Answer the following questions. Be prepared to explain your answers to the class.

  1. In the following three questions, your equations should use ONLY NATURAL NUMBERS (you can also use an equals sign, a variable, and arithmetic operations (addition, subtraction, multiplication, division)).
    1. Give an example of an equation that has a solution in the integers but does not have a solution in the natural numbers.
    2. Give an example of an equation that has a solution in the rational numbers but not in the integers.
    3. Give an example of an equation that has a solution in the real numbers but not in the rational numbers.
  2. Explain how to view a fraction as each of the following (feel free to explain in your own words, use example(s), and so on):
    • a multiplication
    • a division
    • a ratio
  3. Using the definition of number as “a point on a number line”, describe how to locate the number 23/5 on a number line.
    Your description should rely only the basic knowledge and skills necessary for the definition of a number.
  4. Create a definition for addition on the number line. That is, given two numbers a and b (points on the number line), describe how to locate the point a+b on the number line.
    Your description should rely only the basic knowledge and skills necessary for the definition of a number.

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