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1 FROM ARITHMETIC TO ALGEBRA 1

1．Introduction 1

2．Formulas 2

3．Natural numbers 8

4．Definitions and meanings 12

5．Substitution in the algebraic expression 15

6．Sets 16

2 SIGNED NUMBERS 25

7．Addition of signed numbers 28

8．Subtraction of signed numbers 32

9．Multiplication of signed numbers 34

10．Division of signed numbers 37

3 ADDITION AND SUBTRACTION 44

11．Introduction 44

12．Addition of monomials 45

13．Addition of polynomials 46

14．Subtraction of monomials 48

15．Subtraction of polynomials 49

16．Adding and subtracting larger units 50

17．Adding and subtracting terms that are not similar 52

18．A special type of addition and subtraction of polynomials 53

19．Numerical values of algebraic expressions 55

4 MULTIPLICATION AND DIVISION 61

20．Multiplying a polynomial by a monomial 63

21．Multiplying a polynomial by a polynomial 64

22．Dividing a monomial by a monomial 68

23．Dividing a polynomial by a monomial 71

24．Dividing a polynomial by a polynomial 72

5 PARENTHESES AND OTHER SYMBOLS USED FOR GROUPING 80

25．Removing parentheses 80

26．The coefficient of the parentheses 84

27．Evaluation of expressions containing parentheses 85

28．Inserting parentheses 86

6 FIRST-DEGREE EQUATIONS 92

29．Definition of the equation 92

30．Axioms used in the solution of equations 92

31．Stated problems 97

7 SPECIAL PRODUCTS AND FACTORING 111

32．Factors and factoring 111

33．The difference of two squares 114

34．Factoring the trinomial 117

35．The sum and difference of two cubes 124

36．Factoring by grouping 126

37．Factoring larger units 127

38．Numerical multiplication by use of binomial factors 129

8 FRACTIONS 134

39．Reducing fractions 134

40．Multiplying and dividing fractions 138

41．The lowest common multiple 143

42．Adding and subtracting fractions 145

43．Substitution in fractional expressions 150

44．Complex fractions 152

45．Fractional equations 154

46．Stated problems 158

9 CHANGING THE SUBJECT OF A FORMULA 164

47．Stated problems 168

10 FUNCTIONS AND GRAPHS 173

48．Functions and functional notation 173

49．Rectangular coordinates 176

50．The graph of linear equations 179

51．Applications of the graph of linear equations 182

52．Graph of inequalities 185

53．Graph of statistical data 188

11 SYSTEMS OF EQUATIONS 194

54．The intersection of sets 194

55．The intersection of sets of ordered pairs 195

56．Solving systems of equations by addition and subtraction 197

57．Solving systems of equations by substitution 201

58．Systems of equations involving fractions 206

59．Solving systems of linear equations by the graphical method 209

60．Graphical intersection of more than two sets 215

61．Stated problems 217

12 EXPONENTS AND RADICALS 225

62．Laws of positive integral exponents 225

63．Negative exponents 229

64．Fractional exponents 231

65．Multiplication of radicals 233

66．Simplification of radicals 235

67．Addition and subtraction of radicals 237

68．Division of radicals 239

13 QUADRATIC EQUATIONS 247

69．Definitions 247

70．Square root 247

71．Solving the incomplete quadratic equation 250

72．Solving quadratic equations by factoring 252

73．Solving quadratic equations by completing the square 254

74．Solving quadratic equations by the formula 256

75．Imaginary numbers 262

76．Quadratic equations with imaginary roots 264

77．Stated problems 267

14 RATIO，PROPORTION，AND VARIATION 272

78．Ratio 272

79．Proportion 273

80．Stated problems involving proportion 276

81．Variation 279

Answers to the odd-numbered problems 285

Appendix．Table of powers and roots 311