Math Finals Vocabulary Flashcards

Questions and Answers

What does the symbol with a zero and a slash through it mean?

No solution

What property allows us to simplify the expression $5(2n - 9)$?

Distributive

What are the three possible outcomes when solving an equation with variables on both sides?

No solution, ARN, One answer

If the solution to an equation solved is ARN, what does this mean?

You have infinite answers Signup and view all the answers

What is a math problem that doesn't contain an equal sign or an inequality symbol called?

Expression Signup and view all the answers

What is a letter used to represent a number in math?

Variable Signup and view all the answers

What are the pieces or parts of an algebraic expression called?

Terms Signup and view all the answers

What do you call a math problem that contains an equal sign?

Equation Signup and view all the answers

What part of math studies finding unknown pieces of a math problem?

Algebra Signup and view all the answers

If terms have the same variable, they are referred to as what?

Like terms Signup and view all the answers

What is the number in an expression that doesn't have any variables called?

Constant Signup and view all the answers

What is the process of gathering all terms that are the same called?

Collecting Signup and view all the answers

The answer to an equation that has been solved is known as the?

Solution Signup and view all the answers

An equation that has no solution is called what?

Inconsistent Signup and view all the answers

An equation that has one solution is referred to as what?

Independent Signup and view all the answers

An equation that has infinite solutions is called an?

Identity Signup and view all the answers

What set of numbers includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers?

Real numbers Signup and view all the answers

What is the term for doing some work or making a problem smaller in math?

Simplify Signup and view all the answers

What is the answer to a subtraction problem called?

Difference Signup and view all the answers

What is the name given to the square root symbol?

Radical Signup and view all the answers

What do you call the value raised to the 3rd power?

Cubed Signup and view all the answers

What is the set of numbers that includes 0, 1, 2, 3, ... called?

Whole numbers Signup and view all the answers

What does the absolute value of a number represent?

The number of spaces from zero Signup and view all the answers

What is the answer to a multiplication problem called?

Product Signup and view all the answers

What is the set of numbers that contains -3, -2, -1, 0, 1, 2, 3 called?

Integers Signup and view all the answers

What is the answer to an addition problem called?

Sum Signup and view all the answers

What do you call a math problem that contains an inequality symbol?

Inequality Signup and view all the answers

Division by zero is not possible; it is said to be __________.

Undefined Signup and view all the answers

What is a short way of writing multiplication of the same number called?

Powers Signup and view all the answers

What is the answer to a division problem called?

Quotient Signup and view all the answers

What is the set of numbers that can be expressed as a fraction called?

Rational Signup and view all the answers

In the expression $4^3$, the 4 is referred to as the?

Base Signup and view all the answers

What do you call a number that has a square root that's a whole number?

Perfect square Signup and view all the answers

What is another name for counting numbers 1, 2, 3, ...?

Natural numbers Signup and view all the answers

What is a nickname for the second power?

Squared Signup and view all the answers

What is any number that cannot be written as a fraction called?

Irrational Signup and view all the answers

In the expression $4^3$, the 3 is called the?

Exponent Signup and view all the answers

What is the term for the number inside of a square root symbol?

Radicand Signup and view all the answers

What do we use when solving a math problem that has more than one operation?

Order of operations Signup and view all the answers

What are laws or rules in math called?

Properties Signup and view all the answers

What is the form of a number written with a decimal behind the first non-zero number, multiplied by a power of 10?

Scientific Notation Signup and view all the answers

What does it mean to evaluate a problem in math?

To find the solution Signup and view all the answers

If you do not see a number in front of a variable, what number can be put there?

1 Signup and view all the answers

What property allows us to change $1x$ to just $x$?

Identity Signup and view all the answers

What does the multiplication property of zero state?

That any number multiplied by zero is zero Signup and view all the answers

What do the commutative properties state?

That it is ok to move the terms in addition and factors in multiplication Signup and view all the answers

What does the distributive property state?

That multiplication on the outside of parentheses can be applied to each term inside Signup and view all the answers

What do the associative properties allow in math?

To move or adjust parentheses in operations Signup and view all the answers

What do the identity properties state?

That anything added to zero remains the same and anything multiplied by one remains unchanged Signup and view all the answers

What does the multiplication property of -1 state?

That multiplying by -1 gives the opposite of the number Signup and view all the answers

What does the definition of division state?

That every division problem can be rewritten as a multiplication problem Signup and view all the answers

What do the inverse properties state about addition and multiplication?

That a number plus its opposite equals zero, and a number times its reciprocal equals one Signup and view all the answers

What is the term for rewriting any subtraction problem as addition?

Definition of subtraction Signup and view all the answers

What does the transitive property state?

That if two things are equal to the same thing, they are equal to each other Signup and view all the answers

What does the reflexive property state?

That anything is equal to itself Signup and view all the answers

Study Notes

Mathematical Terms and Definitions

The symbol with a zero and a slash indicates "no solution."
The distributive property allows simplification of expressions such as 5(2n-9).
When solving equations with variables on both sides, outcomes include no solution, infinitely many solutions (ARN), or one distinct solution.
An equation with infinitely many solutions is referred to as ARN (All Real Numbers).
An expression is a mathematical phrase that does not include an equal sign or inequality symbol.
A variable is a letter that represents a number in mathematical expressions.

Structure of Expressions and Equations

Terms are the parts of an algebraic expression.
An equation contains an equal sign, representing a statement of equality.
Algebra involves finding unknown values in math problems.
Like terms share the same variables in algebraic expressions.
A constant is a term without any variable.

Solving Equations

Collecting is the process of combining like terms in an expression.
The solution is the answer obtained when an equation is solved.
An inconsistent equation has no solutions.
An independent equation has one solution.
An identity equation has infinite solutions.

Number Sets and Types

Real numbers include natural numbers, whole numbers, integers, rational and irrational numbers.
Whole numbers consist of non-negative integers starting from 0.
Integers include negative numbers, zero, and positive numbers.
Rational numbers can be expressed as fractions.
Irrational numbers cannot be expressed as fractions.

Operations and Properties

Simplifying refers to reducing complexity in a problem.
The difference is the result of a subtraction operation.
A radical is the square root symbol used in mathematics.
Cubed denotes a number raised to the third power, while a number raised to the second power is called squared.
The absolute value measures the distance of a number from zero.

Powers and Roots

The base is the number used as a factor in an expression raised to a power.
A perfect square has a square root that is a whole number, for example, 4, 9, 16, and 25.
In the expression 4 to the 3rd power, 4 is considered the base and 3 is the exponent.

Evaluation and Notation

Order of operations is crucial when solving problems involving multiple operations.
Scientific notation expresses numbers as a product of a decimal and a power of ten.
Evaluating means to compute or find the answer to a mathematical problem.

Mathematical Properties

The number 1 can be considered a multiplicative identity, as multiplying any number by 1 leaves it unchanged.
The multiplication property of zero states anything multiplied by zero equals zero.
The commutative property allows the rearrangement of terms in addition or multiplication.
The associative property enables grouping changes in addition and multiplication without altering the result.
The transitive property asserts that if two things are both equal to a third, they are equal to each other.
The reflexive property states that any quantity is equal to itself.

Additional Properties

The inverse property highlights that adding a number and its negative results in zero, while multiplying a number by its reciprocal yields one.
The definition of division states that division can be expressed as multiplication by the reciprocal.

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Description

Test your knowledge with these vocabulary flashcards designed for Math Finals. Each card contains definitions of key mathematical terms and properties that are essential for understanding algebraic concepts. Prepare yourself for success in your math exams!