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1. Explain what the following table depicts. Why is it constructed in this way? (Why no zero on the left column? Why positive/negative on only one number?
|Numerator ( |0 |(1 |(2 |. . . |
|(Denominator | | | | |
|1 |0/1 = 0 |(1/1 = (1 |(2/1 = (2 | |
|2 |0/2 = 0 |(1/2 = ( 1/2 |(2/2 = (1 | |
|3 |0/3 = 0 |(1/3 = (1/3 |(2/3 = (2/3 | |
|. . . | | | | |
2. Use the definitions of real numbers and rational numbers to write a GOOD definition of irrational numbers.
3. Why are additive inverses important in later algebra?
4. Why would an additive identity be important in algebra?
5. Why are multiplicative inverses important in later algebra?
6. Why would a multiplicative identity be important in algebra?
7. Explain for which operations the distributive property holds. Why does it not for others?
8. Is subtraction commutative? Explain.
9. You would probably agree that (14( = -14 is a false statement. Would you also agree that (a( = - a is a false statement? Why or why not?
10. One way to verbalize the equation (-5)(-5) = 25 is that “two factors of -5 are 25.” Explain how this verbalization and equation are the same. Why might this verbalization be beneficial to a student?
11. Five factors of what number are 1? Three factors of what number are 27?
12. Build a Venn diagram of sets of numbers. Include at least the following: Rational, irrational, real, integers, non-zero integers, complex numbers, transcendental numbers, zero, whole numbers, and natural numbers.
13. How many primes should there be in the interval [1, 212]? How do you know? How many primes should there be in the interval [278, 875]? How do you know?
14. A student in your class is trying to find the greatest factor of 90. He starts with one and progresses through each number, dividing it into 90 in turn. As you check with him later, you realize that he has tried all the numbers, right up to 90. What might the student have known that could have reduced the amount of work that he is doing?
15. Explain why division by zero is not defined. Use at least two different ways to demonstrate.
16. Define equality and explain how it is used in algebra.
17.
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