Number Systems and Operations

10 Questions

Which property of natural numbers states that the order of the numbers does not change the result of an operation?

Commutativity

What is the identity element for addition of natural numbers?

Which type of sequence has a common difference between consecutive terms?

Arithmetic sequence

What is the equation of a rational number equation in standard form?

ax + by = c

Which of the following is NOT a property of natural numbers?

Transitivity

Which type of sequence is characterized by a common ratio between consecutive terms?

Geometric sequence

What is the Fibonacci sequence?

A sequence of integers in which each term is the sum of the two preceding terms

Which of the following is an example of an inconsistent equation?

2x + 2 = 2x + 2

Which operation on natural numbers is not commutative?

Subtraction

What is the purpose of solving equivalent equations?

To determine if two equations have the same solution

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
Subtraction:
- Not commutative: a - b ≠ b - a
- Not associative: (a - b) - c ≠ a - (b - c)
Multiplication:
- Commutative: a × b = b × a
- Associative: (a × b) × c = a × (b × c)
- Identity: a × 1 = a
Division:
- Not commutative: a ÷ b ≠ b ÷ a
- Not associative: (a ÷ b) ÷ c ≠ a ÷ (b ÷ c)

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, where a, b, and c are 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.