MATHEMATICS 801 WHOLE NUMBERS CONTENTS I. THE SET OF WHOLE NUMBERS......... 2 Verbalizing Whole Numbers............ 3 Composition of Whole Numbers......... 4 Representing Whole Numbers by Graphs.. 8 II. OPERATIONS WITH WHOLE NUMBERS.... 20 Addition of Whole Numbers............ 20 Subtraction of Whole Numbers.......... 25 Multiplication of Whole Numbers........ 28 Division of Whole Numbers............. 34 III. APPLICATIONS WITH WHOLE NUMBERS.. 44 Word Problems...................... 44 Geometry with Whole Numbers.......... 51 Recreation with Whole Numbers......... 56 Author: Editor: Consulting Editor: Revision Editor: Richard J. Fleming, M.A. Richard W. Wheeler, M.A.Ed. Robert L. Zenor, M.A., M.S. Alan Christopherson, M.S. 804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759 MCMXCVI by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc. All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
WHOLE NUMBERS As your study of mathematics continues in this LIFEPAC, the idea of whole numbers is developed and dealt with. The topics covered are considered basic to the whole subject of mathematics. You will find here a complete study of whole numbers. You will begin with rather easy material and conclude with interesting applications. OBJECTIVES Read these objectives. The objectives tell you what you will be able to do when you have successfully completed this LIFEPAC. When you have finished this LIFEPAC, you should be able to: 1. Read and write numbers both in numerals and in words. 2. Identify the place value of any whole number. 3. Read, write, and expand large numbers. 4. Round whole numbers. 5. Draw simple graphs to represent whole numbers. 6. Add whole numbers. 7. Subtract whole numbers. 8. Multiply whole numbers. 9. Divide whole numbers. 10. Apply the mastery of whole number operations to word problems. 11. Apply the mastery of whole number operations to geometry. 12. Enjoy recreational activities related to the study of whole numbers. 1
Survey the LIFEPAC. questions here. Ask yourself some question about this study. Write your I. THE SET OF WHOLE NUMBERS SECTION OBJECTIVES 1. Read and write numbers both in numerals and in words. 2. Identify the place value of any whole number. 3. Read, write, and expand large numbers. 4. Round whole numbers. 5. Draw simple graphs to represent whole numbers. The set of whole numbers combines the set of counting numbers {1, 2, 3, 4, } with the set of zero {0}. {1, 2, 3, 4, } {0} = {0, 1, 2, 3, 4, } Whole numbers = {0, 1, 2, 3, 4, }. Remember that the set of whole numbers is an infinite set. The numbers continue on and on. We do not know the last whole number. We can write whole numbers as numerals (0, 1, 2, 3, ) or we can write them in words (zero, one, two, three, ). We write numbers in a certain structure called a base ten system. Our number system is a place value system. Are you familiar with some of the names of the place value system? 2
Do you like to work with large numbers? Very often we round large numbers to work with them. Whole numbers can also be represented in various types of graphs. VERBALIZING WHOLE NUMBERS Whole numbers can be expressed as either numerals or words. WHOLE NUMBERS FROM NUMERALS TO WORDS Four thousand, two hundred twelve are the number words for 4,212. Notice where commas and hyphens are used. Commas are used when a numeral contains four or more digits; a comma is written in numerals and written in words. Hyphens are used between the words for the numerals from twenty-one through ninety-nine. Notice also that and is not used when reading just a whole number. Models: 27 is twenty-seven. 281 is two hundred eighty-one. Write each number in words. 1.1 36 1.9 3,726 1.2 14 1.3 72 1.10 14,625 1.4 102 1.5 111 1.11 25,118 1.6 236 1.12 425,665 1.7 1,400 1.8 2,610 1.13 614,862 WHOLE NUMBERS FROM WORDS TO NUMERALS A whole number written as a word can be rewritten in numerals. Models: Thirty-seven is 37. One hundred eight is 108. 3
Write each number in numerals. 1.14 thirteen 1.15 twenty-seven 1.16 fifty-nine 1.17 two hundred six 1.18 three hundred twenty-four 1.19 five hundred eighty-eight 1.20 two thousand, six hundred forty-five 1.21 seven thousand, sixty-six 1.22 fifteen thousand, eight hundred thirty 1.23 twenty-seven thousand, four hundred twenty-one 1.24 one hundred thirty-three thousand, seven hundred eleven 1.25 three hundred twenty-five thousand, two hundred sixty-two 1.26 one million, five hundred thousand, eight hundred ninety-nine 1.27 three million, four hundred thirty-seven thousand, one hundred seventy-one COMPOSITION OF WHOLE NUMBERS Let s look at the structure of whole numbers. To read a whole number determine the place value of each digit of the number. A digit is any of the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 occurring in a number. If you understand place value you will never have trouble with large numbers. A useful tool in working with large numbers is rounding. PLACE VALUE Our number system is a place value system. Each number value is determined by the place that the digit is written. 4