Fundamentals of Mathematics, 2008a

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4 Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions A detailed treatment of the operations of addition and subtraction of fractions and the logic behind these operations is given in this chapter. Again, we believe that the logical treatment and many practice exercises will help students retain the information, thus enabling them to use it in the study of rational expressions in an algebra course. We have tried to make explanations dynamic. A method for comparing fractions is introduced, which gives the student another way of understanding the relationship between the words denominator and denomination. This method serves to show the student that it is sometimes possible to compare two dierent types of quantities. We also study a method of simplifying complex fractions and of combining operations with fractions. Decimals The student is introduced to decimals in terms of the base ten number system, fractions, and digits occurring to the right of the units position. A method of converting a fraction to a decimal is discussed. The logic behind the standard methods of operating on decimals is presented and many examples of how to apply the methods are given. The word of as related to the operation of multiplication is discussed. Nonterminating divisions are examined, as are combinations of operations with decimals and fractions. Ratios and Rates We begin by dening and distinguishing the terms ratio and rate. The meaning of proportion and some applications of proportion problems are described. Proportion problems are solved using the "Five-Step Method." We hope that by using this method the student will discover the value of introducing a variable as a rst step in problem solving and the power of organization. The chapter concludes with discussions of percent, fractions of one percent, and some applications of percent. Techniques of Estimation One of the most powerful problem-solving tools is a knowledge of estimation techniques. We feel that estimation is so important that we devote an entire chapter to its study. We examine three estimation techniques: estimation by rounding, estimation by clustering, and estimation by rounding fractions. We also include a section on the distributive property, an important algebraic property. Measurement and Geometry This chapter presents some of the techniques of measurement in both the United States system and the metric system. Conversion from one unit to another (in a system) is examined in terms of unit fractions. A discussion of the simplication of denominate numbers is also included. This discussion helps the student understand more clearly the association between pure numbers and dimensions. The chapter concludes with a study of perimeter and circumference of geometric gures and area and volume of geometric gures and objects. Signed Numbers A look at algebraic concepts and techniques is begun in this chapter. Basic to the study of algebra is a working knowledge of signed numbers. Denitions of variables, constants, and real numbers are introduced. We then distinguish between positive and negative numbers, learn how to read signed numbers, and examine the origin and use of the double-negative property of real numbers. The concept of absolute value is presented both geometrically (using the number line) and algebraically. The algebraic denition is followed by an interpretation of its meaning and several detailed examples of its use. Addition, subtraction, multiplication, and division of signed numbers are presented rst using the number line, then with absolute value. Available for free at Connexions
Algebraic Expressions and Equations The student is introduced to some elementary algebraic concepts and techniques in this nal chapter. Algebraic expressions and the process of combining like terms are discussed in Section 11.2 and Section 11.3. The method of combining like terms in an algebraic expression is explained by using the interpretation of multiplication as a description of repeated addition (as in Section 2.1). 5 Available for free at Connexions
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154 CHAPTER 3. 3.2 Exponents and Ro
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156 3.2.4 Roots CHAPTER 3. EXPONENT
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158 CHAPTER 3. EXPONENTS, ROOTS, AN
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164 3.3.3.1 Sample Set B CHAPTER 3.
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176 3.4.6.1 Sample Set C CHAPTER 3.
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186 3.6.3.2 Practice Set B CHAPTER
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188 3.6.5.2 Practice Set C CHAPTER
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200 CHAPTER 3. Solutions to Exercis
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214 CHAPTER 4. INTRODUCTION TO FRAC
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220 4.2.6 Exercises CHAPTER 4. INTR
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226 Thus, CHAPTER 4. INTRODUCTION T
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236 4.4.3.1.1 Sample Set B CHAPTER
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238 CHAPTER 4. 4.4.4 Raising Fracti
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250 √ 9 100 = 3 10 Example 4.45 4
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262 CHAPTER 4. 4.7.2 Multiplication
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268 CHAPTER 4. 4.8 Summary of Key C
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278 CHAPTER 4. Solutions to Exercis
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296 CHAPTER 5. ADDITION AND SUBTRAC
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340 CHAPTER 6. DECIMALS • underst
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344 CHAPTER 6. DECIMALS 0.17 6.2.5.
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346 CHAPTER 6. DECIMALS 6.2.6.1 Exe
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348 CHAPTER 6. DECIMALS 4 + .006 1
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352 CHAPTER 6. DECIMALS 6.4.3 Exerc
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354 CHAPTER 6. DECIMALS Exercise 6.
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356 CHAPTER 6. DECIMALS 841.0056 47
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358 CHAPTER 6. DECIMALS The sum is
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362 CHAPTER 6. DECIMALS Thus, 6.5
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364 CHAPTER 6. DECIMALS Table 6.15
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366 CHAPTER 6. DECIMALS 6.6.6.1 Sam
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372 CHAPTER 6. DECIMALS 6.7.3 A Met
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374 CHAPTER 6. DECIMALS Method of D
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378 CHAPTER 6. DECIMALS 816.241 10)
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382 CHAPTER 6. DECIMALS Table 6.29
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384 CHAPTER 6. DECIMALS Repeating D
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386 CHAPTER 6. DECIMALS .1818 11)2.
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390 CHAPTER 6. DECIMALS .125 8)1.00
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396 CHAPTER 6. DECIMALS 6.10.3 Exer
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398 CHAPTER 6. DECIMALS 6.11 Summar
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400 CHAPTER 6. DECIMALS 6.12.1.2 Co
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404 CHAPTER 6. DECIMALS Solutions t
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406 CHAPTER 6. DECIMALS Solution to
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420 CHAPTER 7. RATIOS AND RATES 7.2
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422 CHAPTER 7. RATIOS AND RATES are
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450 CHAPTER 7. RATIOS AND RATES Wha
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478 CHAPTER 8. TECHNIQUES OF ESTIMA
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578 CHAPTER 10. SIGNED NUMBERS 10.2
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632 CHAPTER 11. ALGEBRAIC EXPRESSIO
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694 INDEX Index of Keywords and Ter
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696 INDEX Ÿ 3.4(172), Ÿ 3.5(180),
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698 INDEX reading, Ÿ 1.3(15) readi
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700 ATTRIBUTIONS Module: "Addition
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702 ATTRIBUTIONS Module: "Multiplic
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704 ATTRIBUTIONS Module: "Introduct
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706 ATTRIBUTIONS Module: "Addition
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708 ATTRIBUTIONS Module: "Decimals:
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712 ATTRIBUTIONS Module: "Technique
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714 ATTRIBUTIONS Module: "Signed Nu
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716 ATTRIBUTIONS Module: "Algebraic
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Fundamentals of Mathematics Fundame
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Fundamentals of Mathematics, 2008a

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