Foundations of Algebra Chapter 1 Flashcards

Questions and Answers

What is a variable?

A whole number and its opposites

The process for evaluating a math problem

An amount that can be counted or measured

A symbol that represents one or more numbers (correct)

What are integers?

Whole numbers and their opposites

What is the Order of Operations?

The process for evaluating a math problem

What defines real numbers?

Rational or irrational numbers Signup and view all the answers

What is the Additive Inverse of a number?

The opposite of any number is -a Signup and view all the answers

What does it mean to evaluate an expression?

To substitute a given number for each variable and then simplify Signup and view all the answers

What does simplify mean?

To replace an expression with its simplest name or form Signup and view all the answers

What are Equivalent Expressions?

Equations that have the same solution Signup and view all the answers

What is an algebraic expression?

A mathematical phrase that includes one or more variables Signup and view all the answers

What is a coefficient?

The numerical factor when a term has a variable Signup and view all the answers

What is meant by 'like terms'?

Terms with exactly the same variable factors in a variable expression Signup and view all the answers

What is a quantity?

An amount that can be counted or measured Signup and view all the answers

What is a numerical expression?

A mathematical phrase involving numbers and operations symbols, but no variables Signup and view all the answers

What is a power in mathematics?

The base and the exponent of an expression of the form a raised to the n Signup and view all the answers

What is an exponent?

A number that shows repeated multiplication Signup and view all the answers

What is the base in an expression?

A number that is multiplied repeatedly Signup and view all the answers

What is a radicand?

The number or expression inside a radical symbol Signup and view all the answers

What is a radical?

A symbol which is used to indicate square roots Signup and view all the answers

What is a rational number?

A number that can be written as a fraction Signup and view all the answers

What are natural numbers?

The set of numbers 1, 2, 3, 4,... Also called counting numbers Signup and view all the answers

What defines whole numbers?

Natural numbers (counting numbers) and zero Signup and view all the answers

What is an irrational number?

Any real number that can't be expressed as a fraction of two integers Signup and view all the answers

What is absolute value?

The distance a number is from zero on a number line, ALWAYS POSITIVE Signup and view all the answers

What is the opposite of a number?

Two numbers that are of equal distance from 0 on the number line in opposite directions Signup and view all the answers

What is the reciprocal or multiplicative inverse?

One of a pair of numbers whose product is 1 Signup and view all the answers

What is the Distributive Property?

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

What is a constant in algebra?

A term that has no variable Signup and view all the answers

What is an open sentence in mathematics?

An equation with one or more variables Signup and view all the answers

What is an equation?

A mathematical sentence that contains an equals sign Signup and view all the answers

What is a solution of an equation (one variable)?

A value for a variable that makes an equation true Signup and view all the answers

What is a solution of an equation (two variables)?

Any ordered pair (x,y) that makes the equation true Signup and view all the answers

What is a square root?

The square root of x is the number that, when multiplied by itself, gives x Signup and view all the answers

What is a perfect square?

A square of a whole number Signup and view all the answers

What is an inequality?

A mathematical expression that compares the values of two expressions using an inequality symbol Signup and view all the answers

Study Notes

Key Algebra Concepts

Variable: Symbol (typically a letter) representing one or more numbers. Essential for forming equations and expressions.
Integers: Collection of whole numbers including both positive and negative values, along with zero.
Order of Operations: Established process to evaluate mathematical expressions (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Real Numbers: Complete set of numbers encompassing both rational (fractions, integers) and irrational numbers (non-repeating, non-terminating decimals).
Additive Inverse: For any number 'a', its additive inverse is '-a', such that their sum equals zero.
Evaluate: Substituting numbers for given variables and simplifying the expression.
Simplify: Process of reducing a mathematical expression to its most basic form.
Equivalent Expression: Different expressions that yield the same value for their respective variables.
Algebraic Expressions: Composed of numerical values, variables, and operations, these phrases do not have an equality sign.
Coefficient: Number in front of a variable in a term, indicating how many times the variable is multiplied.
Term: Units in an expression that can be a single number, variable, or a combination of numbers and variables.
Like Terms: Terms that share exactly the same variable(s) raised to the same power, allowing for them to be combined.

Types of Numbers

Quantity: A measurable or countable amount.
Numerical Expression: Consists solely of numbers and operational symbols without any variables.
Power: Represents a number multiplied by itself a defined number of times, characterized by a base and an exponent.
Exponent: Indicates how many times to multiply the base by itself.
Base: The number that is repeatedly multiplied in a power expression.
Radicand: The number or expression located under a radical sign, indicating the value to extract the root from.
Radical: Symbol used to denote the square root or other roots of a number.
Rational Number: Any number expressible as a fraction where both numerator and denominator are integers.
Natural Numbers: Counting numbers starting from 1 (1, 2, 3,...).
Whole Numbers: Combination of natural numbers and zero (0, 1, 2, 3,...).
Irrational Number: Cannot be expressed as a fraction of two integers; represented by non-terminating, non-repeating decimals.
Absolute Value: The distance of a number from zero on a number line, always expressed as a positive value.
Opposite: Two numbers that are symmetrically located relative to zero on the number line.
Reciprocal (Multiplicative Inverse): For any non-zero number, the reciprocal is a number which when multiplied with the original equals one (e.g., the reciprocal of 2/3 is 3/2).

Key Algebra Properties

Distributive Property: A critical algebraic principle that allows for distribution of multiplication over addition (a(b + c) = ab + ac).
Constant: A value that remains fixed; it does not change or contain any variables.
Open Sentence: An equation featuring one or more variables, indicating that it may hold different truths based on the variable's value.
Equation: A mathematical statement asserting that two expressions are equal (represented with an equals sign).
Solution of an Equation (one variable): Specific value assigned to a variable that makes the equation valid.
Solution of an Equation (two variables): Any ordered pair (x,y) that satisfies the equality of the equation.
Square Root: A value which, when multiplied by itself, retrieves the original number (e.g., √4 = 2).
Perfect Square: The result of squaring a whole number (e.g., 1, 4, 9 are perfect squares).
Inequality: Mathematical expressions that show the comparative relationships between two values or expressions using inequality symbols (>, <, ≥, ≤).

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Enhance your understanding of the foundational concepts of algebra with these flashcards covering key terms like variables, integers, and the order of operations. Perfect for students starting their journey in algebra, this quiz will help reinforce essential definitions and concepts. Test your knowledge and get ready for more advanced topics!