Algebra Foundations Vocabulary

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Questions and Answers

What is the definition of absolute value?

The opposite of a number

The distance from zero on the number line (correct)

A number that can be expressed as a ratio

A constant value

What is the additive identity?

What is the additive inverse?

The opposite or negative of a number

What is an algebraic expression?

A mathematical expression containing one or more variables Signup and view all the answers

What does the associative property state?

How numbers are grouped in a sum or product does not change the value Signup and view all the answers

What is the base in an exponential expression?

The number which is repeated as a factor Signup and view all the answers

What is a coefficient?

The constant preceding the variables in a product Signup and view all the answers

What does the commutative property state?

The order in which numbers are added or multiplied does not change the value Signup and view all the answers

What is a constant?

A numerical value; a term containing no variables Signup and view all the answers

What is the distributive property?

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

What does it mean to evaluate an expression?

To find the numerical value of Signup and view all the answers

What is an exponent?

The superscript number in an exponential expression; it tells how many times a factor is repeated Signup and view all the answers

What is an expression?

A mathematical phrase that cannot be proved true or false Signup and view all the answers

What is an integer?

A number belonging to the set made up of whole numbers and their opposites Signup and view all the answers

What is an irrational number?

A number with an infinite decimal representation that does not repeat Signup and view all the answers

What are like terms?

Terms that have the same variable(s), with each variable raised to the same exponent Signup and view all the answers

What is the multiplicative inverse?

The reciprocal of a number; if x is a number other than zero, then 1/x is the multiplicative inverse Signup and view all the answers

What is a natural number?

A number belonging to the set made up of the numbers that are used to count: 1, 2, 3, and so on Signup and view all the answers

What is a rational number?

A number that can be written as a ratio of two integers in the form A/B with B ≠ 0 Signup and view all the answers

What is substitution in algebra?

Replacing a quantity with its equal Signup and view all the answers

What is a term in mathematics?

A number or a variable, or an indicated product of a number and variable(s) Signup and view all the answers

What is a whole number?

A number belonging to the set made up of zero and the natural numbers Signup and view all the answers

Study Notes

Algebra Foundations Vocabulary

Absolute Value: Represents the distance of a number from zero on the number line, regardless of direction.
Additive Identity: The number zero; adding it to any real number does not change the value of that number.
Additive Inverse: The inverse of a number that results in zero when added; for example, the additive inverse of 5 is -5.
Algebraic Expression: A combination of numbers, variables, and arithmetic operations, but does not have an equality sign.
Associative Property: States that the way numbers are grouped in addition or multiplication does not affect the outcome, e.g., (a + b) + c = a + (b + c).
Base: In an exponential expression, the base is the number that gets multiplied by itself.
Coefficient: A constant factor that multiplies a variable in a term; for instance, in 3x, 3 is the coefficient.
Commutative Property: Indicates that the order of addition or multiplication does not alter the result, e.g., a + b = b + a.
Constant: A specific numeric value that does not change; can be a standalone term without variables.
Distributive Property: Shows how to multiply a single term by terms in parentheses, expressed as a(b + c) = ab + ac.
Evaluate: The process of calculating the numerical value of an expression.
Exponent: The superscript indicating how many times the base is multiplied by itself; for example, in x^3, 3 is the exponent.
Expression: A mathematical phrase composed of numbers, variables, and operators, but lacking an equality statement.
Integer: Any whole number, including negatives, zero, and positive numbers, forming a complete set: {..., -3, -2, -1, 0, 1, 2, 3, ...}.
Irrational Number: A number that cannot be expressed as a simple fraction; it has a non-repeating, non-terminating decimal (e.g., π or √2).
Like Terms: Terms that share the same variables raised to identical powers; they can be combined in algebraic expressions.
Multiplicative Inverse: The reciprocal of a number; for any number x, the multiplicative inverse is 1/x, and their product equals one (1).
Natural Number: Positive integers beginning from one onward, used primarily for counting: 1, 2, 3, ...
Rational Number: Any number that can be expressed as a fraction, where both numerator and denominator are integers, and the denominator is not zero.
Substitution: The process of replacing a variable with its equivalent value in an equation or expression.
Term: The individual components of an expression that can be a number, a variable, or a product of both.
Whole Number: A number in the set that includes zero and all natural numbers, defined as non-negative integers.

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Test your knowledge of essential algebra vocabulary terms with this quiz. Learn about concepts such as absolute value, additive identity, and more to strengthen your algebra skills. Perfect for students looking to solidify their understanding of foundational algebra terminology.