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Questions and Answers
What does the symbol with a zero and a slash through it mean?
What does the symbol with a zero and a slash through it mean?
No solution
What property allows us to simplify the expression $5(2n - 9)$?
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?
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?
If the solution to an equation solved is ARN, what does this mean?
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What is a math problem that doesn't contain an equal sign or an inequality symbol called?
What is a math problem that doesn't contain an equal sign or an inequality symbol called?
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What is a letter used to represent a number in math?
What is a letter used to represent a number in math?
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What are the pieces or parts of an algebraic expression called?
What are the pieces or parts of an algebraic expression called?
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What do you call a math problem that contains an equal sign?
What do you call a math problem that contains an equal sign?
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What part of math studies finding unknown pieces of a math problem?
What part of math studies finding unknown pieces of a math problem?
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If terms have the same variable, they are referred to as what?
If terms have the same variable, they are referred to as what?
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What is the number in an expression that doesn't have any variables called?
What is the number in an expression that doesn't have any variables called?
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What is the process of gathering all terms that are the same called?
What is the process of gathering all terms that are the same called?
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The answer to an equation that has been solved is known as the?
The answer to an equation that has been solved is known as the?
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An equation that has no solution is called what?
An equation that has no solution is called what?
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An equation that has one solution is referred to as what?
An equation that has one solution is referred to as what?
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An equation that has infinite solutions is called an?
An equation that has infinite solutions is called an?
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What set of numbers includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers?
What set of numbers includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers?
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What is the term for doing some work or making a problem smaller in math?
What is the term for doing some work or making a problem smaller in math?
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What is the answer to a subtraction problem called?
What is the answer to a subtraction problem called?
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What is the name given to the square root symbol?
What is the name given to the square root symbol?
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What do you call the value raised to the 3rd power?
What do you call the value raised to the 3rd power?
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What is the set of numbers that includes 0, 1, 2, 3, ... called?
What is the set of numbers that includes 0, 1, 2, 3, ... called?
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What does the absolute value of a number represent?
What does the absolute value of a number represent?
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What is the answer to a multiplication problem called?
What is the answer to a multiplication problem called?
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What is the set of numbers that contains -3, -2, -1, 0, 1, 2, 3 called?
What is the set of numbers that contains -3, -2, -1, 0, 1, 2, 3 called?
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What is the answer to an addition problem called?
What is the answer to an addition problem called?
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What do you call a math problem that contains an inequality symbol?
What do you call a math problem that contains an inequality symbol?
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Division by zero is not possible; it is said to be __________.
Division by zero is not possible; it is said to be __________.
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What is a short way of writing multiplication of the same number called?
What is a short way of writing multiplication of the same number called?
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What is the answer to a division problem called?
What is the answer to a division problem called?
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What is the set of numbers that can be expressed as a fraction called?
What is the set of numbers that can be expressed as a fraction called?
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In the expression $4^3$, the 4 is referred to as the?
In the expression $4^3$, the 4 is referred to as the?
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What do you call a number that has a square root that's a whole number?
What do you call a number that has a square root that's a whole number?
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What is another name for counting numbers 1, 2, 3, ...?
What is another name for counting numbers 1, 2, 3, ...?
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What is a nickname for the second power?
What is a nickname for the second power?
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What is any number that cannot be written as a fraction called?
What is any number that cannot be written as a fraction called?
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In the expression $4^3$, the 3 is called the?
In the expression $4^3$, the 3 is called the?
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What is the term for the number inside of a square root symbol?
What is the term for the number inside of a square root symbol?
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What do we use when solving a math problem that has more than one operation?
What do we use when solving a math problem that has more than one operation?
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What are laws or rules in math called?
What are laws or rules in math called?
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What is the form of a number written with a decimal behind the first non-zero number, multiplied by a power of 10?
What is the form of a number written with a decimal behind the first non-zero number, multiplied by a power of 10?
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What does it mean to evaluate a problem in math?
What does it mean to evaluate a problem in math?
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If you do not see a number in front of a variable, what number can be put there?
If you do not see a number in front of a variable, what number can be put there?
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What property allows us to change $1x$ to just $x$?
What property allows us to change $1x$ to just $x$?
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What does the multiplication property of zero state?
What does the multiplication property of zero state?
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What do the commutative properties state?
What do the commutative properties state?
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What does the distributive property state?
What does the distributive property state?
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What do the associative properties allow in math?
What do the associative properties allow in math?
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What do the identity properties state?
What do the identity properties state?
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What does the multiplication property of -1 state?
What does the multiplication property of -1 state?
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What does the definition of division state?
What does the definition of division state?
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What do the inverse properties state about addition and multiplication?
What do the inverse properties state about addition and multiplication?
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What is the term for rewriting any subtraction problem as addition?
What is the term for rewriting any subtraction problem as addition?
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What does the transitive property state?
What does the transitive property state?
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What does the reflexive property state?
What does the reflexive property state?
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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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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!
