Pre-Algebra Practice

Transcription

1 By Dr. Barbara Sandall, Ed.D., Dr. Melfried Olson, Ed.D., and Travis Olson, M.S. COPYRIGHT 2006 Mark Twain Media, Inc. ISBN Printing No EB Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa Publishing Company, Inc. The purchase of this book entitles the buyer to reproduce the student pages for classroom use only. Other permissions may be obtained by writing Mark Twain Media, Inc., Publishers. This product has been correlated to state, national, and Canadian provincial standards. Visit to search and view its correlations to your standards. All rights reserved. Printed in the United States of America.

2 Table of Contents Table of Contents Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms Real Numbers...5 Checking Progress: Real Numbers...8 Chapter 2: Operations of Numbers and Variables...9 Addition and Subtraction of Numbers and Variables...9 Multiplication of Numbers and Variables...11 Division of Numbers and Variables...13 Order of Operations...15 Checking Progress: Operations of Numbers and Variables...18 Chapter 3: Integers...19 Positive and Negative Numbers...19 Addition and Subtraction of Integers...19 Multiplication and Division of Integers...22 Checking Progress: All Integers...24 Chapter 4: Properties...25 Identity and Inverse Properties of Addition and Multiplication...25 Commutative Properties of Addition and Multiplication...27 Associative Properties of Addition and Multiplication...29 Distributive Properties...31 Checking Progress: All Properties...33 Chapter 5: Exponents and Exponential Expressions...35 Exponents and Exponential Expressions...35 Multiplying Exponential Expressions with Coefficients...38 Addition and Subtraction of Exponential Expressions with Like Terms...40 Multiplication and Division of Exponential Expressions...42 Raising to a Power, Including Negative Exponents...45 Scientific Notation...48 Checking Progress: Exponents and Exponential Expressions...50 iii

3 Table of Contents Table of Contents (cont.) Chapter 6: Square Roots...51 Square Numbers and Roots...51 Rules for Simplifying Radical Expressions...52 Adding and Subtracting Radicals...57 Checking Progress: Square Roots and Radicals...59 Chapter 7: Using Algebra to Generalize Patterns...60 Patterns in Number Lists and Tables...60 Generalizing Patterns in Algebraic Expressions and Equations...68 Solving Simple Linear Equations...70 Checking Progress: Using Algebra to Generalize Patterns...73 Chapter 8: Problem-Solving Strategies...75 Problem-Solving With Tables...75 Problem-Solving with Linear Equations...78 Checking Progress: Problem-Solving Strategies...82 Check-Up Problems...84 Real Numbers...84 Operations of Numbers and Variables...85 Integers...86 Properties...87 Exponents and Exponential Expressions...88 Square Roots...89 Using Algebra to Generalize Patterns...90 Problem-Solving Strategies...92 Answer Keys...94 Practice Answer Keys...94 Check-up Answer Keys References iv

4 Basic Overview: Real Numbers All types of numbers are needed in working to solve problems. Algebra uses numbers, symbols, and letters to solve problems. Types of numbers described in this section include real, rational, irrational, integers, whole, and natural. Examples of Real Numbers: Real numbers are a combination of all the number systems listed below. Rational numbers can be expressed as the ratio of two integers (denominator not equal to zero), and when expressed in decimal form, they either repeat or terminate Irrational numbers cannot be expressed as a ratio of two integers, and when expressed in decimal form, they neither repeat nor terminate. 2 3 π is the symbol for pi. The decimal form of pi is and it continues. This pattern never ends, and it does not repeat. Integers include natural numbers, their opposites or negative numbers, and zero: ,777 Whole numbers are the natural numbers plus zero: ,289 2 Natural numbers are sometimes called counting numbers: 3 1,

5 (cont.) Practice: Which Number is Which? Directions: Using the words listed below, fill in the blanks with the correct number type(s). Real Number Rational Number Integer Whole Number Irrational Number Number Type or Types Tq We π ,323,332,333,323,333, ,300, Qy Et x 6

6 (cont.) Challenge Problems: Real Numbers Directions: Using the words listed below, fill in the blanks with the correct number type(s). Real Number Rational Number Integer Whole Number Irrational Number Number Type or Types FeK *s π 5π

7 (cont.) Checking Progress: Real Numbers Directions: Using the words listed below, fill in the blanks with the correct number type(s). Real Number Rational Number Integer Whole Number Irrational Number Number Type or Types Wr Eu 5. π ,134,134, π 4 8