ARITHMETIC: A Textbook for Math 01 3rd edition (2012) Anthony Weaver Department of Mathematics and Computer Science Bronx Community College Page 2 3rd Edition. Copyright c Anthony Weaver, June 2012, Department of Mathematics and Computer ! Science, CPH 315, Bronx Community College, 2155 University Avenue, Bronx, NY 10453. Thanks to the following colleagues for various combinations of proof-reading, technical help, im- provements in pedagogy and/or exposition: Nikos Apostolakis, Luis Fernandez, Marie Hercule, Uma Iyer, Toni Kasper, Alexander Kheyfits, Roman Kossak, George Leibman, Emanuel Paki, Maria Psarelli, Philipp Rothmaler, Camilo Sanabria. Responsibility for errors remains with me. – A.W. June, 2012. Page 3 Page 4 Contents 1 Whole Numbers 9 1.0.1 Exercises . 10 1.1 Adding Whole Numbers . 10 1.1.1 Commutativity, Associativity, Identity . 10 1.1.2 Multi-digit addition . 11 1.1.3 Exercises . 12 1.2 Subtracting Whole Numbers . 14 1.2.1 Commutativity, Associativity, Identity . 15 1.2.2 Multi-digit subtractions . 15 1.2.3 Checking Subtractions . 16 1.2.4 Borrowing . 16 1.2.5 Exercises . 18 1.3 Multiplying Whole Numbers . 20 1.3.1 Commutativity, Associativity, Identity, the Zero Property . 21 1.3.2 Multi-digit multiplications . 21 1.3.3 Exercises . 25 1.4 Powers of Whole Numbers . 26 1.4.1 Squares and Cubes . 27 1.4.2 Exercises . 27 1.4.3 Square Roots . 28 1.4.4 Exercises . 29 1.5 Division of Whole Numbers . 29 1.5.1 Quotient and Remainder . 30 1.5.2 Long Division . 31 1.5.3 Exercises . 35 1.6 Order of operations . 36 1.6.1 Exercises . 38 1.7 Average . 39 1.7.1 Exercises . 39 1.8 Perimeter, Area and the Pythagorean Theorem . 40 1.8.1 Exercises . 47 2 Fractions and Mixed Numbers 49 2.1 What fractions mean . 49 2.2 Proper and Improper Fractions . 50 2.2.1 Zero as Numerator and Denominator . 51 5 2.2.2 Exercises . 52 2.3 Mixed Numbers . 53 2.3.1 Converting an improper fraction into a mixed or whole number . 53 2.3.2 Exercises . 54 2.3.3 Converting a mixed or whole number to an improper fraction . 55 2.3.4 Exercises . 56 2.4 Multiplication of Fractions . 57 2.4.1 Exercises . 59 2.5 Equivalent Fractions . 59 2.5.1 Cancellation and Lowest Terms . 60 2.5.2 Exercises . 62 2.6 Prime Factorization and the GCF . 62 2.6.1 Exercises . 64 2.6.2 Finding the GCF . 64 2.6.3 Exercises . 65 2.6.4 Cancelling the GCF for lowest terms . 65 2.6.5 Exercises . 66 2.7 Pre-cancelling when Multiplying Fractions . 67 2.7.1 Exercises . 69 2.8 Adding and Subtracting Fractions . 69 2.8.1 Exercises . 70 2.8.2 Adding and Subtracting Unlike Fractions . 71 2.8.3 The LCM . 72 2.8.4 Exercises . 73 2.8.5 The LCD . 74 2.8.6 Exercises . 75 2.9 Comparison of Fractions . 76 2.9.1 Exercises . 78 2.10 Division of Fractions . 78 2.10.1 Reciprocals . 78 2.10.2 Exercises . 79 2.10.3 Division is Multiplication by the Reciprocal of the Divisor . 79 2.10.4 Exercises . 81 2.11 Mixed Numbers and Mixed Units . 82 2.11.1 Vertical Addition and Subtraction . 82 2.11.2 Exercises . 84 2.11.3 Measurements in Mixed Units . 85 2.11.4 Exercises . 87 2.12 Combined operations with fractions and mixed numbers . 87 2.12.1 Exercises . 89 3 Decimals and Percents 91 3.1 Decimal place values . 92 3.1.1 Exercises . 93 3.2 Significant and Insignificant 0’s . 93 3.3 Comparing Decimals . 94 3.3.1 Exercises . 95 Page 6 3.4 Rounding-off . 95 3.4.1 Exercises . 97 3.5 Adding and Subtracting Decimals . 97 3.5.1 Exercises . 99 3.6 Multiplying and Dividing Decimals by Powers of 10 . 99 3.6.1 Exercises . 101 3.7 Multiplication of general decimals . 101 3.7.1 Exercises . 102 3.8 Division of a decimal by a whole number . 103 3.8.1 Exercises . 108 3.9 Division of a decimal by a decimal . 108 3.9.1 Exercises . 109 3.10 Percents, Conversions . ..