Properties of Real Numbers

Slides:



Advertisements
Similar presentations
Chapter 1 Review In Algebra, we use symbols to stand for various numbers. One type of symbol used is a variable. An expression that contains at least one.
Advertisements

Section 1.1 Part II Properties of Numbers, Equality, and Inequality.
Algebraic Expressions and Formulas
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
Properties of Real Numbers Math 0099
Properties of Real Numbers. 2 PROPERTIES OF REAL NUMBERS COMMUTATIVE PROPERTY: Addition:a + b = b + a = = =
Properties 6.19 Identify properties for addition and multiplication Multiplicative property of zero Inverse property for multiplication.
CHAPTER 9 Introduction to Real Numbers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 9.1Introduction to Algebra.
(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition.
Properties of Real Numbers
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 Notes Warm Up 1. If y = 16, y – 3.6 = ____ 3. = ____
Operations: Add, Subtract, Multiply, Divide
Chapter 6 Section 4 Addition and Subtraction of Rational Expressions.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 1.7 – Slide 1.
Properties of Real Numbers List of Properties of Real Numbers Commutative Associative Distributive Identity Inverse.
8.5 – Add and Subtract Rational Expressions. When you add or subtract fractions, you must have a common denominator. When you subtract, make sure to distribute.
Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative Properties 3.Associative Properties 4.Identity Properties.
Properties of Real Numbers
by D. Fisher (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.
(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition.
Properties of Addition and Multiplication. Distributive Property A(B + C) = AB + BC 4(3 + 5) = 4x3 + 4x5.
PROPERTIES OF REAL NUMBERS. COMMUTATIVE PROPERTY OF ADDITION What it means We can add numbers in any order Numeric Example Algebraic Example
Properties of Real Numbers Commutative Property of Addition a + b = b + a Ex) (- 7) + ( 3) = ( 3) + ( -7) = - 4 Ex) = Commutative Property.
Properties Objective: To use the properties of numbers. Do Now 1.) = 3.) ( 2  1 )  4 = 2.) =4.) 2  ( 1  4 ) =
Properties of Real Numbers CommutativeAssociativeDistributive Identity + × Inverse + ×
Example 1 Multiplying Fractions a. 5 2 – 3 2 – Use rule for multiplying fractions. = 2 – () 2 – 5 3 Use rule for multiplying fractions. = – 5 Evaluate.
by D. Fisher (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.
(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition.
(2 x 1) x 4 = 2 x (1 x 4) Associative Property of Multiplication 1.
Chapter 1 Section 1.3 Properties of and Operations with Real Numbers.
Number Properties. Commutative Property of Addition Words: In a sum, you can add terms in any order. Numbers: 5 + (-6) Algebra: a + b b + a.
Chapter 1 Review. Examples: Write the numeric expression 1.) Eight more than a number n 2.) The difference of six and a number 3.) The product of three.
Section 2.4 – The Complex Numbers. The Complex Number i Express the number in terms of i.
Simplify and Evaluate algebraic expressions
Properties of Operations
Objective The student will be able to:
Real Numbers and Their Properties
Copyright © 2011 Pearson Education, Inc.
Distributive Property
Properties of Real Numbers
Properties of Real Numbers
A.2 Simplifying Simplify means combine Like Terms.
Properties of Real Numbers Math 0099
Drill #3 Evaluate each expression if a = 6, b = ½, and c =
7.1 The Distributive Property
Properties of Real Numbers
Warm Up Place the following numbers in ascending order, then circle the integers. ½, -2, -12/3, ¾, 0.3, 0, 5/5 Hint: Use your calculator to turn the fractions.
Properties of Addition and Multiplication
Properties for Addition and Multiplication only
Algebraic Properties.
Real Numbers and Number Operations
Properties of Real Numbers
2.1 Properties of Real Numbers
Properties of Real Numbers
or write out factors in expanded form.
Write out factors in expanded form.
The Distributive Property
Properties in Math.
Distributive Property
1.3 Properties of Real Numbers
Name:______________________________ Date:________________
Properties A property is something that is true for all situations.
The Distributive Property Guided Notes
Properties of Real Numbers Math 0099
Warm up: Name the sets of numbers to which each number belongs: -2/9
Properties of real numbers
Exercise Find the following products mentally. 5(20) 100 5(7) 35 5(27)
Using the Distributive Property to Simplify Algebraic Expressions
Algebra and Indices.
Presentation transcript:

Properties of Real Numbers

Two expressions that have the same value for all allowable replacements are called equivalent.

x + x

x + x and 2x

x + x and 2x are equivalent expressions.

The Identity Property of 0

The Identity Property of 0 For any real number a,

The Identity Property of 0 For any real number a,

The Identity Property of 0 For any real number a,

The Identity Property of 0 For any real number a,

The Identity Property of 0 For any real number a, (The number 0 is the additive identity)

The Identity Property of 0 For any real number a, (The number 0 is the additive identity)

The Identity Property of 1

The Identity Property of 1 For any real number a,

The Identity Property of 1 For any real number a,

The Identity Property of 1 For any real number a,

The Identity Property of 1 For any real number a,

The Identity Property of 1 For any real number a, (The number 1 is the multiplicative identity)

The Identity Property of 1 For any real number a, (The number 1 is the multiplicative identity)

Write a fraction equivalent to 2/3 with a denominator of 3x.

Write a fraction equivalent to 2/3 with a denominator of 3x.

Write a fraction equivalent to 2/3 with a denominator of 3x.

Write a fraction equivalent to 2/3 with a denominator of 3x.

Write a fraction equivalent to 2/3 with a denominator of 3x.

Write a fraction equivalent to 2/3 with a denominator of 3x.

Write a fraction equivalent to 2/3 with a denominator of 3x.

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

Simplify

The Commutative Law

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

The Commutative Law Evaluate

Evaluate x + y and y + x

Evaluate x + y and y + x when x = 23

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

Evaluate x + y and y + x when x = 23 and y = -12

The commutative law for addition

The commutative law for addition For any numbers a and b,

The commutative law for addition For any numbers a and b, a + b

The commutative law for addition For any numbers a and b, a + b = b + a

The commutative law for addition For any numbers a and b, a + b = b + a The commutative law for multiplication

The commutative law for addition For any numbers a and b, a + b = b + a The commutative law for multiplication ab

The commutative law for addition For any numbers a and b, a + b = b + a The commutative law for multiplication ab = ba

Use the commutative laws to write an expression equivalent to

Use the commutative laws to write an expression equivalent to

Use the commutative laws to write an expression equivalent to

Use the commutative laws to write an expression equivalent to

Use the commutative laws to write an expression equivalent to

Use the commutative laws to write an expression equivalent to

Use the commutative laws to write an expression equivalent to Commutative law of addition

Use the commutative laws to write an expression equivalent to Commutative law of addition

Use the commutative laws to write an expression equivalent to Commutative law of addition

Use the commutative laws to write an expression equivalent to Commutative law of addition Commutative law of multiplication

Use the commutative laws to write an expression equivalent to Commutative law of addition Commutative law of multiplication

Use the commutative laws to write an expression equivalent to Commutative law of addition Commutative law of multiplication

The Associative Laws

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The Associative Laws Calculate and compare

The associative law of addition For any numbers a, b, and c,

The associative law of addition For any numbers a, b, and c,

The associative law of addition For any numbers a, b, and c, The associative law of multiplication

The associative law of addition For any numbers a, b, and c, The associative law of multiplication

Use the associative law to write an expression equivalent to

Use the associative law to write an expression equivalent to

Use the associative law to write an expression equivalent to

Use the associative law to write an expression equivalent to

Use the associative law to write an expression equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Use the commutative and associative laws to write at least 3 expressions that are equivalent to

Compute in two ways:

Compute in two ways:

Compute in two ways:

Compute in two ways:

Compute in two ways:

Compute in two ways:

Compute in two ways:

Compute in two ways:

Compute in two ways:

The distributive law of Multiplication over Addition For any numbers a, b, and c

The distributive law of Multiplication over Addition For any numbers a, b, and c a(b + c)

The distributive law of Multiplication over Addition For any numbers a, b, and c a(b + c) = ab

The distributive law of Multiplication over Addition For any numbers a, b, and c a(b + c) = ab + ac

The distributive law of Multiplication over Subtraction For any numbers a, b, and c

The distributive law of Multiplication over Subtraction For any numbers a, b, and c a(b - c)

The distributive law of Multiplication over Subtraction For any numbers a, b, and c a(b - c) = ab

The distributive law of Multiplication over Subtraction For any numbers a, b, and c a(b - c) = ab - ac

What are the terms of 3x – 4y + 2z

What are the terms of 3x – 4y + 2z

What are the terms of 3x – 4y + 2z

What are the terms of 3x – 4y + 2z

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Multiply

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Name the property

Factoring To factor an expression is to find an equivalent expression that is a product.

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Factor

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

Collect like terms

1.7 Numbers 1 - 118