Adapted from Walch Education   An irrational number is a number that cannot be expressed as the ratio of two integers. In other words, it cannot be.

Slides:

Advertisements

Similar presentations

Taking the Square Root of Both Sides Adapted from Walch EducationAdapted from Walch Education.

Advertisements

Real Numbers Review #1. The numbers 4, 5, and 6 are called elements. S = {4, 5, 6} When we want to treat a collection of similar but distinct objects.

ALGEBRA 1 BASICS CHEAT SHEET THINGS YOU SHOULD KNOW . . .

(as opposed to fake numbers?)

Factors, Fractions, and Exponents

Rational Numbers and Decimals

The Real Number System. The natural numbers are the counting numbers, without _______. Whole numbers include the natural numbers and ____________. Integers.

Adapted from Walch Education Rational exponents are another way to write radical expressions. the rules and properties that apply to integer exponents.

Defining Complex Numbers Adapted from Walch EducationAdapted from Walch Education.

Thinking Mathematically The Irrational Numbers. The set of irrational numbers is the set of number whose decimal representations are neither terminating.

Introduction The properties of integer exponents also apply to irrational exponents. In this section, we will see how the following properties can be used.

Warm Up Write each number as a percent. -15, -7, -4, 0, 4, 7{…, -2, -1, 0, 1, 2, 3, …} Add the negative natural numbers to the whole numbers Integers.

Chapter 6: The Real Numbers and Their Representations

Do Now 1/12/10 Copy HW in your planner. –Text p. 222, #20-60 evens Open your notebook to a new page and put the following heading on the top of the page.

The root word of rational is ratio.

The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all.

5-2 Rational Numbers. Converting Decimals to Fractions To convert a decimal to a fraction: 1)Determine where the decimal ends 2)Place the numerals after.

1.2 Properties of Real Numbers. Sets Of Numbers – Naturals Numbers: counting numbers {1, 2, 3, 4…} – Wholes Numbers: counting numbers and zero {0, 1,

By: Keely Hunter 6 th period Tecnology.  Any whole number and/or the additive inverse of a whole number is an integer.

Introduction An exponent is a quantity that shows the number of times a given number is being multiplied by itself in an exponential expression. In other.

Rational numbers. Whole numbers Whole numbers Rational numbers Whole numbers Natural numbers Integers / ¾ 18% A rational number.

1 -2 Properties of Real Numbers. Types of Numbers  Often, numbers are grouped or classified as specific types of numbers. We will explore the following.

REAL NUMBERS (as opposed to fake numbers?) Two Kinds of Real Numbers Rational Numbers Irrational Numbers.

Rational and Irrational Numbers. Standards: Use properties of rational and irrational numbers.  MGSE9–12.N.RN.2 Rewrite expressions involving radicals.

Do Now: Solve for x in the following equation: Hint: and.

Exponents 8 th Grade Pre-Algebra. Real Numbers Rational Numbers: Any number that can be written as a fraction Integers Positive and negative whole numbers.

Do Now 4/19/10 Copy HW in your planner. Copy HW in your planner. Text p. 655, #4-48 multiples of 4, #56 & 60 Text p. 655, #4-48 multiples of 4, #56 & 60.

Adding and Subtracting Polynomials Adapted for Walch Education.

Thinking Mathematically Number Theory and the Real Number System 5.5 Real Numbers and Their Properties.

1-1 Properties of Real Numbers

Real Numbers Review #1. The numbers 4, 5, and 6 are called elements. S = {4, 5, 6} When we want to treat a collection of similar but distinct objects.

Chapter 1: Real Numbers and Equations Section 1.1: The Set of Real Numbers.

Chapter 4 Powers and Roots. Real Numbers Rational Review Natural Numbers Whole Numbers Integers Fractions Repeating or Terminating Decimals New Perfect.

Simplified Radical Form Objective: 1)Describe simplified Radical Form 2)Simplify radical expressions by a) Factoring out perfect squares b) Combine Like.

Do Now 2/1/10 Take out HW from Friday Take out HW from Friday Text p. 258, #8-40 evens, & 11 Text p. 258, #8-40 evens, & 11 Copy HW in your planner. Copy.

Properties of Real Numbers

Review for Unit 2 Quiz 1. Review for U2 Quiz 1 Solve. We will check them together. I will answer questions when we check answers. Combine like terms.

Complex Number Systems and Simplifying Algebraic Expressions Critical Thinking Skill: Demonstrate Understanding of Concepts.

Do Now 9/23/ A= 16 A = 4² A= 36 A = 6² 4 What is the area for each figure? What are the dimensions for each figure? Write an equation for area of.

Company LOGO Factoring Adapted from Walch Education.

Section 5-4 The Irrational Numbers Objectives: Define irrational numbers Simplify radicals Add, subtract, multiply, and divide square roots Rationalize.

Solve Quadratic Equations by Finding Square Roots Chapter 1.5.

Square Roots All positive real numbers have two square roots, a positive and negative square root. All positive real numbers have two square roots, a positive.

Properties of Real Numbers

Module XIII, Lesson 3 Online Algebra

1-1 REAL NUMBERS Bell-work 1.) 2x + 1 = x + 6.

Introduction The properties of integer exponents also apply to irrational exponents. In this section, we will see how the following properties can be used.

Real Numbers and Their Properties

Day 4 – August 22nd Objective: Review number/term properties

First Quarter Reviewer

Rational Exponents.

Rational & Irrational Numbers

The Complex Number System

(as opposed to fake numbers?)

Unit 1: Rational Numbers and Exponents

(as opposed to fake numbers?)

Warm-Up #12 (Monday, 9/28) 3 ∙ ∙ (2 5 − 125)

Introduction The properties of integer exponents also apply to irrational exponents. In this section, we will see how the following properties can be used.

Introduction The properties of integer exponents also apply to irrational exponents. In this section, we will see how the following properties can be used.

5.7 Rational Exponents Fraction Exponents.

(as opposed to fake numbers?)

(as opposed to fake numbers?)

Real Numbers Natural Numbers Whole Numbers Integers Rational Numbers

Chapter Sections 1.1 – Study Skills for Success in Mathematics

Introduction An exponent is a quantity that shows the number of times a given number is being multiplied by itself in an exponential expression. In other.

Rational and Irrational numbers

Rational and Irrational Numbers

(as opposed to fake numbers?)

Do Now 4/29/19 Take out CW/HW from last week. Practice worksheet 9.1

(as opposed to fake numbers?)

Presentation transcript:

Adapted from Walch Education

  An irrational number is a number that cannot be expressed as the ratio of two integers. In other words, it cannot be written as a fraction that has whole numbers for both the numerator and denominator. The decimal representations of irrational numbers neither end nor repeat. The root of a number for which there is no exact root is an irrational number : Rational and Irrational Numbers and Their Properties 2 Key Concepts

  If the expression is written using a power and a root, it can be rewritten using a rational exponent and then solved using the multiplicative inverse of the rational fraction. Or, each operation, the root and the power, can be “undone” in separate steps. The same operation must be performed on both sides of the equation : Rational and Irrational Numbers and Their Properties 3 Key concepts, continued…

 In the following equations, x is the variable and a, b, m, and n represent integers, with m ≠ 0 and n ≠ : Rational and Irrational Numbers and Their Properties 4 Key concepts, continued… Power:Root:

  The sum of two rational numbers is a rational number. The product of two rational numbers is a rational number. The sum of a rational number and an irrational number is an irrational number. The product of a rational number and an irrational number is an irrational number. Addition and multiplication are closed operations within integers, meaning that the sum of any integers is an integer, and the product of any integers is also an integer : Rational and Irrational Numbers and Their Properties 5 Important

 Simplify the expression 4.1.2: Rational and Irrational Numbers and Their Properties 6 Practice

  The Product of Powers Property states that if the bases are the same, the expression can be written as the single base raised to the sum of the powers : Rational and Irrational Numbers and Their Properties 7 Apply the Product of Powers Property to simplify the expression

  Simplify the expression 4.1.2: Rational and Irrational Numbers and Their Properties 8 You try!

 Thanks for Watching! ~ms. dambreville