Chapter 4 Highlights

1
Chapter 4 Highlights
2
Vocabulary

• Algebraic fraction

3
Vocabulary

• Algebraic fraction
• Base

4
Vocabulary

• Algebraic fraction
• Base
• Common multiples

5
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number

6
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible

7
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form

8
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form
• Exponent

9
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form
• Exponent
• Factor trees

10
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form
• Exponent
• Factor trees

• Factors

11
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form
• Exponent
• Factor trees

• Factors
• Greatest common factor (GCF)

12
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form
• Exponent
• Factor trees

• Factors
• Greatest common factor (GCF)
• Least common denominator

13
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form
• Exponent
• Factor trees

• Factors
• Greatest common factor (GCF)
• Least common denominator
• Monomial

14
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form
• Exponent
• Factor trees

• Factors
• Greatest common factor (GCF)
• Least common denominator
• Monomial
• Multiple

15
Vocabulary

• Algebraic fraction
• Base
• Common multiples
• Composite number
• Divisible
• Expanded form
• Exponent
• Factor trees

• Factors
• Greatest common factor (GCF)
• Least common denominator
• Monomial
• Multiple
• Negative exponents

16
Vocabulary

• Order of operations

17
Vocabulary

• Order of operations
• Powers

18
Vocabulary

• Order of operations
• Powers
• Prime factorization

19
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number

20
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number
• Product of powers

21
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number
• Product of powers

• Quotient of powers

22
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number
• Product of powers

• Quotient of powers
• Ratio

23
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number
• Product of powers

• Quotient of powers
• Ratio
• Simplest form

24
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number
• Product of powers

• Quotient of powers
• Ratio
• Simplest form
• Standard form

25
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number
• Product of powers

• Quotient of powers
• Ratio
• Simplest form
• Standard form
• Draw a diagram

26
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number
• Product of powers

• Quotient of powers
• Ratio
• Simplest form
• Standard form
• Draw a diagram
• Guess and check

27
Vocabulary

• Order of operations
• Powers
• Prime factorization
• Prime number
• Product of powers

• Quotient of powers
• Ratio
• Simplest form
• Standard form
• Draw a diagram
• Guess and check
• Look for a pattern

28
Understanding and using vocabulary

• Complete each statement.
• The greatest integer that is a factor of each of
  two or more integers is called their
  ________________ .

29
Understanding and using vocabulary

• Complete each statement.
• The greatest integer that is a factor of each of
  two or more integers is called their
  ________________ .
• Numbers that are expressed using exponents are
  called ____________ .

30
Understanding and using vocabulary

• Complete each statement.
• The greatest integer that is a factor of each of
  two or more integers is called their
  ________________ .
• Numbers that are expressed using exponents are
  called ____________ .
• The _________ of a whole number divide that
  number with a remainder of zero.

31
Understanding and using vocabulary

• Complete each statement.
• The greatest integer that is a factor of each of
  two or more integers is called their
  ________________ .
• Numbers that are expressed using exponents are
  called ____________ .
• The _________ of a whole number divide that
  number with a remainder of zero.
• A __________ is a whole number greater than one
  that has exactly two factors, 1 and itself.

32
Understanding and using vocabulary

• Complete each statement.
• The product of a number and any whole number is
  called a ___________ of the original number.

33
Understanding and using vocabulary

• Complete each statement.
• The product of a number and any whole number is
  called a ___________ of the original number.
• ___________ is writing numbers using place values
  and exponents.

34
Understanding and using vocabulary

• Complete each statement.
• The product of a number and any whole number is
  called a ___________ of the original number.
• ___________ is writing numbers using place values
  and exponents.
• The least common multiple of the denominators of
  two or more fractions is called the _____________.

35
Understanding and using vocabulary

• Complete each statement.
• The product of a number and any whole number is
  called a ___________ of the original number.
• ___________ is writing numbers using place values
  and exponents.
• The least common multiple of the denominators of
  two or more fractions is called the
  _____________.
• A ____________ is an integer, a variable, or a
  product of integers or variables.

36
Understanding and using vocabulary

• Complete each statement.
• The product of a number and any whole number is
  called a ___________ of the original number.
• ___________ is writing numbers using place values
  and exponents.
• The least common multiple of the denominators of
  two or more fractions is called the
  _____________.
• A ____________ is an integer, a variable, or a
  product of integers or variables.
• A comparison of two numbers by division is called
  a __________.

37
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863

38
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863 none

39
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635

40
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635 5

41
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200

42
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200 2, 3, 5, 6, 10

43
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577

44
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577 3

45
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577
• 40,180

46
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577
• 40,180 2, 5, 10

47
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577
• 40,180
• 582

48
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577
• 40,180
• 582 2, 3, 6

49
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577
• 40,180
• 582
• 5103

50
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577
• 40,180
• 582
• 5103 3

51
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577
• 40,180
• 582
• 5103
• 1962

52
Study Guide and Assessment Exercises

• Using divisibility rules, state whether each
  number is divisible by 2, 3, 5, 6, or 10.
• 863
• 635
• 4200
• 14,577
• 40,180
• 582
• 5103
• 1962 2, 3, 6

53
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666

54
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666 65

55
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)

56
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2) (c2)3

57
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)

58
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4) (-4)4

59
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1

60
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1 13 or 1

61
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1
• Write each power as a multiplication expression.
• (-16)3

62
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1
• Write each power as a multiplication expression.
• (-16)3 (-16) (-16) (-16)

63
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1
• Write each power as a multiplication expression.
• (-16)3
• K9

64
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1
• Write each power as a multiplication expression.
• (-16)3
• K9 K K K K K K K K K

65
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1
• Write each power as a multiplication expression.
• (-16)3
• K9
• (-w)4

66
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1
• Write each power as a multiplication expression.
• (-16)3
• K9
• (-w)4 (-w) (-w) (-w) (-w)

67
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1
• Write each power as a multiplication expression.
• (-16)3
• K9
• (-w)4
• 3211

68
Study Guide and Assessment Exercises

• Write each multiplication expression using
  exponents.
• 66666
• (c2) (c2) (c2)
• (-4) (-4) (-4) (-4)
• (11)1
• Write each power as a multiplication expression.
• (-16)3
• K9
• (-w)4
• 3211 32 32 32 32 32 32 32 32 32 32 32

69
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120

70
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120 22235

71
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114

72
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114 -12319

73
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114
• 630x3

74
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114
• 630x3 23357xxx

75
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114
• 630x3
• Find the GCF of each set of numbers or monomials.
• 70, 66

76
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114
• 630x3
• Find the GCF of each set of numbers or monomials.
• 70, 66 2

77
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114
• 630x3
• Find the GCF of each set of numbers or monomials.
• 70, 66
• 1092, 325

78
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114
• 630x3
• Find the GCF of each set of numbers or monomials.
• 70, 66
• 1092, 325 13

79
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114
• 630x3
• Find the GCF of each set of numbers or monomials.
• 70, 66
• 1092, 325
• 100x, 84xy, -76x2

80
Study Guide and Assessment Exercises

• Factor each number or monomial completely.
• 120
• -114
• 630x3
• Find the GCF of each set of numbers or monomials.
• 70, 66
• 1092, 325
• 100x, 84xy, -76x2 4x

81
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88

82
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88 9/11

83
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140

84
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140 19/20

85
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140
• 225/315

86
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140
• 225/315 5/7

87
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140
• 225/315
• Find the least common multiple of each set of
  numbers or algebraic expressions.
• 11ab, 6b

88
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140
• 225/315
• Find the least common multiple of each set of
  numbers or algebraic expressions.
• 11ab, 6b 66ab

89
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140
• 225/315
• Find the least common multiple of each set of
  numbers or algebraic expressions.
• 11ab, 6b
• 12, 4, 5

90
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140
• 225/315
• Find the least common multiple of each set of
  numbers or algebraic expressions.
• 11ab, 6b
• 12, 4, 5 60

91
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140
• 225/315
• Find the least common multiple of each set of
  numbers or algebraic expressions.
• 11ab, 6b
• 12, 4, 5
• 10j, 6jk, 3

92
Study Guide and Assessment Exercises

• Write each fraction in simplest form. If the
  fraction is already in simplest form, write
  simplified.
• 72/88
• 133/140
• 225/315
• Find the least common multiple of each set of
  numbers or algebraic expressions.
• 11ab, 6b
• 12, 4, 5
• 10j, 6jk, 3 30jk

93
Study Guide and Assessment Exercises

• Replace each _at_ with lt, gt, or to make each
  statement true.
• 6/7 _at_ 5/14

94
Study Guide and Assessment Exercises

• Replace each _at_ with lt, gt, or to make each
  statement true.
• 6/7 _at_ 5/14 gt

95
Study Guide and Assessment Exercises

• Replace each _at_ with lt, gt, or to make each
  statement true.
• 6/7 _at_ 5/14
• 9/16 _at_ 8/15

96
Study Guide and Assessment Exercises

• Replace each _at_ with lt, gt, or to make each
  statement true.
• 6/7 _at_ 5/14
• 9/16 _at_ 8/15 gt

97
Study Guide and Assessment Exercises

• Replace each _at_ with lt, gt, or to make each
  statement true.
• 6/7 _at_ 5/14
• 9/16 _at_ 8/15
• 9/100 _at_ 1/9

98
Study Guide and Assessment Exercises

• Replace each _at_ with lt, gt, or to make each
  statement true.
• 6/7 _at_ 5/14
• 9/16 _at_ 8/15
• 9/100 _at_ 1/9 lt

99
Study Guide and Assessment Exercises

• Replace each _at_ with lt, gt, or to make each
  statement true.
• 6/7 _at_ 5/14
• 9/16 _at_ 8/15
• 9/100 _at_ 1/9
• 1/11 _at_ 2/23

100
Study Guide and Assessment Exercises

• Replace each _at_ with lt, gt, or to make each
  statement true.
• 6/7 _at_ 5/14
• 9/16 _at_ 8/15
• 9/100 _at_ 1/9
• 1/11 _at_ 2/23 gt