Arithmetic

Table of contents

1. Preface
   1. Context of this book
   2. Mental arithmetic
2. Numeral systems
   1. Tallying
   2. Roman numeral system
   3. Decimal numeral system
3. Names of large numbers
   1. Introduction
   2. Different scales
      1. Short scale
      2. Long scale
      3. Peletier long scale
   3. The naming system
   4. Other names: a googol
   5. How many?
4. Scientific notation
   1. Introduction
   2. Normalized scientific notation
   3. Engineering notation
   4. Significant figures
      1. Rounding
5. Addition
   1. Elementary addition
   2. Adding terms > 10
   3. Addition algorithm
      1. Practice application
6. Subtraction
   1. Elementary subtraction
   2. Regrouping
   3. Borrowing
   4. Subtraction algorithm
      1. Practice application
   5. Non-associative
7. Multiplication
   1. Elementary multiplication
   2. Multiplying factors > 10
      1. Distributive property
   3. Multiplication algorithm
      1. Practice application
8. Division
   1. Elementary division
      1. Zero
   2. Euclidean division
   3. The long division algorithm
      1. Practice application
9. Negative numbers
   1. What are negative numbers?
      1. The number line
      2. Number line arithmetic
   2. Arithmetic with negative numbers
      1. Adding a negative number
      2. Subtracting a negative number: minus negative
      3. Multiplication with negative numbers
      4. Division with negative numbers
   3. Rules
10. Order and precedence
    1. Conventional order
       1. Mnemonics
    2. Commutativity and associativity
11. Prime numbers
    1. Fundamental theorem of arithmetic
       1. Definitions
       2. Prime and composite numbers
    2. Algorithms
       1. Sieve of Eratosthenes
       2. Trial division
    3. Divisibility rules
12. Rational numbers and fractions
    1. Fractional numbers
    2. Rational numbers
    3. Fractions
       1. Common fractions
       2. Proper fractions and mixed numbers
13. Arithmetic with fractions
    1. Introduction
    2. Arithmetic operations
       1. Adding and subtracting fractions
       2. Multiplying fractions
       3. Rules
    3. Reducing a fraction
    4. Comparing fractions
14. Greatest common divisor and least common multiple
    1. Greatest common divisor
       1. Euclidean algorithm
    2. Least common multiple
       1. Examples
15. Decimal numbers
    1. What are decimal numbers?
    2. Decimal notation
    3. Non-terminating decimal expansions
       1. Conversion
       2. Rounding
    4. Arithmetic with decimal numbers
    5. Fractions vs. decimals
16. Ratio, rate and proportion
    1. Terminology
       1. Ratio
       2. Rate
       3. Proportion
    2. Directly proportional relationships
    3. Solving proportions
       1. Examples
17. Percentages
    1. What are percentages?
    2. Percentages in word problems
       1. Examples
    3. Compound percentages
       1. Percentage points
18. Appendix A