Section 1 1 Numbers and Their Properties OBJECTIV
Section 1. 1 Numbers and Their Properties
OBJECTIV ES A Write a set of numbers using roster or set–builder notation.
OBJECTIV ES B Write a rational number as a decimal.
OBJECTIV ES C Classify a number as natural, whole, integer, rational, irrational, or real.
OBJECTIV ES D Find the additive inverse of a number.
OBJECTIV ES E Find the absolute value of a number.
OBJECTIV ES F Given two numbers, use the correct notation to indicate equality or which is larger.
DEFINITION NATURAL NUMBERS The set of numbers used for counting.
DEFINITION WHOLE NUMBERS The set of natural numbers and zero.
DEFINITION INTEGERS The set of whole numbers and their opposites(negatives).
DEFINITION RATIONAL NUMBERS All numbers that can be written as the ratio of two integers.
DEFINITION IRRATIONAL NUMBERS Numbers that cannot be written as ratios of two integers.
DEFINITION REAL NUMBERS Numbers that are either rational or irrational:
DEFINITION ADDITIVE INVERSE The additive inverse(opposite) of a is –a.
DEFINITION ABSOLUTE VALUE The distance between a and 0 on the realnumber line
CAUTION The absolute value is always positive or zero.
DEFINITION TRICHOTOMY LAW If given any two real numbers, only one of three 1. a isthings equal tois b, true: denoted by a = b, or 2. a is less than b, denoted by a < b, or
Chapter 1 The Real Numbers Section 1. 1 A Practice Test Exercise #1
Use roster notation to list the natural numbers between 5 and 9. The set of natural numbers between 5 and 9 is {6, 7, 8} Note 5 and 9 are not included
Chapter 1 The Real Numbers Section 1. 1 B Practice Test Exercise #2
Chapter 1 The Real Numbers Section 1. 1 C Practice Test Exercise #3
Classify the given number by making a check mark ( ) in the appropriate row(s). Natural number Whole number Integer Rational number Irrational number Real number
Chapter 1 The Real Numbers Section 1. 1 D Practice Test Exercise #4
Chapter 1 The Real Numbers Section 1. 1 E Practice Test Exercise #5
Find:
Chapter 1 The Real Numbers 1. 1 F Practice Test Exercise #6
Fill in the blank with <, >, or = to make the resulting statement true:
Section 1. 2 Operations and Properties of Real Numbers
OBJECTIV ES A Add, subtract, multiply, and divide signed numbers.
OBJECTIV ES B Identify uses of the properties of the real numbers.
PROCEDURE TO ADD TWO NUMBERS WITH THE SAME SIGN: Add their absolute values and give the sum the common sign.
PROCEDURE TO ADD TWO NUMBERS WITH DIFFERENT SIGNS: 1. Find the absolute value. 2. Subtract the smaller from the greater number. 3. Use the sign of the number with the greater absolute
DEFINITION ADDITIVE IDENTITY For any real number a:
DEFINITION SUBTRACTION OF SIGNED NUMBERS If a and b are real numbers:
DEFINITION ADDITIVE INVERSE For any real number a:
PROCEDURE SIGNIFY MULTIPLICATION
PROCEDURE MULTIPLYING NUMBERS WITH OPPOSITE SIGNS To multiply a positive number by a negative number, multiply their absolute values and make the product negative.
DEFINITION SIGNS OF MULTIPLICATION PRODUCTS Same signs: Positive(+) Different signs: Negative( –)
DEFINITION IDENTITY FOR MULTIPLICATION For any real number a:
DEFINITION MULTIPLICATION OF FRACTIONS
DEFINITION DIVISION OF REAL NUMBERS If a and b are real numbers and b is not zero:
DEFINITION SIGNS OF A FRACTION For any real number a and nonzero real number b, there are two cases of signs:
DEFINITION ZERO IN DIVISION For a ≠ 0:
CAUTION
DEFINITION MULTIPLICATIVE INVERSE (RECIPROCAL) Every nonzero real number a has a reciprocal such that:
DEFINITION DIVISION OF FRACTIONS
Chapter 1 The Real Numbers Section 1. 2 A Practice Test Exercise #7
Find.
Chapter 1 The Real Numbers Section 1. 2 A Practice Test Exercise #8
Find.
Chapter 1 The Real Numbers Section 1. 2 A Practice Test Exercise #9
Find. Least common denominator = 8. Now add numerators.
Find. Least common denominator = 12.
Now add numerators.
Chapter 1 The Real Numbers Section 1. 2 A Practice Test Exercise #10
Find.
Chapter 1 The Real Numbers Section 1. 2 A Practice Test Exercise #11
Find. 1 1
Find. 1 4 1 3
Chapter 1 The Real Numbers Section 1. 2 B Practice Test Exercise #12
Name the property illustrated in the statement. Commutative Property of Addition Associative Property of Addition
Chapter 1 The Real Numbers Section 1. 2 B Practice Test Exercise #13
Name the property illustrated in the statement. Inverse Property of Multiplication. Inverse Property of Addition.
Section 1. 3 Properties of Exponents
OBJECTIV ES A Evaluate expressions containing natural numbers as exponents.
OBJECTIV ES B Write an expression containing negative exponents as a fraction.
OBJECTIV ES C Multiply and divide expressions containing exponents.
OBJECTIV ES D Raise a power to a power.
OBJECTIV ES E Raise a quotient to a power.
OBJECTIV F Convert between ES ordinary decimal notation and scientific notation, and use scientific notation in
DEFINITION EXPONENT AND BASE If a is a real number and n is a natural number:
Chapter 1 The Real Numbers Section 1. 3 A Practice Test Exercise #14
Evaluate.
Chapter 1 The Real Numbers Section 1. 3 B Practice Test Exercise #15
Write without negative exponents.
Chapter 1 The Real Numbers Section 1. 3 C Practice Test Exercise #16
Perform the indicated operation and simplify.
Perform the indicated operation and simplify.
Perform the indicated operation and simplify.
Chapter 1 The Real Numbers Section 1. 3 D, E Practice Test Exercise #17
Simplify.
Simplify.
Chapter 1 The Real Numbers Section 1. 3 F Practice Test Exercise #18
The exponent of 10, (– 3), means move the decimal point 3 places to the left.
Chapter 1 The Real Numbers Section 1. 3 F Practice Test Exercise #19
The exponent of 10, (5), means move the decimal point 5 places to the right.
Chapter 1 The Real Numbers Section 1. 3 F Practice Test Exercise #20
Perform the calculation and write your answer in scientific notation.
Perform the calculation and write your answer in scientific notation.
Section 1. 4 Algebraic Expressions and The Order of Operations
OBJECTIV ES A Evaluate numerical expressions with grouping symbols.
OBJECTIV ES B Evaluate expressions using the correct order of operations.
OBJECTIV ES C Evaluate algebraic expressions.
OBJECTIV ES D Use the distributive property to simplify expressions.
OBJECTIV ES E Simplify expressions by combining like terms.
OBJECTIV ES F Simplify expressions by removing grouping symbols and combining like terms.
PROCEDURE ORDER OF OPERATIONS 1. Do the operations in the (). 2. Evaluate exponential (MD) expressions. 3. Perform multiplications (AS) and divisions from left to right. P E
PROCEDURE Identity for Multiplication For any real number a:
PROCEDURE Additive Inverse For any real number a:
PROCEDURE Additive Inverse of a Sum
PROCEDURE Additive Inverse of a Difference
DEFINITION LIKE TERMS Constant terms or terms with exactly the same variable factors are called similar or like terms.
Chapter 1 The Real Numbers Section 1. 4 A Practice Test Exercise #21
Evaluate. 11 1
Chapter 1 The Real Numbers Section 1. 4 B Practice Test Exercise #22
Evaluate.
Chapter 1 The Real Numbers Section 1. 4 C Practice Test Exercise #23
Evaluate. a.
Evaluate. b.
Chapter 1 The Real Numbers Section 1. 4 D, E Practice Test Exercise #24
Simplify.
Chapter 1 The Real Numbers Section 1. 4 F Practice Test Exercise #25
Simplify.
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