All Things Algebra Unit 1 Vocabulary

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Questions and Answers

What does the term 'set' refer to?

A type of equation

A single object in mathematics

A mathematical operation

A collection of objects such as numbers (correct)

What is an 'element' in the context of sets?

An object that is in the set.

Define 'subset'.

Consists of elements from the given set.

What is an 'identity' in algebra?

An equation that is true for all values of the variables. Signup and view all the answers

What does 'formula' mean in mathematics?

An equation that states a relationship between 1 quantity and 1 or more other quantities. Signup and view all the answers

Define 'literal equation'.

An equation where the letters represent both variables and known constants. Signup and view all the answers

What is an 'inequality'?

A relationship between 2 expressions that are not equal. Signup and view all the answers

What is 'compound inequality'?

Made up of 2 or more inequalities. Signup and view all the answers

Define 'absolute value'.

Distance from 0 on a number line. Signup and view all the answers

What is an 'irrational number'?

Can't be expressed as a ratio of 2 integers; nonterminating or non-repeating decimal. Signup and view all the answers

What defines a 'rational number'?

Can be written as a ratio or fraction of 2 integers. Signup and view all the answers

Define 'real number'.

Rational and/or irrational numbers. Signup and view all the answers

What is a 'natural number'?

A positive integer (not including 0). Signup and view all the answers

Define 'whole number'.

An integer that is 0 or greater. Signup and view all the answers

What defines an 'integer'?

The natural numbers, the negatives of these numbers, or 0. Signup and view all the answers

What is an 'equation'?

2 mathematical expressions set equal to one another using an equal sign. Signup and view all the answers

Define 'ascending order'.

Least to greatest. Signup and view all the answers

What does 'descending order' mean?

Greatest to least. Signup and view all the answers

What is the 'order of operations'?

Parenthesis-exponents-multiplication/division (left to right)-addition/subtraction (left to right). Signup and view all the answers

Define 'expression'.

One term or a group of terms and may include variables, constants, operators, and grouping symbols. Signup and view all the answers

Study Notes

Set Theory and Numbers

Set: A collection of objects such as numbers, used in mathematics to group related elements.
Element: An individual object within a set, essential for defining the contents of the set.
Subset: A smaller set formed from elements of a larger set, containing some or all elements.

Mathematical Concepts

Identity: An equation that holds true for all values of its variables, indicating a universal truth.
Formula: An equation establishing a relationship between one quantity and one or more other quantities, often used in calculations.
Literal Equation: An equation using letters to represent both variables and constants, commonly seen in algebraic expressions.

Inequalities

Inequality: A mathematical expression indicating that two values are not equal, involving greater than or less than relationships.
Compound Inequality: An expression formed from two or more inequalities, providing a range of possible solutions.

Number Types

Absolute Value: Represents the distance of a number from zero on a number line, regardless of direction (always non-negative).
Rational Number: A number that can be expressed as a fraction or ratio of two integers, including whole numbers and decimals that terminate or repeat.
Irrational Number: Cannot be expressed as a ratio of two integers; characterized by non-terminating, non-repeating decimal expansion.
Real Number: Encompasses both rational and irrational numbers, forming the entire set of numbers on the number line.
Natural Number: Positive integers starting from 1; does not include zero.
Whole Number: Non-negative integers, including zero.
Integer: The set of whole numbers both positive and negative, including zero.

Equations and Expressions

Equation: A mathematical statement where two expressions are set equal to each other, connected by an equal sign.
Expression: A combination of terms, which may involve variables, constants, operators, and parentheses, but does not include an equality sign.

Order and Operations

Ascending Order: Arrangement of numbers from least to greatest, useful in organizing data.
Descending Order: Arrangement of numbers from greatest to least, helpful in prioritizing values.
Order of Operations: The sequence to follow when evaluating expressions, typically parenthesis-first, then exponents, followed by multiplication/division (left to right), and finally addition/subtraction (left to right).

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