CHAPTER 1 / SUMMARY How well do you know this chapter? Complete the following questions to find out. Take a look back at the section if you need help. SECTION 1.1 The Set of Real Numbers 1. A(n) is a collection of objects. 2. The set of numbers is {1, 2, 3, . . .}. 3. The set of numbers is {0, 1, 2, 3, . . .}. 4. The set of is the set of positive and negative whole numbers. 5. A(n) number is a number that can be written as the quotient of integers. 6. A(n) number is a number whose decimal form continues indefinitely without a repeating pattern. 7. The statement a < b is read as a b. The statement a > b is read as a b. 8. The of a number is a number with the same distance from zero but lies on the other side of zero on the number line. 9. The of a number is the distance the number is from zero on the real number line. SECTION 1.2 Fractions Review 10. A number with factors of 1 and the number itself is a(n) number. 11. A fraction is a(n) of numbers. The top is called the and the bottom is called the . 12. A fraction is in if the top and bottom of the fraction do not have any common factors. 13. The of enables us to divide the top and bottom of the fraction by their common factor. a · c b · c = . 14. The numbers a and 1 a are . 15. To divide fractions, by the of the second fraction. 16. We can add or subtract fractions with denominators. 17. The is the number that all denominators divide into evenly. SECTION 1.3 The Order of Operations, Algebraic Expressions, and Equations 18. A(n) indicates repeated multiplication. 19. In the expression bn, b is called the and n is called the or . 20. The of provides us a way to simplify numerical expressions. First, simplify what is in symbols, then evaluate , or from left to right, and finally or from left to right. 21. A(n) represents an unknown number and is represented by a . 22. A(n) is an expression that involves variables and/or numbers. 23. To evaluate an algebraic expression, replace the with the and simplify. 24. A statement that two expressions are equal is a(n) . 25. A(n) of an equation is a value that makes the equation true. SECTION 1.4 Addition of Real Numbers 26. To add numbers with the same sign, add their and keep the the same. 27. To add numbers with different signs, subtract their . The sign of the answer has the same sign as the number with the . SECTION 1.5 Subtraction of Real Numbers 28. Subtracting real numbers is the same as the of a number. a - b = . SECTION 1.6 Multiplication and Division of Real Numbers 29. The product of real numbers with the same signs is . The product of real numbers with opposite signs is . 30. A negative base raised to an even power is . 31. A negative base raised to an odd power is . 32. To divide real numbers is the same as by the . a ÷ b = . 33. Zero divided by a nonzero number is . A number divided by zero is . SECTION 1.7 Properties of Real Numbers 34. The property of addition states that changing the order of the things being added doesn’t change the result. a + b = . 35. The property of addition states that the grouping of the things being added doesn’t change the result. a + (b + c) = . 36. is the identity element of addition. 37. The property of addition states that adding to a number doesn’t change its value. a + = a. 38. The property of addition states that adding a number and its is zero. a + = 0. 39. The property of multiplication states that changing the order of the things being multiplied doesn’t change the result. ab = . 86 Chapter 1 Real Numbers and Algebraic Expressions
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