46 Chapter 1 Real Numbers and Algebraic Expressions 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 Sets and the Real Numbers 1. A(n) is a collection of objects. Each object in the is called a(n) or a(n) . 2. Sets can be represented in two ways: the method or notation. 3. The symbol denotes the of two sets. The symbol denotes the of two sets. 4. The set of numbers is 51, 2, 3, . . .6 . 5. The set of numbers is 50, 1, 2, 3, . . .6 . 6. The set of is 5 . . . , -3, -2, -1, 0, 1, 2, 3, . . .6 . 7. A(n) number is a number that can be written as the quotient of integers. 8. A(n) number is a number whose decimal form continues indefinitely without a repeating pattern. 9. We can graph or plot real numbers on a(n) . Numbers to the left of zero are numbers. Numbers to the right of zero are numbers. Zero is called the and is neither nor . 10. 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. 11. The of a number is the distance the number is from zero on the real number line. SECTION 1.2 Operations with Real Numbers and Algebraic Expressions 12. To add numbers with the same sign, add their and keep the the same. 13. To add numbers with different signs, subtract their . The sign of the answer has the same sign as the number with the . 14. Subtracting real numbers is the same as the of a number. In symbols, a - b = . 15. The product of real numbers with the same signs is . The product of real numbers with opposite signs is . 16. To divide real numbers is the same as by the , a ÷ b = . 17. Zero divided by a nonzero number is . A nonzero number divided by zero is . 18. A(n) indicates repeated multiplication. 19. In the expression bn, b is called the and n is called the . 20. A negative base raised to an even exponent is . 21. A negative base raised to an odd exponent is . 22. The of provides us a way to simplify numerical expressions. First, simplify what is in symbols, then simplify , or from left to right, and finally or from left to right. 23. A(n) represents an unknown number and is represented by a(n) . 24. A(n) is an expression that involves variables and/or numbers. 25. To evaluate an algebraic expression, replace the with the and simplify. SECTION 1.3 Properties of Real Numbers and Simplifying Algebraic Expressions 26. A(n) element is a number which leaves another number unchanged when an operation is performed on it. Zero is the . One is the . In symbols, a + = a and a · = a. 27. A(n) is a number which produces the identity element when an operation is performed on it. The additive inverse of number a is . The multiplicative inverse of a number a, a ≠ 0 is . In symbols, a + = 0 and a · = 1. 28. The property of real numbers states that the order in which we add or multiply real numbers doesn’t change the result. In symbols, a + b = and ab = . 29. The property of real numbers states that the grouping of the things being added or multiplied doesn’t change the result. In symbols, a + (b + c) = and a(bc) = . 30. The property enables us to multiply a number by a sum or difference. a(b + c) = . 31. The of a term is the number multiplied by the variable. 32. Terms that have identical variables raised to the same exponents are terms. 33. To combine like terms, add their and keep the the same. CHAPTER 1 / SUMMARY
hendricks_intermediate_algebra_1e_ch1_3
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