Podcast
Questions and Answers
Where does 'the square root of 100' first appear in the real number system?
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?
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?
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?
Where does 'the opposite of the square root of 72' first appear in the real number system?
Signup and view all the answers
Where does '36/9' first appear in the real number system?
Where does '36/9' first appear in the real number system?
Signup and view all the answers
Where does the symbol 'pi' first appear in the real number system?
Where does the symbol 'pi' first appear in the real number system?
Signup and view all the answers
Where does '2 1/6' first appear in the real number system?
Where does '2 1/6' first appear in the real number system?
Signup and view all the answers
Where does '0' first appear in the real number system?
Where does '0' first appear in the real number system?
Signup and view all the answers
Where does '-5' first appear in the real number system?
Where does '-5' first appear in the real number system?
Signup and view all the answers
List ALL the sets to which each number belongs.
List ALL the sets to which each number belongs.
Signup and view all the answers
Identify the property for each equation or expression shown for 7.Associative, 8.Inverse, 9.Transitive, 10.Reflexive.
Identify the property for each equation or expression shown for 7.Associative, 8.Inverse, 9.Transitive, 10.Reflexive.
Signup and view all the answers
Identify the property for each equation or expression shown for 11.Identity, 12.Inverse, 13.Zero product, 14.Distributive.
Identify the property for each equation or expression shown for 11.Identity, 12.Inverse, 13.Zero product, 14.Distributive.
Signup and view all the answers
Identify the property for each equation or expression shown for 15.Commutative, 16.Symmetric.
Identify the property for each equation or expression shown for 15.Commutative, 16.Symmetric.
Signup and view all the answers
Solve for 26.
Solve for 26.
Signup and view all the answers
Solve for 14.
Solve for 14.
Signup and view all the answers
Solve for 5.
Solve for 5.
Signup and view all the answers
Solve for -15.
Solve for -15.
Signup and view all the answers
Solve for 5.
Solve for 5.
Signup and view all the answers
Solve for 9.
Solve for 9.
Signup and view all the answers
Solve for -48.
Solve for -48.
Signup and view all the answers
Solve for 1.
Solve for 1.
Signup and view all the answers
Solve for -2.
Solve for -2.
Signup and view all the answers
Solve for 13.
Solve for 13.
Signup and view all the answers
Translate the expression 7n + 3.
Translate the expression 7n + 3.
Signup and view all the answers
Translate the expression 2n-1.
Translate the expression 2n-1.
Signup and view all the answers
Translate & Solve: 'Four times the difference of a number and nine is -30'.
Translate & Solve: 'Four times the difference of a number and nine is -30'.
Signup and view all the answers
Translate & Solve: 'Five more than the quotient of a number and eight is 42'.
Translate & Solve: 'Five more than the quotient of a number and eight is 42'.
Signup and view all the answers
Translate & Solve: 'The auditorium can hold a maximum of 150 people'.
Translate & Solve: 'The auditorium can hold a maximum of 150 people'.
Signup and view all the answers
Translate & Solve: 'You must be at least 25 to rent a car'.
Translate & Solve: 'You must be at least 25 to rent a car'.
Signup and view all the answers
Solve for the expressions: -4n - 5, 4x - 12y + 4, -3x + 4, 8x - 29.
Solve for the expressions: -4n - 5, 4x - 12y + 4, -3x + 4, 8x - 29.
Signup and view all the answers
Solve for the equations: x = 6, x = -20.
Solve for the equations: x = 6, x = -20.
Signup and view all the answers
Solve for the equation: 3x - 7 = 11.
Solve for the equation: 3x - 7 = 11.
Signup and view all the answers
Solve and Graph for x < 3.
Solve and Graph for x < 3.
Signup and view all the answers
Solve and Graph for x >= -8.
Solve and Graph for x >= -8.
Signup and view all the answers
Solve and Graph for x <= 16.
Solve and Graph for x <= 16.
Signup and view all the answers
Solve and Graph for x < 7.
Solve and Graph for x < 7.
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
