Questions and Answers
What is a variable?
What is an algebraic expression?
A mathematical phrase consisting of numbers, variables, and operation or grouping symbols.
What defines an equation?
A mathematical statement that two expressions have the same value.
The Commutative Property of Addition states that changing the order of addends does change their sum.
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State the Associative Property of Addition.
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What does the Distributive Property state?
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Study Notes
Variables
- Quantities that can change or vary.
- Can be represented by symbols such as 𝑥 or 𝑦.
- Represent either specific numbers or a set of numbers that solve an algebraic expression.
Algebraic Expressions
- Mathematical phrases made up of numbers, variables, and operation symbols.
- Example: 4𝑥 + 3𝑦 − 2(𝑥 + 𝑧) demonstrates combining terms and variables.
Equations
- Mathematical statements asserting that two expressions hold the same value.
- Examples include:
- 4𝑎 + 4 = 125
- 𝑥² + 3𝑥 + 6 = 0
- 2𝑛 = 8, showcasing various forms of equations.
Commutative Property of Addition
- States that the order of addends does not affect the sum.
- Mathematically expressed as 𝑎 + 𝑏 = 𝑏 + 𝑎.
- Example with numbers: 25 + 58 + 75 can be rearranged as 25 + 75 + 58, simplifying the calculation to 158.
Associative Property of Addition
- Indicates that the grouping of numbers does not change the sum.
- Expressed as (𝑎 + 𝑏) + 𝑐 = 𝑎 + (𝑏 + 𝑐).
- Example: (2 + 3) + 5 = 2 + (3 + 5) shows flexibility in grouping.
Distributive Property
- Describes how to multiply a single term by a sum of terms, maintaining equality.
- Formulated as 𝑥(𝑦 + 𝑧) = 𝑥𝑦 + 𝑥𝑧.
- Examples:
- 3(4 + 2) = 3⋅4 + 3⋅2
- 5(1 + 8) = 5⋅1 + 5⋅8, illustrating distribution in practice.
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Description
Explore key concepts in Algebra 1 Chapter 3 with these flashcards. Learn about variables and algebraic expressions, essential for solving equations. Master these foundational ideas for your algebra studies.
