Questions and Answers
What is inductive reasoning?
The process of discovering rules.
What is deductive reasoning?
The process of applying rules.
What is a numeral?
A symbol used to express the idea of a number.
What does it mean if something is abstract?
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What does concrete mean in mathematics?
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What is a digit?
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What are counting (natural) numbers?
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What are integers?
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What are real numbers?
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What are imaginary numbers?
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What is the commutative property for addition?
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What is the commutative property for multiplication?
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What is the associative property for addition?
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What is the associative property for multiplication?
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What is the distributive property?
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What is the additive identity?
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What is the multiplicative identity?
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What is absolute value?
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What happens to the sign when multiplying or dividing like signs?
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What happens to the sign when multiplying or dividing unlike signs?
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What does absolute value symbol look like?
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What is algebraic subtraction?
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What does it mean to simplify a fraction?
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What is a ratio?
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What is a prime number?
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What is the numerator in a fraction?
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What is the denominator in a fraction?
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What does % stand for?
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Can you memorize these Fraction-Decimal-Percent conversions?
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What is the reciprocal of x?
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What does proportional mean?
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What is analogy?
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Study Notes
Reasoning Types
- Inductive reasoning involves discovering rules through patterns and observations.
- Deductive reasoning applies established rules to arrive at conclusions.
Number Concepts
- Numeral is a symbol representing a number.
- Counting (natural) numbers include numbers used for counting, starting from 1 and including 0.
- Whole numbers consist of natural numbers and negative numbers, known as integers.
- Real numbers encompass positive and negative numbers, including all decimals and fractions.
- Imaginary numbers result from square roots of negative numbers, represented by "i" where (i^2 = -1).
Mathematical Properties
- Commutative property states that the order of addition ( (a + b = c \Rightarrow b + a = c) ) and multiplication ( (ab = c \Rightarrow ba = c) ) does not affect the result.
- Associative property shows that regardless of how numbers are grouped, addition ( (a + b + c = (a + b) + c = a + (b + c)) ) and multiplication ( (a·b·c = (a·b)c = a(b·c)) ) yield the same outcome.
- Distributive property allows distribution of a multiplier across addition ( a(b+c) = ab + ac ).
Mathematical Identities
- Additive identity: ( a + 0 = a ), meaning any number plus zero remains unchanged.
- Multiplicative identity: ( a·1 = a ), meaning any number multiplied by one remains unchanged.
Value Concepts
- Absolute value measures the distance from zero and is always a positive number.
- Like signs in multiplication/division yield a positive result, while unlike signs yield a negative result.
Fraction Basics
- Fraction consists of a numerator (top part) and a denominator (bottom part).
- Ratio expresses the relative size between two quantities.
- Percent (%) represents a fraction per 100, facilitating easier comparisons.
Important Conversions
- Key fraction, decimal, and percent conversions include:
- ( 1/2 = 0.50, 50% )
- ( 1/4 = 0.25, 25% )
- ( 1/8 = 0.125, 12.5% )
- ( 1/3 = 0.3, 33.3% )
- ( 1/6 = 0.16, 16.6% )
- ( 1/5 = 0.2, 20% )
- ( 1/10 = 0.1, 10% )
Other Concepts
- Prime numbers are divisible only by themselves and 1 (e.g., 2, 3, 5, 7, 11).
- Reciprocal of x is defined as ( 1/x ).
- Proportional describes a relationship where there is a constant ratio between two variables.
- Analogy highlights similarity in specific aspects between different things.
Studying That Suits You
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Description
Test your understanding of key terms and definitions in Shormann Algebra 1 with these flashcards. This quiz covers important concepts like inductive and deductive reasoning as well as numeral definitions. Perfect for reinforcing your knowledge and preparing for exams.