Arithmetic and Algebra Again, 2/e Leaving Math Anxiety Behind Forever

by Immergut, Brita; Burr-Smith, Jean

• ISBN13: 9780071435338
• ISBN10: 0071435336
• Edition: 2nd
• Format: Paperback
• Copyright: 2005-02-08
• Publisher: McGraw-Hill Education

Summary

The bestselling guide updated and expanded for today's mathphobesWritten by two pioneers of the concept of math anxiety and how to overcome it,Arithmetic and Algebra Againhas helped tens of thousands of people conquer their irrational fear of math.This revised and expanded second edition of the perennial bestseller: Features the latest techniques for breaking through common anxieties about numbers Takes a real-world approach that lets mathphobes learn the math they need as they need it Covers all key math areas--from whole numbers and fractions to basic algebra Features a section on practical math for banking, mortgages, interest, and statistics and probability Includes a new section on the graphing calculator, a chapter on the metric system, a section on word problems, and all updated exercises

Author Biography

Britta Immergut, Ed.D. is professor of mathematics at Fiorello LaGuardia Community College, in New York City. She has designed and taught courses for math-anxious adults for many years. Jean Burr Smith taught mathematics for 22 years at Middlesex Community College in Connecticut. One of the originators of the concept of math anxiety, she has received numerous awards for her math teaching techniques.

Table of Contents

Preface to the Second Edition	v
To the Instructor	vii
Tips for Parents and Tutors	ix
To the Student	xi
PART ONE ARITHMETIC
The Arithmetic of Whole Numbers	3	(34)
Where it all began	3	(1)
Basic Ideas	3	(2)
Vocabulary	3	(2)
Operations	5	(14)
The Number Line	5	(1)
Addition	6	(2)
Multiplication	8	(4)
Properties	12	(2)
Subtraction	14	(2)
Division	16	(3)
Using a Calculator	19	(1)
Order of Operations	20	(5)
Checkpoint	23	(1)
Summary	23	(1)
Vocabulary	24	(1)
Check List	25	(1)
Readiness Check	25	(1)
Place Value and Names for Larger Numbers	25	(2)
Rounding and Approximating Numbers	27	(2)
Rounding	27	(1)
Approximating the Answer	28	(1)
Applications	29	(8)
Summary	34	(1)
Vocabulary	35	(1)
Check List	35	(1)
Review Exercises	35	(1)
Readiness Check	36	(1)
Integers	37	(24)
The other side of zero	37	(1)
Absolute Value	38	(2)
The Number Line for the Integers	38	(1)
Absolute Value	39	(1)
Addition and Subtraction of Integers	40	(8)
Addition	40	(2)
Applications	42	(1)
Subtraction	43	(2)
Applications	45	(1)
Combining More Than Two Integers	46	(1)
Positive and Negative Numbers on the Calculator	47	(1)
Multiplication and Division of Integers	48	(4)
Multiplication	48	(1)
Division	49	(1)
Multiplication and Division with More Than Two Numbers	50	(1)
Applications	51	(1)
Exponents and Radicals	52	(3)
Exponential Notation	52	(2)
Radicals	54	(1)
Order of Operations	55	(6)
Summary	57	(1)
Vocabulary	58	(1)
Check List	59	(1)
Review Exercises	59	(1)
Readiness Check	60	(1)
Decimals and Percents	61	(29)
Ordering by tens	61	(1)
Decimals	61	(6)
Place Values	61	(2)
Reading Decimals	63	(1)
Ordering Decimals	64	(2)
Rounding Decimals	66	(1)
Basic Operations with Decimals	67	(12)
Addition and Subtraction	67	(3)
Multiplication and Division by Powers of 10	70	(1)
Multiplication	71	(3)
Division	74	(2)
Terminating and Nonterminating Decimals	76	(1)
Irrational Numbers	77	(1)
Applications	78	(1)
Percents	79	(11)
Conversions from Percent to Decimal	79	(1)
Conversions from Decimal to Percent	79	(1)
``Percent of''	80	(5)
Estimating the Answer	85	(1)
Applications	86	(1)
Summary	87	(1)
Vocabulary	88	(1)
Check List	88	(1)
Review Exercises	88	(1)
Readiness Check	89	(1)
Fractions	90	(32)
The broken numbers	90	(1)
Vocabulary	90	(3)
Equivalent Fractions and Simplifying	93	(7)
Equivalent Fractions	93	(2)
Reducing to Lowest Terms	95	(1)
Divisibility by 2, 3, and 5	95	(1)
Prime Factorization	96	(1)
The Greatest Common Factor	97	(2)
Applications	99	(1)
Multiplication and Division of Fractions	100	(6)
Multiplication	100	(4)
Division	104	(2)
Addition and Subtraction of Fractions	106	(6)
Addition	106	(3)
Adding Mixed Numbers	109	(1)
Subtracting	109	(1)
Subtracting Mixed Numbers	110	(2)
Fractions with the Calculator	112	(1)
Applications	113	(1)
Relationships among Decimals, Fractions, and Percents	114	(4)
Decimals to Fractions	114	(1)
Fractions to Decimals	115	(1)
Percents into Fractions	116	(1)
Fractions into Percents	117	(1)
Ordering Fractions	118	(4)
Summary	118	(1)
Vocabulary	119	(1)
Check List	119	(1)
Review Exercises	120	(1)
Readiness Check	121	(1)
Measurements	122	(21)
Which wrench do I use?	122	(1)
Powers of 10	122	(3)
Multiplication and Division by Powers of 10	124	(1)
Scientific Notation	125	(2)
The Metric System	127	(7)
Area	132	(1)
Volume	133	(1)
Applications	134	(1)
The Customary System of Measurement	134	(2)
Conversions between the Customary and Metric Systems	136	(7)
Summary	137	(1)
Vocabulary	138	(1)
Check List	138	(1)
Review Exercises	138	(1)
Readiness Check	139	(4)
PART TWO ALGEBRA
Basic Operations	143	(27)
Letters for numbers	143	(1)
Vocabulary	143	(1)
Addition and Subtraction	144	(2)
Exponential Notation	146	(4)
Multiplying Numbers in Exponential Notation	147	(1)
Power to a Power	148	(1)
Product to a Power	149	(1)
Division with Exponents	150	(5)
Zero as a Power	152	(1)
Negative Exponents	153	(2)
The Distributive Principle	155	(4)
Factoring	159	(1)
Evaluating Expressions	160	(3)
Applications	163	(7)
Formulas	163	(1)
Geometry	163	(1)
Physics	164	(1)
Business	165	(1)
Summary	165	(2)
Vocabulary	167	(1)
Check List	167	(1)
Review Exercises	167	(2)
Readiness Check	169	(1)
Equations and Inequalities	170	(25)
Mathematical sentences	170	(1)
Solving Equations	170	(6)
Equations with One Variable	170	(4)
Equations with Variables on Both Sides	174	(2)
Solving Equations with Fractions and Decimals	176	(3)
Formulas	179	(5)
Geometry	179	(2)
Physics	181	(2)
Business	183	(1)
Inequalities	184	(3)
Systems of Linear Equations	187	(8)
The Elimination or Addition Method	187	(2)
The Substitution Method	189	(3)
Summary	192	(1)
Vocabulary	192	(1)
Check List	192	(1)
Review Exercises	193	(1)
Readiness Check	193	(2)
Graphing	195	(32)
The art in mathematics	195	(1)
Drawing Graphs	195	(4)
Graphing with Ordered Pairs	199	(4)
Graphing Ordered Pairs	202	(1)
Graphing Related Pairs	203	(10)
Vertical and Horizontal Lines	210	(3)
Slope and y-Intercept	213	(8)
Slope	213	(6)
Intercept	219	(2)
Graphing Using Slope and y-Intercept	221	(3)
The Graphing Calculator	224	(3)
Summary	224	(1)
Vocabulary	224	(1)
Check List	225	(1)
Review Exercises	225	(1)
Readiness Check	226	(1)
Word Problems	227	(32)
The agony or joy of mathematics	227	(1)
Translating Words to Symbols	227	(3)
Writing Equations and Inequalities	230	(2)
Equations	230	(2)
Inequalities	232	(1)
Strategies for Solving Word Problems	232	(18)
Number Problems	233	(3)
Percent Problems	236	(3)
Ratio and Proportion Problems	239	(2)
Geometry Problems	241	(2)
Motion Problems	243	(2)
Age Problems	245	(1)
Work Problems	246	(2)
Coin and Mixture Problems	248	(2)
Additional Word Problems	250	(9)
Summary	252	(2)
Vocabulary	254	(1)
Check List	254	(1)
Review Exercises	254	(1)
Readiness Check	255	(4)
PART THREE PRACTICAL MATHEMATICS
Applications	259	(26)
Using mathematics	259	(1)
Percents	260	(3)
Business Problems	263	(4)
Payroll	264	(1)
Inventory	265	(1)
Postage	265	(2)
Shopping	267	(4)
Best Buys	268	(1)
International Best Buys	269	(2)
Personal Finance	271	(3)
Bank Accounts	271	(1)
Stock Market	271	(1)
Stocks and Bonds	272	(1)
Depreciation	273	(1)
Taxes	274	(3)
Income Tax	274	(2)
Sales Tax	276	(1)
Property Tax	277	(1)
Travel	277	(8)
Time Problems	277	(3)
Money Conversions	280	(1)
Summary	281	(1)
Vocabulary	282	(1)
Check List	282	(1)
Review Exercises	282	(1)
Readiness Check	283	(2)
Mathematics in Banking	285	(11)
Pay interest and earn interest	285	(1)
Loans and Mortgages	285	(4)
Simple Interest	285	(1)
Loans	286	(1)
Credit Cards	286	(2)
Mortgages	288	(1)
Bank Interest	289	(7)
Formula for Compound Interest	290	(1)
Annual Yield	291	(1)
The Rule of 70	292	(2)
Summary	294	(1)
Vocabulary	294	(1)
Check List	294	(1)
Review Exercises	295	(1)
Readiness Check	295	(1)
Statistics	296	(17)
Organizing information	296	(1)
Descriptive Statistics	296	(10)
Frequency Distribution	296	(1)
Graphs	297	(3)
Grouped Intervals	300	(6)
Measures of Central Tendency and Dispersion	306	(7)
Mean, Median, and Mode	306	(2)
Measures of Variance and Dispersion	308	(1)
Standard Deviation	308	(2)
Summary	310	(1)
Vocabulary	310	(1)
Check List	311	(1)
Review Exercises	311	(1)
Readiness Check	312	(1)
Probability	313	(10)
Heads or tails?	313	(1)
Probability and Odds	313	(6)
Probability	313	(5)
Odds	318	(1)
Sets	319	(4)
Set Notation	319	(1)
Venn Diagrams	320	(1)
Summary	321	(1)
Vocabulary	321	(1)
Check List	321	(1)
Review Exercises	322	(1)
Readiness Check	322	(1)
Calculators	323	(8)
Use of technology	323	(1)
Arithmetic	323	(4)
Basic Operations with Whole Numbers, Decimals, and Percents	323	(1)
Integers	324	(1)
Powers	325	(1)
Fractions	326	(1)
Algebra	327	(1)
Formulas	327	(1)
Practical Mathematics	328	(3)
Answers to Exercises	331	(47)
Answers to Readiness Checks	378	(7)
Index	385