Shormann Algebra 1 Quarterly Exam 1

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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?

Dealing with properties and ideas of things, regardless of feelings or emotions. Signup and view all the answers

What does concrete mean in mathematics?

It describes real objects. Signup and view all the answers

What is a digit?

Any of the Hindu-Arabic numerals 1 through 9, and 0. Signup and view all the answers

What are counting (natural) numbers?

Numbers used to count objects, including 1, 2, 3, and the number 0. Signup and view all the answers

What are integers?

Whole numbers, and all negative numbers. Signup and view all the answers

What are real numbers?

Any number used to describe a positive or negative number. Signup and view all the answers

What are imaginary numbers?

The result of taking the square root of a negative number. Signup and view all the answers

What is the commutative property for addition?

If a + b = c, then b + a = c. Signup and view all the answers

What is the commutative property for multiplication?

If ab = c, then ba = c. Signup and view all the answers

What is the associative property for addition?

(a + b) + c = a + (b + c). Signup and view all the answers

What is the associative property for multiplication?

(a·b)c = a(b·c). Signup and view all the answers

What is the distributive property?

a(b+c) = a·b + a·c. Signup and view all the answers

What is the additive identity?

a + 0 = a. Signup and view all the answers

What is the multiplicative identity?

a·1 = a. Signup and view all the answers

What is absolute value?

A number which describes the distance from zero. Signup and view all the answers

What happens to the sign when multiplying or dividing like signs?

It results in a positive answer. Signup and view all the answers

What happens to the sign when multiplying or dividing unlike signs?

It results in a negative answer. Signup and view all the answers

What does absolute value symbol look like?

Two vertical bars enclosing a number, like this: |a|. Signup and view all the answers

What is algebraic subtraction?

If a and b are real numbers, then a - b = a + (-b). Signup and view all the answers

What does it mean to simplify a fraction?

You can change the way any fraction looks without changing its value. Signup and view all the answers

What is a ratio?

The size of one thing relative to another. Signup and view all the answers

What is a prime number?

A number that is only divisible by itself and 1. Signup and view all the answers

What is the numerator in a fraction?

The top value in a fraction. Signup and view all the answers

What is the denominator in a fraction?

The bottom value in a fraction. Signup and view all the answers

What does % stand for?

Symbol for percent, which is an abbreviation for 'per 100'. Signup and view all the answers

Can you memorize these Fraction-Decimal-Percent conversions?

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%. Signup and view all the answers

What is the reciprocal of x?

1/x. Signup and view all the answers

What does proportional mean?

Having a constant ratio. Signup and view all the answers

What is analogy?

Resemblance in some particulars between things otherwise unalike. Signup and view all the answers

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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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.