1 (part 2) One Step Inequalities (Multiplication) Objective: To solve and graph simple inequalities involving multiplication and division.

Objective The student will be able to: recognize and use the commutative and associative properties and the properties of equality.

Ch 2.5 Variable on Both Sides Objective: To solve equations where one variable exists on both sides of the equation.

WARM-UP. COMMUTATIVE AND ASSOCIATIVE PROPERTY  Write down in your notes what you think is the meaning of the commutative property. WHAT IS THE COMMUTATIVE.

1.6. DEFINITIONS  An equation is a statement that two expressions are equal.  Usually contains 1 or more variables  A variable is a symbol that represents.

Algebra Properties Definition Numeric Example  Algebraic Example.

Ch 1.7 (part 1) One Step (Addition & Subtraction) Objective: To solve one-step variable equations using the Inverse Property of Addition.

PROPERTIES OF OPERATIONS Section 5.3. PROPERTIES OF OPERATIONS  The _________ Property states that the order in which numbers are added or multiplied.

Objective - To simplify expressions using commutative and associative properties. Commutative - Order doesn’t matter! You can flip-flop numbers around.

Unit 1, Lesson 6: The Number Properties

Objective - To simplify variable expressions involving parenthesis and exponents. Simplify the following.

Properties of Numbers. Additive Identity Adding “0” to a number gives you the same initial number. Example = = 99.

Properties Associative, Commutative and Distributive.

Associative Property MGSE9-12.N.CN.2: Associative property (addition, subtraction and multiplication)

Ch 1.2 Objective: To simplify expressions using the order of operations.

Ch 2.3 & 2.4 Objective: To solve problems involving operations with integers.

Properties of Addition and Multiplication. Commutative Property  Commute or move around  Changing the order of the numbers in the problem does not change.

Commutative Property of Addition By: Zach Jamison Period 5.

By: Tameicka James Addition Subtraction Division Multiplication

Multiplication and Division Properties. Multiplication Properties Commutative Property Associative Property Identity Property Zero Property Distributive.

2.2 Solving Two- Step Equations. Solving Two Steps Equations 1. Use the Addition or Subtraction Property of Equality to get the term with a variable on.

Properties in Math. Commutative Property of addition Says that you can switch the addends around and still get the same sum. Ex: = Ex: 6 +

Objective- To justify the step in solving a math problem using the correct property Distributive Property a(b + c) = ab + ac or a(b - c) = ab - ac Order.

(2 x 1) x 4 = 2 x (1 x 4) Associative Property of Multiplication 1.

Same Signs Different Signs 1) =+7 Objective- To solve problems involving operations with integers. Combining.

1-4 Properties How are real-life situations commutative?

 Commutative Property of Addition  When adding two or more numbers or terms together, order is NOT important.  a + b = b + a  =

Objective The student will be able to:

Name: _____________________________

Addition/ Subtraction

Objective: To solve two-step variable equations

CST 24 – Logic.

Properties of Equality

Learning Target I can solve and graph multi-step, one-variable inequalities using algebraic properties.

Properties of Operations

Chapter 1 Section 8 Properties of Numbers.

Ch 2.3 One Step (Multiplication & Division)

1 Step Equation Practice + - x ÷

Set includes rational numbers and irrational numbers.

Ch 2.2 One Step (Addition & Subtraction)

Year 1 Number – number and place value

Equations and Inequalities

Commutative and Associative Properties

Properties of Mathematics Pamphlet

Real Numbers and their Properties

Subtract the same value on each side

1.8 – Algebraic Proofs Objective:

Properties of Equality

Lesson 1.3 Properties of Real Numbers

Year 2 Number – number and place value

Objective The student will be able to:

Properties of Real Numbers

Objective The student will be able to:

Properties of Operations

Lesson 3 Properties of Operations

By: Savana Bixler Solving Equations.

Objectives: Solve two step and multi-step equations.

Presentation transcript:

Ch 1.6 Commutative & Associative Properties Objective: To understand the difference between the Commutative and Associative Properties

Definitions a + b = b + a 3 + 5 = 5 + 3 4  7 = 7  4 Commute (travel) Commutative Property of Addition a + b = b + a a “travels” to the other side of b 3 + 5 = 5 + 3 Example: Commutative Property of Multiplication a “travels” to the other side of b 4  7 = 7  4 Example:

Are the following operations commutative? 1) Subtraction Counterexamples a - b = b - a 2 - 0 = 0 - 2 2 = -2 Therefore, subtraction is not commutative. 2) Division Therefore, division is not commutative. Counterexample - a single example that proves a statement false.

Examples 2) 8 + 7 = 7 + 8 1) 3 + 1 = 1 + 3 4) 4  9 = 9  4 3) 2  7 = Apply the commutative property 2) 8 + 7 = 7 + 8 1) 3 + 1 = 1 + 3 4) 4  9 = 9  4 3) 2  7 = 7  2 5) 5 + (2  6) = (2  6) + 5 6) (3 + 4)  7 = 7  (3 + 4)

Classwork 7 + 4 = 5 + 6 = 3  8 = 9  2 = (1 + 4)  6 = (2 + 6)  3 = Apply the commutative property 1) 7 + 4 = 2) 5 + 6 = 3) 3  8 = 4) 9  2 = 5) (1 + 4)  6 = 6) (2 + 6)  3 = 1 + (5  7) = 7) 8 + (7  4) = 8) 9) 5  (4 + 6) = 10) (2  2) + 3 =

Definitions ( a + b ) + c = a + ( b + c ) (4 + 11) + 6 = 4 + (11 + 6) Associate (partner) Associative Property of Addition Parenthesis change “partners” – only the parenthesis move ( a + b ) + c = a + ( b + c ) (4 + 11) + 6 = 4 + (11 + 6) Example: Associative Property of Multiplication Parenthesis change “partners” – only the parenthesis move Example:

Are the following operations associative? 1) Subtraction (a - b) - c = a - (b - c) (10 - 5) - 2 = 10 - (5 - 2) Therefore, subtraction is not associative. 5 - 2 = 10 - 3 3 = 7 2) Division Therefore, division is not associative.

Examples 1) 5 + (5 + 7) = ( ) 5 + 5 + 7 6  4  5 ( ) 2) (6  4)  5 = Apply the associative property 1) 5 + (5 + 7) = ( ) 5 + 5 + 7 6  4  5 ( ) 2) (6  4)  5 = 3) (9 + 2) + 8 = 9 + 2 + 8 ( ) 4) 5  (2  9) = ( ) 5  2  9

Classwork (3 + 4) + 1 = (9 + 4) + 6 = (3  4)  5 = (9  2)  10 = Apply the associative property 1) (3 + 4) + 1 = 2) (9 + 4) + 6 = 3) (3  4)  5 = 4) (9  2)  10 = 5) 4 + (1 + 6) = 6) 3 + (2 + 6) = 2  (5  7) = 7) 8  (7  4) = 8) 9) 4 + (6 + 5) = 10) (3  2)  2 =

Commutative vs. Associative ( Flip-flop ) Associative ( Re-group ) Flip-flop Re-grouping