A RI T H M E T IC : A T extbook for M ath 01 3rd edition ...
ARITHMETIC: A Textbook for Math 01
3rd edition (2012)
Anthony Weaver Department of Mathematics and Computer Science
Bronx Community College
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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, improvements 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.
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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
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