Basic Algebra Chapter 1 Flashcards

Questions and Answers

What is a background set?

Any number in form a/b

A set within a set

The largest set of numbers (correct)

The smallest set of numbers

What is a subset?

A set within a set; a set whose elements are members of a larger set.

What are irrational numbers?

Non-repeating, non-terminating decimals.

What are rational numbers?

Any number in the form a/b, where a and b are both integers. Signup and view all the answers

What does the closure property of addition state?

a + b is real. Signup and view all the answers

What does the closure property of multiplication state?

ab is a real number. Signup and view all the answers

What is the associative property of addition?

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

What is the associative property of multiplication?

(ab)c = a(bc). Signup and view all the answers

What is the commutative property of addition?

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

What is the commutative property of multiplication?

ab = ba. Signup and view all the answers

What is the identity property of addition?

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

What is the identity property of multiplication?

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

What is the inverse property of addition?

a + (-a) = 0. Signup and view all the answers

What is the inverse property of multiplication?

a x (1/a) = 1. Signup and view all the answers

What does the distributive property of multiplication over addition express?

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

What is a variable?

A symbol, usually a letter, used to represent any member of a given set. Signup and view all the answers

What is an algebraic expression?

A variable, or the sum, difference, product or quotient of one or more variables. Signup and view all the answers

What does evaluating an expression involve?

Finding the simplest form of the expression after replacing each variable by a given number. Signup and view all the answers

What is a sum?

The result of adding numbers or variables. Signup and view all the answers

What are terms in an expression?

The numbers or variables being added or subtracted. Signup and view all the answers

What is a product?

The result of multiplying numbers, called factors, together. Signup and view all the answers

What is division?

The result of dividing one number by another; the result is the quotient. Signup and view all the answers

What is a mathematical model?

An equation used to represent a real-life situation. Signup and view all the answers

What is a power?

Product of equal factors. Signup and view all the answers

What is a base in mathematics?

The repeated factor. Signup and view all the answers

What does an exponent indicate?

The number of times the base occurs as a factor. Signup and view all the answers

What does simplifying an expression entail?

Replacing the expression with the simplest equivalent form. Signup and view all the answers

What is a literal equation?

An equation that contains one or more variables. Signup and view all the answers

Study Notes

Basic Algebra Concepts

Background Set: Refers to the largest set of numbers, specifically real numbers.
Subset: A collection of elements that belong to a larger set, encompassing all members of that larger set.

Types of Numbers

Irrational Numbers: Decimals that do not repeat or terminate, indicating non-repeating values.
Rational Numbers: Any number that can be expressed as a fraction a/b, where both a and b are integers.

Properties of Operations

Closure Property of Addition: The sum of two real numbers is always a real number (a + b is real).
Closure Property of Multiplication: The product of two real numbers is always a real number (ab is real).

Associative Properties

Associative Property of Addition: Grouping of numbers doesn't affect the sum: (a + b) + c = a + (b + c).
Associative Property of Multiplication: Grouping of numbers doesn't affect the product: (ab)c = a(bc).

Commutative Properties

Commutative Property of Addition: Order of addition does not matter: a + b = b + a.
Commutative Property of Multiplication: Order of multiplication doesn't change the result: ab = ba.

Identity Properties

Identity Property of Addition: Adding zero to a number leaves it unchanged: a + 0 = a.
Identity Property of Multiplication: Multiplying a number by one retains the original number: a x 1 = a.

Inverse Properties

Inverse Property of Addition: A number added to its opposite results in zero: a + (-a) = 0.
Inverse Property of Multiplication: A number multiplied by its reciprocal equals one: a x (1/a) = 1.

Distributive Property

Distributive Property of Multiplication Over Addition: Distributing multiplication across addition allows for both forms: a(b + c) = ab + ac and (a + b)c = ac + ab.

Basic Definitions

Variable: A symbol (often a letter) representing an element from a specified set, known as the domain or replacement set.
Algebraic Expression: Combines variables through addition, subtraction, multiplication, or division.
Evaluating the Expression: The process of simplifying an expression after substituting variables with specific values.

Mathematical Operations

Sum: The result obtained from the addition of numbers or variables.
Terms: Individual elements that are added or subtracted in an expression.
Product: The outcome of multiplying numbers together, known as factors.
Division: The operation of dividing one number by another, resulting in the quotient.

Applications and Models

Mathematical Model: An equation representing real-life situations through mathematical expressions.
Power: The product formed by multiplying equal factors.
Base: The number that is repeatedly multiplied in a power expression.
Exponent (Positive): Indicates how many times the base is used as a factor.

Simplifying Expressions

Simplifying an Expression: The process of transforming an expression into its simplest form by performing all possible operations.
Literal Equation: An equation involving one or more variables, emphasizing the role of letters in equations.

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Description

Test your understanding of essential algebra concepts with these flashcards from Chapter 1. This quiz covers fundamental definitions, including sets, rational numbers, and irrational numbers. Perfect for students looking to reinforce their algebra knowledge.