Save this PDF as:

Size: px
Start display at page:

Transcription

1 Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles November 4/5, 2014 Exponents Quick Warm-up Evaluate the following: Multiplication Where does the idea of multiplications stem from? Multiplication is simply a shorter way of writing a repeated addition. For example = 3 4, here we have the number 3 added with itself 4 times. So we simplify this to 3 times 4. Looking at the questions in the quick warm up write the additions ad multiplications and the multiplications as repeated addition. Exponents An exponentiation is a repeated multiplication. Similar to how a multiplication is a repeated addition. Remember, 5 3 is simply Similarly an exponentiation, 5 3 is simply

2 As shown in the picture above, we call the lower number the base, the upper number the exponent and when refering to the base and exponent as a whole we will say the power. When we see this notation we say Two to the exponent three. Note: the second and third exponents are often referred to as squared and cubed, respectively. So we might say two cubed instead of Two to the exponent three. Examples: Write the following as a multiplication then evaluate = = Write the following numbers as exponents with the given bases 1. 32, base 2 = , base , base , base , base 4 Order of Operation: BEDMAS If you are given , do you do the + or the first? You do the first. We have these order of operations to make sure everyone calculates the same way. If there was no defined order then someone could do: = 7 2 = 14 And someone else:

3 = = 11 This gives to answer for the same math problem. This is bad!!! So we have BEDMAS.What is BEDMAS? It is a trick to remember the order of operations. Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Example: = = = 31 More Examples: ( ) 3 (2 + 3) Special Cases Base 10: what is 10 7? How about 10 n? Base 10 powers are 1 followed by n zeros, where n is the exponent. The first power: What is 5 1? How about ? Any number raised to the exponent of 1 is equal to the base. The power of zero: What is 8 0? How about ? Any non-zero number raised to the exponent of 0 is equal to 1 Now that we have covered the basics of exponents we can look at operations on exponents. Multiplication Since a power is simply a repeated multiplication it would only be natural to have rules for multiplying and dividing powers. How could we simplify : 3

4 2 2 This one is easy it is 2 2 Do you agree that the above could have been written as ? What can we say about the exponents when looking at the following equality? = 2 2 It looks like we are adding the exponents. Consider the multiplication This can be written as Again as This is 8 2 s multiplied together, it is also 2 8. So we get = 2 8 Rule:The multiplication of 2 powers with the same base is simplified to that same base whose exponent is the sum of the 2 exponents: a m a n = a (m+n) NOTE: THE BASES HAVE TO BE THE SAME Examples: Simplify to a single exponent if possible

5 division: Consider This can be written as Again as = = 22 Now with a little work on the fraction we get Here we cancel out some 2 s and we are left with two 2 s Rule: The division of two powers with the same base is simplified to that same base whose exponent is the difference of the 2 exponents: a m a n = a(m n) Knowing this rule, can we now explain why n 0 = 1? Let look at our rule but we are going to let n = m. a m a m = a(m m) What is any number minus that same number? It s zero! What is any number divided by that same number? It s one! this means that our equation above becomes: a 0 = 1 5

6 This is how we can show the property of the exponent zero. Examples: Simplify the following (if the bases are numbers, give their value) = h 45 h 44 Power of a Power What? (3 4 ) 5 is this even legal? Yes, and its not much more than we already covered. Look at (3 4 ) 5 If we consider the inner exponentiation to simply be a number we can write From before we know this to be equal to 3 20 since = 20. We can also see this as 4 5 = 20. A power raised to a power is simplified by multiplying the exponents. (a n ) m = a n m Extended to more than one power, each exponent gets multiplied. (a n b k ) m = a n m b k m Simplify: 1. (5 3 ) 4 2. ( ) (2 3 4) 3 4. (4 3 ) 2 6

7 5. (34 7 ) 8 6. ((6 2 ) 2 ) 2 7. *** ( ) 3 Negative Exponents: Simplify According to our previous rules, this gives 2 2. What does this mean? Looking at this as we did before we see that This can be written as = 2 2 Simplify to get So a negative exponent in the numerator becomes a positive if it is sent to the denominator. Similarly a negative exponent in the denominator becomes a positive exponent in the 1 numerator. That is, 2 2 = 22 Examples: Simplify the following. Write the answers with positive exponents

8 PROBLEMS 1. Write the following as exponents (a) (b) 7 to the (c) (d) (e) (f) (g) Evaluate the following: (a) (b) (c) (d) (e) (f) (g) What is BEDMAS and what does it stand for? BEDMAS is a trick to remember the order of operations and it stands for: bracket, exponent, division, multiplication, addition, subtraction 4. Evaluate (a) (b) (c) (2 4 2) (d) ( ) Simplify if possible (It may help to write down the rules we covered): (a)

9 (b) (c) (d) (e) (f) (g) Simplify if possible: (a) (b) (c) = (d) (e) (f) Simplify if possible: (a) (4 2 ) (b) (3 12 ) = 1 (c) ((4 2 ) 4 ) (d) ( ) (e) ( ) (f) (g) 3 (3 4 ) (6 1 ) If the population of rabbits triples every year, how many rabbits will there be in 5 years if there are currently 2? After one year 2 3, after 2 years 2 3 3, after 3 years , continuing we get = 486 9

10 9. If a bacteria population starts at 100 quadruples every hour, how many bacteria will there be in 6 hours? = = The memory capacity of a computer doubles every year. If you can store 1000 songs on your MP3 player now, how many songs will you be able to store in 10 years? = = You go back in time and tell you parents to buy into Apple. Your parents wisely listen you and invest \$1000. Since then, The value of apple has tripled 4 times. how much would your parents \$1000 investment be worth now? 1000 tripled 4 times means = 3 4 so your parents 1000 dollar investment would be worth = ** Express 81 7 as a power of base 3. If we look at 81 we notice we can write it as 3 4 since 3 4 = 81 So we can write the above as (3 4 ) 7 From here we can multiply 4 by 7 to get the answer ** Express as a power of base We can simplify this similar to question 11. Here we will change every thing to a power of base 2 then use the rules we learned. (2 4 ) 4 (2 6 ) ** ( ) ** If you have 0 < 10 n < , What is the max value of 3 n? The max value is when n = 0, and therefore 3 n = 1 10

Grade 7/8 Math Circles October 7/8, Exponents and Roots - SOLUTIONS

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 7/8, 2014 Exponents and Roots - SOLUTIONS This file has all the missing

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form.

Grade 9 Mathematics Unit : Powers and Exponent Rules Sec.1 What is a Power 5 is the BASE 5 is the EXPONENT The entire 5 is called a POWER. 5 = written as repeated multiplication. 5 = 3 written in standard

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write

4.0 Exponent Property Review First let s start with a review of what exponents are. Recall that 3 means taking four 3 s and multiplying them together. So we know that 3 3 3 3 381. You might also recall

Determining When an Expression Is Undefined

Determining When an Expression Is Undefined Connections Have you ever... Tried to use a calculator to divide by zero and gotten an error Tried to figure out the square root of a negative number Expressions

General Exponent Rules: Exponents, Radicals, and Scientific Notation x m x n = x m+n Example 1: x 5 x = x 5+ = x 7 (x m ) n = x mn Example : (x 5 ) = x 5 = x 10 (x m y n ) p = x mp y np Example : (x) =

Rules for Exponents and the Reasons for Them

Print this page Chapter 6 Rules for Exponents and the Reasons for Them 6.1 INTEGER POWERS AND THE EXPONENT RULES Repeated addition can be expressed as a product. For example, Similarly, repeated multiplication

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Grade 6 Math Circles October 8/9, 2013 Algebra Note: Some material and examples from the Tuesday lesson were changed for the Wednesday lesson. These notes

a b Grade 6 Math Circles Fall 2010 Exponents and Binary Numbers Powers What is the product of three 2s? =

1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Powers What is the product of three 2s? 2 2 2 = What is the product of five 2s? 2 2 2 2 2 = Grade 6 Math

Property: Rule: Example:

Math 1 Unit 2, Lesson 4: Properties of Exponents Property: Rule: Example: Zero as an Exponent: a 0 = 1, this says that anything raised to the zero power is 1. Negative Exponent: Multiplying Powers with

(- 7) + 4 = (-9) = - 3 (- 3) + 7 = ( -3) = 2

WORKING WITH INTEGERS: 1. Adding Rules: Positive + Positive = Positive: 5 + 4 = 9 Negative + Negative = Negative: (- 7) + (- 2) = - 9 The sum of a negative and a positive number: First subtract: The answer

Algebra 1A and 1B Summer Packet

Algebra 1A and 1B Summer Packet Name: Calculators are not allowed on the summer math packet. This packet is due the first week of school and will be counted as a grade. You will also be tested over the

Exponent Properties Involving Products

Exponent Properties Involving Products Learning Objectives Use the product of a power property. Use the power of a product property. Simplify expressions involving product properties of exponents. Introduction

eday Lessons Mathematics Grade 8 Student Name:

eday Lessons Mathematics Grade 8 Student Name: Common Core State Standards- Expressions and Equations Work with radicals and integer exponents. 3. Use numbers expressed in the form of a single digit times

Algebra 1: Topic 1 Notes

Algebra 1: Topic 1 Notes Review: Order of Operations Please Parentheses Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction Table of Contents 1. Order of Operations & Evaluating

CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME!

CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME! You may have come across the terms powers, indices, exponents and logarithms. But what do they mean? The terms power(s),

MBA Jump Start Program

MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Online Appendix: Basic Mathematical Concepts 2 1 The Number Spectrum Generally we depict numbers increasing from left to right

Practice Math Placement Exam

Practice Math Placement Exam The following are problems like those on the Mansfield University Math Placement Exam. You must pass this test or take MA 0090 before taking any mathematics courses. 1. What

PREPARATION FOR MATH TESTING at CityLab Academy

PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRE-TEST

Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers

Page1 Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers Lesson Topic I Can 1 Ordering & Adding Create a number line to order integers Integers Identify integers Add integers 2 Subtracting

Section 1.5 Exponents, Square Roots, and the Order of Operations

Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.

Accuplacer Elementary Algebra Study Guide for Screen Readers

Accuplacer Elementary Algebra Study Guide for Screen Readers The following sample questions are similar to the format and content of questions on the Accuplacer Elementary Algebra test. Reviewing these

Chapter 15 Radical Expressions and Equations Notes

Chapter 15 Radical Expressions and Equations Notes 15.1 Introduction to Radical Expressions The symbol is called the square root and is defined as follows: a = c only if c = a Sample Problem: Simplify

Improper Fractions and Mixed Numbers

This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All

1.1. Basic Concepts. Write sets using set notation. Write sets using set notation. Write sets using set notation. Write sets using set notation.

1.1 Basic Concepts Write sets using set notation. Objectives A set is a collection of objects called the elements or members of the set. 1 2 3 4 5 6 7 Write sets using set notation. Use number lines. Know

1.6 The Order of Operations

1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative

This is a square root. The number under the radical is 9. (An asterisk * means multiply.)

Page of Review of Radical Expressions and Equations Skills involving radicals can be divided into the following groups: Evaluate square roots or higher order roots. Simplify radical expressions. Rationalize

Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER

Rules of Exponents CHAPTER 5 Math at Work: Motorcycle Customization OUTLINE Study Strategies: Taking Math Tests 5. Basic Rules of Exponents Part A: The Product Rule and Power Rules Part B: Combining the

STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS

STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS The intermediate algebra skills illustrated here will be used extensively and regularly throughout the semester Thus, mastering these skills is an

Solving Logarithmic Equations

Solving Logarithmic Equations Deciding How to Solve Logarithmic Equation When asked to solve a logarithmic equation such as log (x + 7) = or log (7x + ) = log (x + 9), the first thing we need to decide

Connect Four Math Games

Connect Four Math Games Connect Four Addition Game (A) place two paper clips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture

3.1. RATIONAL EXPRESSIONS

3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers

Section 4.1 Rules of Exponents

Section 4.1 Rules of Exponents THE MEANING OF THE EXPONENT The exponent is an abbreviation for repeated multiplication. The repeated number is called a factor. x n means n factors of x. The exponent tells

HOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9

HOSPITALITY Math Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre at George

FRACTION REVIEW. 3 and. Any fraction can be changed into an equivalent fraction by multiplying both the numerator and denominator by the same number

FRACTION REVIEW A. INTRODUCTION. What is a fraction? A fraction consists of a numerator (part) on top of a denominator (total) separated by a horizontal line. For example, the fraction of the circle which

Exponents. Laws of Exponents. SWBAT understand the laws of zero, negative, multiplying, dividing, and power to power exponents. September 26, 2012

SWBAT understand the laws of zero, negative, multiplying, dividing, and power to power exponents. Nov 4 10:28 AM Exponents An exponent tells how many times a number, the base, is used as a factor. A power

Welcome to today s topic Parts of Listen & Learn

Number Sense and Algebra Solving Equations: Multiple-step PRESENTED BY ALGESTAR Mathematics, Grade 9 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping NOT the Chat

Chapter 7 - Roots, Radicals, and Complex Numbers

Math 233 - Spring 2009 Chapter 7 - Roots, Radicals, and Complex Numbers 7.1 Roots and Radicals 7.1.1 Notation and Terminology In the expression x the is called the radical sign. The expression under the

Chapter 1: Order of Operations, Fractions & Percents

HOSP 1107 (Business Math) Learning Centre Chapter 1: Order of Operations, Fractions & Percents ORDER OF OPERATIONS When finding the value of an expression, the operations must be carried out in a certain

Operations on Decimals

Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers. Then write the decimal

Exponents and Radicals (a + b) 10 Exponents are a very important part of algebra. An exponent is just a convenient way of writing repeated multiplications of the same number. Radicals involve the use of

Accuplacer Arithmetic Study Guide

Testing Center Student Success Center Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole

COMPASS Numerical Skills/Pre-Algebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13

COMPASS Numerical Skills/Pre-Algebra Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre

Negative Integer Exponents

7.7 Negative Integer Exponents 7.7 OBJECTIVES. Define the zero exponent 2. Use the definition of a negative exponent to simplify an expression 3. Use the properties of exponents to simplify expressions

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Introduction Grade 6 Math Circles November 5/6, 2013 Multiplication At this point in your schooling you should all be very comfortable with multiplication.

4. Changing the Subject of a Formula

4. Changing the Subject of a Formula This booklet belongs to aquinas college maths dept. 2010 1 Aims and Objectives Changing the subject of a formula is the same process as solving equations, in that we

Rational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have

8.6 Rational Exponents 8.6 OBJECTIVES 1. Define rational exponents 2. Simplify expressions containing rational exponents 3. Use a calculator to estimate the value of an expression containing rational exponents

8. Radicals - Rational Exponents Objective: Convert between radical notation and exponential notation and simplify expressions with rational exponents using the properties of exponents. When we simplify

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 8 Powers and Exponents

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 8 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

Math 016. Materials With Exercises

Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of

MATH-0910 Review Concepts (Haugen)

Unit 1 Whole Numbers and Fractions MATH-0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,

1.5. section. Arithmetic Expressions

1-5 Exponential Expression and the Order of Operations (1-9) 9 83. 1 5 1 6 1 84. 3 30 5 1 4 1 7 0 85. 3 4 1 15 1 0 86. 1 1 4 4 Use a calculator to perform the indicated operation. Round answers to three

Decimal and Fraction Review Sheet

Decimal and Fraction Review Sheet Decimals -Addition To add 2 decimals, such as 3.25946 and 3.514253 we write them one over the other with the decimal point lined up like this 3.25946 +3.514253 If one

HFCC Math Lab Beginning Algebra 13 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES

HFCC Math Lab Beginning Algebra 1 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES Before being able to solve word problems in algebra, you must be able to change words, phrases, and sentences

The wavelength of infrared light is meters. The digits 3 and 7 are important but all the zeros are just place holders.

Section 6 2A: A common use of positive and negative exponents is writing numbers in scientific notation. In astronomy, the distance between 2 objects can be very large and the numbers often contain many

Fractions and Linear Equations

Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps

Summer Mathematics Packet Say Hello to Algebra 2. For Students Entering Algebra 2

Summer Math Packet Student Name: Say Hello to Algebra 2 For Students Entering Algebra 2 This summer math booklet was developed to provide students in middle school an opportunity to review grade level

Grade 7/8 Math Circles March 2 & Word Problems

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles March 2 & 3 2016 Word Problems Although they can be confusing, you can tame word

Student Outcomes. Lesson Notes. Classwork. Discussion (10 minutes)

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 5 8 Student Outcomes Students know the definition of a number raised to a negative exponent. Students simplify and write equivalent expressions that contain

MATH Fundamental Mathematics II.

MATH 10032 Fundamental Mathematics II http://www.math.kent.edu/ebooks/10032/fun-math-2.pdf Department of Mathematical Sciences Kent State University December 29, 2008 2 Contents 1 Fundamental Mathematics

2.3. Finding polynomial functions. An Introduction:

2.3. Finding polynomial functions. An Introduction: As is usually the case when learning a new concept in mathematics, the new concept is the reverse of the previous one. Remember how you first learned

Rational Exponents. Given that extension, suppose that. Squaring both sides of the equation yields. a 2 (4 1/2 ) 2 a 2 4 (1/2)(2) a a 2 4 (2)

SECTION 0. Rational Exponents 0. OBJECTIVES. Define rational exponents. Simplify expressions with rational exponents. Estimate the value of an expression using a scientific calculator. Write expressions

5.1 Radical Notation and Rational Exponents

Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots

Whole Numbers. hundred ten one

Whole Numbers WHOLE NUMBERS: WRITING, ROUNDING The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The natural numbers (counting numbers) are 1, 2, 3, 4, 5, and so on. The whole numbers are 0, 1, 2, 3, 4,

Linear Equations and Inequalities

Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................

STATISTICS FOR PSYCH MATH REVIEW GUIDE

STATISTICS FOR PSYCH MATH REVIEW GUIDE ORDER OF OPERATIONS Although remembering the order of operations as BEDMAS may seem simple, it is definitely worth reviewing in a new context such as statistics formulae.

( ) 4, how many factors of 3 5

Exponents and Division LAUNCH (9 MIN) Before Why would you want more than one way to express the same value? During Should you begin by multiplying the factors in the numerator and the factors in the denominator?

9.2 Simplifying Radical Expressions 9.2 OBJECTIVES. Simplify expressions involving numeric radicals 2. Simplify expressions involving algebraic radicals In Section 9., we introduced the radical notation.

Order of Operations More Essential Practice

Order of Operations More Essential Practice We will be simplifying expressions using the order of operations in this section. Automatic Skill: Order of operations needs to become an automatic skill. Failure

Maths Module 4. Powers, Roots and Logarithms. This module covers concepts such as: powers and index laws scientific notation roots logarithms

Maths Module 4 Powers, Roots and Logarithms This module covers concepts such as: powers and index laws scientific notation roots logarithms www.jcu.edu.au/students/learning-centre Module 4 Powers, Roots,

Calculation of Exponential Numbers

Calculation of Exponential Numbers Written by: Communication Skills Corporation Edited by: The Science Learning Center Staff Calculation of Exponential Numbers is a written learning module which includes

Date: Section P.2: Exponents and Radicals. Properties of Exponents: Example #1: Simplify. a.) 3 4. b.) 2. c.) 3 4. d.) Example #2: Simplify. b.) a.

Properties of Exponents: Section P.2: Exponents and Radicals Date: Example #1: Simplify. a.) 3 4 b.) 2 c.) 34 d.) Example #2: Simplify. a.) b.) c.) d.) 1 Square Root: Principal n th Root: Example #3: Simplify.

Black GCF and Equivalent Factorization

Black GCF and Equivalent Factorization Here is a set of mysteries that will help you sharpen your thinking skills. In each exercise, use the clues to discover the identity of the mystery fraction. 1. My

2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses

College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2

Unit 3: Algebra. Date Topic Page (s) Algebra Terminology 2. Variables and Algebra Tiles 3 5. Like Terms 6 8. Adding/Subtracting Polynomials 9 12

Unit 3: Algebra Date Topic Page (s) Algebra Terminology Variables and Algebra Tiles 3 5 Like Terms 6 8 Adding/Subtracting Polynomials 9 1 Expanding Polynomials 13 15 Introduction to Equations 16 17 One

y x x 2 Squares, square roots, cubes and cube roots TOPIC 2 4 x 2 2ndF 2ndF Oral activity Discuss squares, square roots, cubes and cube roots

TOPIC Squares, square roots, cubes and cube roots By the end of this topic, you should be able to: ü Find squares, square roots, cubes and cube roots of positive whole numbers, decimals and common fractions

Sect Exponents: Multiplying and Dividing Common Bases

40 Sect 5.1 - Exponents: Multiplying and Dividing Common Bases Concept #1 Review of Exponential Notation In the exponential expression 4 5, 4 is called the base and 5 is called the exponent. This says

Session 29 Scientific Notation and Laws of Exponents. If you have ever taken a Chemistry class, you may have encountered the following numbers:

Session 9 Scientific Notation and Laws of Exponents If you have ever taken a Chemistry class, you may have encountered the following numbers: There are approximately 60,4,79,00,000,000,000,000 molecules

West Windsor-Plainsboro Regional School District Algebra I Part 2 Grades 9-12

West Windsor-Plainsboro Regional School District Algebra I Part 2 Grades 9-12 Unit 1: Polynomials and Factoring Course & Grade Level: Algebra I Part 2, 9 12 This unit involves knowledge and skills relative

In order to simplifying radical expression, it s important to understand a few essential properties. Product Property of Like Bases a a = a Multiplication of like bases is equal to the base raised to the

Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

Grade 6 Math Circles. Binary and Beyond

Faculty of Mathematics Waterloo, Ontario N2L 3G1 The Decimal System Grade 6 Math Circles October 15/16, 2013 Binary and Beyond The cool reality is that we learn to count in only one of many possible number

HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers

HFCC Math Lab Arithmetic - Addition, Subtraction, Multiplication and Division of Mixed Numbers Part I: Addition and Subtraction of Mixed Numbers There are two ways of adding and subtracting mixed numbers.

3. Power of a Product: Separate letters, distribute to the exponents and the bases

Chapter 5 : Polynomials and Polynomial Functions 5.1 Properties of Exponents Rules: 1. Product of Powers: Add the exponents, base stays the same 2. Power of Power: Multiply exponents, bases stay the same

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 9 Order of Operations

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 9 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

c sigma & CEMTL

c sigma & CEMTL Foreword The Regional Centre for Excellence in Mathematics Teaching and Learning (CEMTL) is collaboration between the Shannon Consortium Partners: University of Limerick, Institute of Technology,

1.3 Order of Operations

1.3 Order of Operations As it turns out, there are more than just 4 basic operations. There are five. The fifth basic operation is that of repeated multiplication. We call these exponents. There is a bit

1.1 Place Value of Whole Numbers

1.1 Place Value of Whole Numbers Whole Numbers: Whole numbers can be listed as 0,1,2,3,4,5,6,7,8,9,10,11,... The "..." means that the pattern of numbers continues without end. Whole Number Operations Workbook

Emily is taking an astronomy course and read the following in her textbook:

6. EXPONENTS Emily is taking an astronomy course and read the following in her textbook: The circumference of the Earth (the distance around the equator) is approximately.49 0 4 miles. Emily has seen scientific

UNIT 1 VOCABULARY: RATIONAL AND IRRATIONAL NUMBERS

UNIT VOCABULARY: RATIONAL AND IRRATIONAL NUMBERS 0. How to read fractions? REMEMBER! TERMS OF A FRACTION Fractions are written in the form number b is not 0. The number a is called the numerator, and tells

Grade 6 Math Circles March 10/11, 2015 Prime Time Solutions

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Lights, Camera, Primes! Grade 6 Math Circles March 10/11, 2015 Prime Time Solutions Today, we re going

Fractions to decimals

Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of

Hawkes Learning Systems: College Algebra

Hawkes Learning Systems: College Algebra Section 1.2: The Arithmetic of Algebraic Expressions Objectives o Components and terminology of algebraic expressions. o The field properties and their use in algebra.

Math 1111 Journal Entries Unit I (Sections , )

Math 1111 Journal Entries Unit I (Sections 1.1-1.2, 1.4-1.6) Name Respond to each item, giving sufficient detail. You may handwrite your responses with neat penmanship. Your portfolio should be a collection

Simplifying Exponential Expressions

Simplifying Eponential Epressions Eponential Notation Base Eponent Base raised to an eponent Eample: What is the base and eponent of the following epression? 7 is the base 7 is the eponent Goal To write