**Learn how to do basic math fast and easily.**

*Speed Mathematics* by Bill Handley is one of the better books on fast basic arithmetic. Handley has a variety of novel tricks to make addition, subtraction, division and multiplication much simpler, which makes it possible to do many problems in your head. The methods are much more enjoyable and easier than the conventional methods taught in most schools.

**Who should use this book**- Beginning math students, homeschoolers, teachers, and anyone who would like to acquire fast, basic calculation skills and improve their understanding and appreciation of math.

**Skills needed to use this book**: You should be able to do very simple math; (think times 2) multiplication, addition, subtraction, etc. You should also be willing to practice the problems given, until you get the basic process down pat.

**Advantages of this book**: It’s a short easy read and the lessons are clear and easy to apply. With sufficient practice the skills become ingrained. Handley uses numerous real life examples which makes it easier to remember some of the concepts. Once you have a firm grasp of the methods, you can apply them in many ways.

**Disadvantages**: Aside from some minor pettifogging, I have two issues with this book. The issues are my own hang-ups and not the book’s fault. I find that in mental calculation I have a tendency to transpose, alter, or drop numbers without even being aware that I’m doing it. This makes it difficult to do mental math; once when I was mentally adding 8 plus 6, I changed the 6 to 8, which gave 16 instead of 14. If you have this problem too, which I suspect is partly a concentration problem, you should be aware that doing problems purely in your mind won’t be as easy for you, although the methods given will make it much easier to do pen and paper calculations. On the bright side, the book provides easy ways to check and to estimate answers. My second related issue is the difficulty of unlearning old habits, when I try to do problems. It’s something of a struggle to get myself to do division the way given in the book, when my mind is telling me to do it the way I learned in grade school. Once I’ve practiced the new methods enough, I expect this issue to become irrelevant.

**Criticisms: I want to address a few criticisms of the book given in the Amazon reviews.**

*Criticism #1*: A dairy farmer told Handley that the book was useless for milking cows.

I would say that the actual physical act of milking is not going to be improved by reading this book. However, the farmer must use math in his business to estimate feed costs, profits, break even points, and other such things. This is where a better understanding of math and increased ability in math does come in handy. This is a common mistake a lot of people make, since they don’t see the math in a given situation they assume it does not exist. In reality, math underlies most of what we do and use; it’s just not very obvious in many situations.

*Criticism #2*: Some people are claiming that the methods in the book Vedic Mathematics are preferable.

I read part of Vedic Mathematics and in my opinion Speed Mathematics is more cohesive and clearer. The layout of Vedic Mathematics is not so good; it was hard to read, and the author used a notation system that was confusing to me.

*Criticism #3*: The reference multiplication method does not work for larger numbers or all numbers and Trachtenberg’s methods are preferable.

I have not read Trachtenberg’s book yet, so I can’t compare. However the reference method does work for all numbers. As is made clear in the book, some problems require using a reference number more than one time. It’s still far easier than multiplying the way most of us were taught. I think any method, whether Handley’s, Trachtenberg’s, etc is going to have drawbacks. Also different people will prefer one method to another. Ultimately, you have to go with the method you find easiest and practice it often enough so it becomes ingrained.

*Criticism #4*: Certain problems, such as 5 times 5, don’t work, when multiplied with a reference number of 10.

5 times 5 does work if you use a different reference number such as 3. The later chapters in the book make it clear how to do so. The method given in the first chapter (shown below in the book summary) leaves out a step, that is necessary to make all numbers work. In the later chapters, this step is made explicit.

**Chapters:**

**Chapter 1. Multiplication: Part One**

Introduces the idea of a reference number. Suppose you want to multiply 6 by 8 and don’t know the times table well. Using 10 as the reference number, you can set up the problem this way:

**Step 1**: Under the 6, write 4 in a circle. Under the 8 write 2 in a circle.

6 x 8 =

④ ② ←4 is the number added to 6 that gives 10; 2 is the number that added to 8 gives 10

**Step 2: **Subtract diagonally. Either subtract 2 from 6 or 4 from 8. You get 4 in either case. Write 4 after the equal sign.

6 x 8 = 4

④ ②

**Step 3:** Multiply the two circled numbers, 4 and 2, to get 8. Write 8 after the 4. 48 is the answer

6 x 8 = 48

④ ②

Simple, right? Notice that the reference number used is 10. There is an implicit step involving the reference number, that is explained in chapter 2. If you don’t know this step, the process will appear not to work for certain problems, such as 5 times 6.

**Chapter 2. Using a reference number**

This chapter clarifies the whole idea of how to use the reference number and how to do problems where the multiplied numbers are bigger than the reference number.

**Chapter 3. Multiplying numbers above and below the reference number.**

This chapter addresses what to do when one number is greater than the reference number and one is less.

**Chapter 4. Checking Answers: Part One**

Teaches how to check answers with substitute numbers and casting out nines. Handley’s teachers (like mine) taught that one should check problems by doing the problem over with two different methods, which is laborious and time consuming. The methods given in this chapter are much easier.

**Chapter 5: Multiplication: Part Two**

Goes further into multiplication strategies, including using any number as a reference number, and multiplying by factors.

**Chapter 6. Multiplying Decimals**

Teaches you how to easily multiply decimals using a reference number.

**Chapter 7. Multiplying Using Two Reference Numbers.**

Useful for numbers that are far apart such as 9 times 53. Handley gives several variations of this method.

**Chapter 8. Addition**

Fast ways to add numbers and checking addition by casting out nines.

**Chapter 9. Subtraction**

Fast ways to subtract numbers mentally and on paper. Checking subtraction by casting out nines.

**Chapter 10. Squaring Numbers**

Several methods to square numbers that end in 5, 6, 9, 1, etc.

**Chapter 11. Short Division**

How to divide small numbers with a reference number.

**Chapter 12: Long Division by Factors**

Teaches some basic principles of division such as dividing by factors and getting remainders.

**Chapter 13. Standard Long Division**

Teaches how to divide by using a substitute number and adjusting during the process.

**Chapter 14. Direct Division**

Shows a way to divide by two or three digit numbers.

**Chapter 15. Division by Addition**

Dividing by multiples of 10ⁿ. Builds on the idea of substitute numbers and addresses possible issues with this method.

**Chapter 16. Checking Answers: Part Two**

Introduces the principle of casting out elevens and using this principle to check division problems.

**Chapter 17. Estimating Square Roots**

Using substitute numbers to approximate square roots.

**Chapter 18. Calculating Square Roots**

Teaches how to get exact square roots by using cross multiplication.

**Chapter 19. Fun Shortcuts**

Multiplication by multiples of 11, multiplication and division by nine, division and multiplication by factors and other useful stuff.

**Chapter 20. Adding and Subtracting Fractions**

A simple but useful chapter, if you are not comfortable with fractions.

**Chapter 21. Multiplying and Dividing Fractions**

Nothing new here, but helpful if you haven’t learned these methods.

**Chapter 22. Direct Multiplication**

A way to quickly multiply numbers without a reference number. He also shows how to combine reference multiplication with direct multiplication.

**Chapter 23. Estimating Answers**

Real life examples of how to estimate your answer. Handley addresses the claim that estimations are no longer needed, when one can simply use a calculator, with an anecdote. One of his students was asked was how much money would be needed to fill up a tank of gas. The student got an answer of several million dollars on his calculator. It took some prodding before the student realized this answer was illogical, and that he had made a numerical error while entering the numbers.

**Chapter 24. Using What You Have Learned**

More real life examples such as converting currency, measures of temperature and length and other useful stuff.

**Afterword**

**Appendix A: Frequently Asked Questions**

Addresses some of the issues parents and teachers might have with the book.

**Appendix B: Estimating Cube Roots**

**Appendix C: Checks for Divisibility**

**Appendix D: Why Our Methods Work**

**Appendix E: Casting Out Nines -Why It Works**

**Appendix F: Squaring Feet and Inches**

**Appendix G: How Do You Get Students to Enjoy Mathematics?**

**Appendix H: Solving Problems**

A list of 16 ways to approach a problem.

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