Josiah Coates - Concise Pre Algebra: Learn Algebra Basics in This Easy to Understand Algebra Workbook Style Textbook | Detailed Lessons and Over 50 Practice Problems with Solutions
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Copyright by Josiah Coates, 2018 To Noah Contents Preface A typical pre-algebra textbook can be over 300 pages long, full of complex theorems and postulates. Working as an engineer for a major international shipping company, I have spent my entire career explaining complex subjects to senior (and highly paid) executives. If I used a math textbook approach to communicating with executives, I would have lost my job a long time ago. Executives, it is believed, are very busy and they need quick and concise explanations to make quick and well-informed decisions. But are middle and high school students any different? Do they have endless time to read 300 pages of postulates and theorems that have no application to modern life? To be fair, pre-algebra along with algebra, geometry and calculus does have some application to the modern workforce. But it is the general concepts of these subjects that are applicable.
The onerous theorems, postulates and definitions lengthy explanations using incomprehensible terminology are, in my opinion, useless. This approach to math should only be taught to students (college students) that have decided to become mathematicians. And there are quite a small number of mathematicians in the world. When I prepare papers and presentations on the most complex engineering topics, topics which are often cutting edge and cannot be easily researched on the internet, I continually revise and revise until the presentation is short, concise and understandable by almost anyone. It would seem only logical that a math textbook should be prepared the same way. The subject matter in this book covers an entire pre-algebra course and can be mastered after about 20 hours of study.
It should take an additional 10 hours to master the practice problems at the end of each chapter. The last two chapters are the most difficult, and comprise the core of pre-algebra. I suggest reading these chapters twice. For any questions or comments, I can be reached at info@concisetextbooks.com. I will respond to any requests for clarification, as I am interested in revising the text in any area where it may be hard to understand. Sincerely, Josiah Coates
Therefore, 1 and 4 are factors of 4. But we also know the following: 
Therefore, 2 is also a factor of 4. The factors of 4 are therefore 1, 2 and 4. What are the factors of 12? 
The factors of 12 are: 1, 2, 3, 4, 6 and 12. As we can see, 1 is always a factor of a number. And the number itself is always a factor. Factors can only be whole numbers but cannot be fractions or decimals.
What are the factors of 24? 
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24. All factors of a number (except the number itself) cannot be greater than the value of the number. For example, of 100 is 50. Therefore, all factors of 100 (other than 100) cannot be greater than 50. Another example, all factors of 30 (other than 30), cannot be greater than 15. The numbers 12 and 24 have a different set of factors.
But some of the factors are the same: 1, 2, 3, 4, 6 and 12. 12: , , , , , 24: , , , , , 8, Therefore, we can say the common factors between 12 and 24 are 1, 2, 3, 4, 6 and 12. Common factors are factors which are shared between two numbers. What are the common factors of 15 and 30? 15: 1, 3, 5, 15 30: 1, 2, 3, 5, 6, 10, 15, 30 Therefore, the common factors of 15 and 30 are 1, 3, 5 and 15. The greatest common factor is the largest number that is a factor of two numbers. For example, the greatest common factor of 12 and 24 is 6.
What is the greatest common factor of 14 and 35? 14: 1, 2, 35: 1, 5, , 35 Therefore, the greatest common factor of 14 and 35 is 7. What is the greatest common factor of 9 and 27? 9: 1, 3, 27: 1, 3, , 27 Therefore, the greatest common factor of 9 and 27 is 9. Multiples are similar to factors, but they are the opposite. A multiple goes on forever. Below are the first five multiples of 10: 10, 20, 30, 40, 50 Below are the first five multiples of 5: 5, 10, 15, 20, 25 There are some common multiples between 10 and 5. This includes 10 and 20.
What are some common multiples of 6 and 9? 9: 9, , 27, , 45, 54 6: 6, 12, , 24, 30, , 42 Therefore, two common multiples of 6 and 9 are 18, and 36. What are some common multiples of 12 and 18? 12: 12, 24, , 48, 60, 18: 18, , 54, , 90 Two common multiples of 12 and 18 are 36 and 72. We are often interested in knowing the least common multiple of two numbers. The least common multiple of 12 and 18 is 36. What is the least common multiple of 4 and 6? 4: 4, 8, , 16, 20 6: 6, , 18, 24, 30 As will be learned later in this book, we need to be able to find the greatest common factor and least common multiples of sets of numbers to be able to solve algebra problems. Practice Problems 1.
What are the factors of 6? Answer: 1, 2, 3, 6 2. What are the factors of 50? Answer: 1, 2, 5, 10, 25, 50 3. What are the factors of 96? Answer: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 4. What are factors of 12? Answer: 1, 2, 3, 4, 6, 12 5. What are the first five multiples of 2? Answer: 2, 4, 6, 8, 10 6. What are the first five multiples of 3? Answer: 3, 6, 9, 12, 15 7.
What are the first five multiples of 10? Answer: 10, 20, 30, 40, 50 8. What are the first five multiples of 9? Answer: 9, 18, 27, 36, 45 9. What are the first five multiples of 13? Answer: 13, 26, 39, 52, 65 10. What is the greatest common factor of 6 and 12? 6: 1, 2, 3, 12: 1, 2, 3, 4, , 12 Answer: 6 11. What is the greatest common factor of 52 and 13? 52: 1, 2, 4, , 26, 52 13: 1, Answer: 13 12. What is the greatest common factor of 81 and 72? 81: 1, 3, , 27, 81 72: 1, 2, 3, 6, 8, , 12, 24, 36, 72 Answer: 9 13.
What is the least common multiple of 9 and 6? 9: 9, , 27, 36, 45, 54 6: 6, 12, , 24, 30 Answer: 18 14. What is the least common multiple of 12 and 15? 12: 12, 24, 36, 48, 15: 15, 30, 45, , 75 Answer: 60 15. What is the least common multiple of 10 and 25? 10: 10, 20 30, 40, , 60 70, 80, 90, 100 25: 25, , 75, 100, 125 Answer: 50
This expression is also an equation: 
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