Answer the following questions. Be prepared to explain your answers to the class.
- 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)).
- Give an example of an equation that has a solution in the integers but does not have a solution in the natural numbers.
- Give an example of an equation that has a solution in the rational numbers but not in the integers.
- Give an example of an equation that has a solution in the real numbers but not in the rational numbers.
- 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
- 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. - 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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