Questions and Answers
Where does 'the square root of 100' first appear in the real number system?
Natural Number
Where does '-0.2222....' first appear in the real number system?
Rational Number because it is a repeating decimal
Where does 'the square root of 4/9' first appear in the real number system?
Rational Number because it equals 2/3
Where does 'the opposite of the square root of 72' first appear in the real number system?
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Where does '36/9' first appear in the real number system?
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Where does the symbol 'pi' first appear in the real number system?
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Where does '2 1/6' first appear in the real number system?
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Where does '0' first appear in the real number system?
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Where does '-5' first appear in the real number system?
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List ALL the sets to which each number belongs.
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Identify the property for each equation or expression shown for 7.Associative, 8.Inverse, 9.Transitive, 10.Reflexive.
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Identify the property for each equation or expression shown for 11.Identity, 12.Inverse, 13.Zero product, 14.Distributive.
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Identify the property for each equation or expression shown for 15.Commutative, 16.Symmetric.
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Solve for 26.
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Solve for 14.
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Solve for 5.
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Solve for -15.
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Solve for 5.
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Solve for 9.
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Solve for -48.
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Solve for 1.
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Solve for -2.
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Solve for 13.
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Translate the expression 7n + 3.
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Translate the expression 2n-1.
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Translate & Solve: 'Four times the difference of a number and nine is -30'.
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Translate & Solve: 'Five more than the quotient of a number and eight is 42'.
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Translate & Solve: 'The auditorium can hold a maximum of 150 people'.
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Translate & Solve: 'You must be at least 25 to rent a car'.
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Solve for the expressions: -4n - 5, 4x - 12y + 4, -3x + 4, 8x - 29.
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Solve for the equations: x = 6, x = -20.
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Solve for the equation: 3x - 7 = 11.
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Solve and Graph for x < 3.
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Solve and Graph for x >= -8.
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Solve and Graph for x <= 16.
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Solve and Graph for x < 7.
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Study Notes
Number Types and Their Properties
- Natural Numbers: Non-negative integers starting from 1; includes numbers like 1, 2, 3, …
- Rational Numbers: Can be expressed as a fraction (p/q) where p and q are integers and q ≠ 0; includes repeating or terminating decimals.
- Irrational Numbers: Cannot be expressed as a simple fraction; non-repeating, non-terminating decimals like pi or the square root of non-perfect squares.
- Whole Numbers: Includes all natural numbers and zero (0, 1, 2, 3,…).
- Integers: All positive and negative whole numbers (…, -3, -2, -1, 0, 1, 2, 3,…).
Identifying Numbers in the Real Number System
- The square root of 100 equals 10, classifying it as a natural number.
- The number -0.2222... is a rational number because it is a repeating decimal.
- The square root of 4/9 equals 2/3, also a rational number.
- The opposite of the square root of 72 is an irrational number since 72 is not a perfect square.
- The division of 36 by 9 equals 4, qualifying as a natural number.
Additional Key Concepts
- The symbol pi (π) is classified as an irrational number due to its infinite decimal expansion.
- The mixed fraction 2 1/6 is rational as it can be transformed into a simple fraction.
Properties of Operations and Relations
- Associative Property: Indicates that the grouping of numbers does not affect the result (e.g., (a+b)+c = a+(b+c)).
- Inverse Property: Relates to operations that return to the identity element (adding a number and its negative).
- Transitive Property: If a=b and b=c, then a=c.
- Reflexive Property: Any number is equal to itself (a=a).
- Identity Property: Adding zero or multiplying by one yields the number itself.
- Zero Product Property: If the product of two factors is zero, at least one of the factors must be zero.
- Distributive Property: a(b + c) = ab + ac.
- Commutative Property: The order of addition or multiplication does not matter (a+b = b+a).
- Symmetric Property: If a=b, then b=a.
Solving and Translating Expressions
- Solving linear equations involves isolating the variable to find specific values that satisfy the equation.
- Example expressions to translate include:
- "Four times the difference of a number and nine is -30" translates to 4(x - 9) = -30.
- "Five more than the quotient of a number and eight is 42" translates to 5 + (x/8) = 42.
- Inequalities can be solved similarly, with graphing indicating the range of possible values (e.g., x < 3).
Graphical Representation of Inequalities
- For expressions like x < 3, an open circle indicates that 3 is not included in the solution.
- A closed circle is used for inequalities that include the endpoint, such as x ≥ -8.
Summary of Variables and Solutions
- Various constants and variables can be solved (e.g., x = -64, x = 6).
- Translating between word problems and algebraic equations is key for understanding and solving mathematical statements effectively.
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Description
Test your knowledge on the fundamentals of algebra with this review quiz focused on natural and rational numbers. Each question provides a definition to help clarify concepts in the real number system. Perfect for reinforcing your understanding of foundational algebra principles.
