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Questions and Answers
Which property of natural numbers states that the order of the numbers does not change the result of an operation?
Which property of natural numbers states that the order of the numbers does not change the result of an operation?
What is the identity element for addition of natural numbers?
What is the identity element for addition of natural numbers?
Which type of sequence has a common difference between consecutive terms?
Which type of sequence has a common difference between consecutive terms?
What is the equation of a rational number equation in standard form?
What is the equation of a rational number equation in standard form?
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Which of the following is NOT a property of natural numbers?
Which of the following is NOT a property of natural numbers?
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Which type of sequence is characterized by a common ratio between consecutive terms?
Which type of sequence is characterized by a common ratio between consecutive terms?
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What is the Fibonacci sequence?
What is the Fibonacci sequence?
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Which of the following is an example of an inconsistent equation?
Which of the following is an example of an inconsistent equation?
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Which operation on natural numbers is not commutative?
Which operation on natural numbers is not commutative?
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What is the purpose of solving equivalent equations?
What is the purpose of solving equivalent equations?
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Study Notes
Properties Of Natural Numbers
- Closure: The result of an operation on natural numbers is always a natural number.
- Commutativity: The order of natural numbers does not change the result of an operation.
- Associativity: The order in which natural numbers are grouped does not change the result of an operation.
- Distributivity: The operation of multiplication can be distributed over addition.
Whole Number Operations
-
Addition:
- Commutative:
a + b = b + a - Associative:
(a + b) + c = a + (b + c) - Identity:
a + 0 = a
- Commutative:
-
Subtraction:
- Not commutative:
a - b ≠ b - a - Not associative:
(a - b) - c ≠ a - (b - c)
- Not commutative:
-
Multiplication:
- Commutative:
a × b = b × a - Associative:
(a × b) × c = a × (b × c) - Identity:
a × 1 = a
- Commutative:
-
Division:
- Not commutative:
a ÷ b ≠ b ÷ a - Not associative:
(a ÷ b) ÷ c ≠ a ÷ (b ÷ c)
- Not commutative:
Integer Sequences
- Arithmetic Sequences: A sequence of integers with a common difference between consecutive terms.
- Geometric Sequences: A sequence of integers with a common ratio between consecutive terms.
- Fibonacci Sequence: A sequence of integers in which each term is the sum of the two preceding terms (1, 1, 2, 3, 5, 8, ...).
Rational Number Equations
-
Solving Equations: Equations of the form
ax + by = c, wherea,b, andcare rational numbers. - Equivalent Equations: Equations that have the same solution(s).
- Inconsistent Equations: Equations that have no solution.
Irrational Number Approximations
- Decimal Approximation: Approximating an irrational number using a finite decimal expansion.
- Fractional Approximation: Approximating an irrational number using a fraction.
- Rounding: Approximating an irrational number by rounding it to a nearby rational number.
- Truncation: Approximating an irrational number by truncating its decimal expansion.
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Description
Test your knowledge of number systems, including properties of natural numbers, whole number operations, integer sequences, rational number equations, and irrational number approximations.
