Questions and Answers
What is an algebra tile?
What is a binomial?
An expression that is the sum or difference of exactly two terms, each of which is a monomial.
What does the Distributive Property state?
For any numbers or expressions a, b, and c, a(b + c) = ab + ac.
What are 'legal' moves in the context of algebra tiles?
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What is an exponent?
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What are integers?
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What is a polynomial?
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What does it mean to solve an equation?
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What is a term in an expression?
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What is the area in this course?
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What does it mean for a set of numbers to be closed under an operation?
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What is an expression?
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What is a product?
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What is the standard form for a linear equation?
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Study Notes
Algebra Tiles
- Algebra tiles are manipulatives representing constant or variable quantities through area.
- Tiles include large squares (x², y²), rectangles (x-by-1, y-by-1, x-by-y), and unit tiles (1-by-1).
- Positive quantities are represented by shaded tiles, while unshaded tiles indicate negative quantities.
Binomial
- Defined as an expression consisting of the sum or difference of exactly two terms.
- Example: −2x + 3y² qualifies as a binomial.
Distributive Property
- Allows expression products to be expressed as sums of terms.
- Formula: a(b + c) = ab + ac. Example: 2(x + 4) becomes 2x + 8 using this property.
- Can be demonstrated using algebra tiles or a generic rectangle.
Legal Moves
- "Legal" moves maintain the equality of expressions on both sides of an equation mat.
- Examples include removing identical tiles from both sides to preserve equality.
Exponent
- In expressions of the form b^a, 'a' is called the exponent specifying how many times the base (b) is multiplied by itself.
- Exponential rules: x^0 = 1 for any non-zero x; negative exponents indicate reciprocals, e.g., x^(-n) = 1/x^n.
Integers
- Defined as the set {...−3, −2, −1, 0, 1, 2, 3,...}, encompassing positive and negative whole numbers and zero.
Polynomial
- An expression formed by the sum or difference of two or more monomials.
- Example: x⁸ - 4x⁶y + 6x⁴y² is classified as a polynomial.
Solve
- Refers to finding all solutions to equations or inequalities.
- Example: Solving x² = 9 results in solutions x = 3 and x = −3.
- An equation can be manipulated to express a variable in terms of others, e.g., from 2y − 8x = 16 to y = 4x + 8.
Term
- A term may be a single number, variable, or products of numbers and variables.
- Terms in the expression 1.2x - 45 + 3xy² are 1.2x, -45, and 3xy².
Area
- In math, area measures the number of square units needed to fill a flat region.
- The concept of area extends to more complex surfaces in advanced study.
Closed Sets
- A numerical set is closed under an operation if applying the operation to any two numbers within the set results in a number still within the set.
- Example: Whole numbers are closed under addition but not under division.
Expression
- An expression consists of individual terms combined by plus or minus signs, lacking an "equals" component.
- Numerical expressions involve only numbers, while algebraic expressions incorporate variables (e.g., y - 3/4 + x).
Product
- The outcome of multiplying two or more values.
- Example: The product of 4 and 5 equals 20; multiplying 3a and 8b² yields 24ab².
Standard Form
- The standard form for a linear equation is expressed as ax + by = c, where a, b, and c are real numbers, and not both a and b can be zero.
- Example: 2.5x − 3y = 12 is in standard form.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz features flashcards based on Chapter 3 of CPM Algebra. It focuses on algebra tiles, their definitions, and applications within algebraic concepts. Ideal for reinforcing understanding of algebraic manipulative tools and their representations.