All the Math You'll Ever Need

A Self-Teaching Guide

Carolyn C. Wheater, Steve Slavin

• Publisher: Jossey-Bass
• Year: 2022
• Print ISBN:
  9781119719182
• Edition: 3
• eBook ISBN:
  9781119719199
• Topic: Mathematics
• Subtopic: Business Mathematics
• Index: Mathematics

A comprehensive and hands-on guide to crucial math concepts and terminology

In the newly revised third edition of All the Math You'll Ever Need: A Self-Teaching Guide, veteran math and computer technology teacher Carolyn Wheater and veteran mathematics author Steve Slavin deliver a practical and accessible guide to math you can use every day and apply to a wide variety of life tasks. From calculating monthly mortgage payments to the time you'll need to pay off a credit card, this book walks you through the steps to understanding basic math concepts.

This latest edition is updated to reflect recent changes in interest rates, prices, and wages, and incorporates information on the intelligent and efficient use of calculators and mental math techniques. It also offers:

• A brand-new chapter on hands-on statistics to help readers understand common graphs
• An easy-to-use-format that provides an interactive method with frequent questions, problems, and self-tests
• Complete explanations of necessary mathematical concepts that explore not just how math works, but also why it works

Perfect for anyone seeking to make practical use of essential math concepts and strategies in their day-to-day life, All the Math You'll Ever Need is an invaluable addition to the libraries of students who want a bit of extra help applying math in the real world.

1
Getting Started

Far too many Americans are mathematically illiterate. Although many of these people are college graduates, they have trouble doing simple arithmetic. One cannot help but wonder how so many people managed to get so far without having mastered basic arithmetic. Math phobia seems to have become fashionable. People who would never think it amusing to claim not to be able to read or write chuckle as they announce, “I can't do math.”

We all have to deal with numbers sometime—in banking, on taxes, in choosing a mortgage. Like it or not, numbers are an important part of our lives, and the importance of numerical literacy is increasing in finance, economics, science, government, and more. It is time math stopped intimidating us.

What we'll be doing in this book is going back to basics. We'll focus on the multiplication table. You'll need to memorize it. If you need an even more basic text, you can refer to one such as Quick Arithmetic: A Self-Teaching Guide, 3rd edition by Robert A. Carmen and Marilyn J. Carmen (Wiley, 2001).

In All the Math You'll Ever Need, the use of complex formulas is generally avoided. Although such formulas have an honored place in mathematics, they rarely need to be memorized. The ones that are used frequently work their way into memory. The others can be looked up when they're needed.

Finally, the use of technical terms is minimized whenever possible. Having the vocabulary to describe mathematical ideas and operations accurately is important to learning but you don't need a lot of fancy language for that. There are no quadratic formulas, logarithmic tables, integrals, or derivatives, and there are only a handful of very simple graphs.

This book was designed to be explored without ever using a calculator or computer. Don't get nervous. You will not be asked to throw away your calculator. Just put it in a safe place for now, to be taken out and used only on proper occasions. A calculator is most effectively used for three tasks: (1) to do calculations that need to be done rapidly, (2) to do repetitive calculations, and (3) to do sophisticated calculations that would take a great deal of time to do without a calculator. Calculators and computers are fast and as accurate as their users allow them to be. Typos are a thing, even on calculators. You need to first know what you want to ask the calculator to do, and then have enough math knowledge to decide if the answer it gives you makes sense.

The trick is to use our calculators for these specific tasks and not for arithmetic functions that we can do in our heads. So put away your calculator and start using your innate mathematical ability.

2
Essential Arithmetic

Every number system (and, yes, there are or have been others) is made up of a set of symbols that we call numbers and one or more operations you can perform with them. Those operations make up what we call arithmetic. The basic operation in our number system is addition, the act of putting together. The other operations—multiplication, subtraction, division—are related to, or built from, addition.

1 ADDITION

Addition is, at its heart, about counting. If you have 6 pair of shoes and you buy 3 new pairs, counting will tell you that you now have 9 pairs. You added 6 + 3 and got an answer of 9 by counting. After a while you don't have to count every time, because you get to know that 6 + 3 = 9.

You store a lot of addition facts like that in your memory, but there's a limit to how much memorization can help. You probably know that 4 + 8 = 12, but you're unlikely to memorize the answer to 5,387 + 9,748. Adding larger numbers requires a little more information about our number system.

Place Value

Our number system is a place value system, meaning that the value of a numeral depends on the place it sits in. In the number 444 each 4 has a different meaning. The 4 on the right is in the ones place so it represents 4 ones or simply 4. The 4 on the left is in the hundreds place and represents 4 hundreds or 400. The middle 4 is in the tens place so it represents 4 tens or 40. The number 444 is a shorthand for 400 + 40 + 4.

That expanded form, 400 + 40 + 4, helps to explain how we add large numbers. We add the ones to the ones, the tens to the tens, the hundreds to the hundreds and on up in the plac...

Table of contents

• Cover
• Table of Contents
• Title Page
• Copyright
• How to Use This Book
• Acknowledgments
• 1 Getting Started
• 2 Essential Arithmetic
• 3 Focus on Multiplication
• 4 Focus on Division
• 5 Mental Math
• 6 Positive and Negative Numbers
• 7 Fractions
• 8 Decimals
• 9 Converting Fractions and Decimals
• 10 Ratios and Proportions
• 11 Solving Problems
• 12 Area and Perimeter
• 13 Circumference and Area
• 14 Percentages
• 15 Solving Simple Equations
• 16 Powers and Roots
• 17 Very Large and Very Small Numbers
• 18 Algebra Problems
• 19 Interest Rates
• 20 Rate, Time, and Distance
• 21 Personal Finance
• 22 Business Math
• 23 A Taste of Statistics
• 24 Review
• Index
• End User License Agreement