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Questions and Answers
What is an algebraic expression?
What is an algebraic expression?
- A multiplication problem
- A phrase involving numbers, variables, and operations (correct)
- An equation with no variables
- A set of numbers only
What is a coefficient?
What is a coefficient?
A number multiplied by a variable in an algebraic expression.
What does it mean to combine like terms?
What does it mean to combine like terms?
Adding or subtracting terms that have the same variable(s) and exponent(s).
The order in which numbers are added or multiplied changes the sum or product.
The order in which numbers are added or multiplied changes the sum or product.
What is a constant term?
What is a constant term?
The Distributive Property is expressed as ___
The Distributive Property is expressed as ___
What does it mean to expand an expression?
What does it mean to expand an expression?
What does it mean to factor an expression?
What does it mean to factor an expression?
What is the greatest common factor?
What is the greatest common factor?
What is a numerical expression?
What is a numerical expression?
What is the order of operations?
What is the order of operations?
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Study Notes
Algebraic Expressions
- An algebraic expression combines numbers, variables, and operations, functioning as a mathematical phrase.
Coefficients
- A coefficient represents a numerical factor multiplied by a variable within an expression.
Combining Like Terms
- Combining like terms involves the addition or subtraction of terms that share identical variables and exponents, simplifying expressions.
Commutative Property
- The Commutative Property states that changing the order of addition or multiplication does not affect the resulting sum or product.
Constant Terms
- A constant term consists of a numerical value without any associated variable, contributing a fixed quantity in expressions.
Distributive Property
- The Distributive Property exemplifies how to multiply a term by a sum: ( a(b + c) = ab + ac ).
Expanding an Expression
- Expanding an expression transforms it into a sum or difference of terms, clarifying its components.
Factoring an Expression
- Factoring involves rewriting an expression as a product of its factors, effectively transforming it into a multiplication problem.
Greatest Common Factor
- The greatest common factor is the largest number that can evenly divide two or more given numbers, crucial for simplifying fractions and expressions.
Numerical Expressions
- A numerical expression consists solely of numbers and mathematical operations, devoid of any variables.
Order of Operations
- The order of operations outlines a sequence for evaluating expressions, articulated by the acronym PEMDAS:
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction.
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