Algebra Chapter 3 Flashcards

Questions and Answers

What is an algebra tile?

A type of polynomial

A term in an equation

A legal move in algebra

A manipulative whose area represents a constant or variable quantity (correct)

What is a binomial?

An expression that is the sum or difference of exactly two terms.

What does the Distributive Property state?

a(b + c) = ab + ac

What is an exponent?

A number that indicates how many times to use the base as a multiplier. Signup and view all the answers

What are integers?

{...−3, −2, −1, 0, 1, 2, 3,...} Signup and view all the answers

What defines a polynomial?

An expression that is the sum or difference of two or more monomials. Signup and view all the answers

What does it mean to solve an equation?

To find all the solutions to an equation or inequality. Signup and view all the answers

What are terms in the context of area?

The number of square units needed to fill up a region on a flat surface. Signup and view all the answers

What is the definition of area?

The number of square units needed to fill up a region on a flat surface. Signup and view all the answers

What are closed sets?

A set of numbers that produces a number in the set when an operation is applied to any two numbers in the set. Signup and view all the answers

What is an equation?

A mathematical sentence stating that two expressions are equivalent. Signup and view all the answers

What is an expression in mathematics?

A combination of individual terms separated by plus or minus signs. Signup and view all the answers

What are 'legal' moves?

Moves that can be made with algebra tiles that keep the relationship between two sides of an equation equal. Signup and view all the answers

What is a product?

The result of multiplying two or more numbers. Signup and view all the answers

What is the standard form for a linear equation?

ax + by = c Signup and view all the answers

What is the base in an exponent?

The number that is raised to a power in an exponential expression. Signup and view all the answers

What do the dimensions of a flat region indicate?

How far it extends in each direction. Signup and view all the answers

What does it mean to evaluate an expression?

Substitute values for the variables and perform operations according to the order of operations. Signup and view all the answers

What are generic rectangles?

Diagrams used to visualize multiplying expressions without algebra tiles. Signup and view all the answers

What is the formula for length multiplied by width?

A formula used to calculate the area of a rectangle. Signup and view all the answers

What is a solution in mathematics?

The number or numbers that make an equation or inequality true. Signup and view all the answers

What is a sum?

The answer to a problem involving addition. Signup and view all the answers

Study Notes

Algebra Tiles

Algebra tiles are manipulatives used to represent constants and variable quantities through their area.
Tiles include large squares (x², y²), rectangles (x, y, xy), and unit squares (1), with shaded tiles for positive and unshaded for negative quantities.

Binomial

A binomial is an algebraic expression consisting of exactly two monomial terms, such as −2x + 3y².

Distributive Property

The Distributive Property combines multiplication of a number by a sum into a sum of products: a(b + c) = ab + ac.
Example: 2(x + 4) = 2x + 8.

Exponent

In expressions of the form b^a, 'a' is the exponent demonstrating repeated multiplication of 'b'.
Zero exponent rule: x⁰ = 1 for x ≠ 0.
Negative exponents indicate the reciprocal: x^(-n) = 1/xⁿ for x ≠ 0.

Integers

Integers include all whole numbers, both positive and negative, along with zero: {..., -3, -2, -1, 0, 1, 2, 3, ...}.

Polynomial

A polynomial is an algebraic expression formed by the sum or difference of two or more monomials; for example, x⁸ - 4x⁶y + 6x⁴y².

Solve

To solve means to find all solutions to equations or inequalities.
Example: Solving x² = 9 reveals x = 3 and x = -3.
Solving for a variable transforms the equation; for example, from 2y - 8x = 16 to y = 4x + 8.

Terms

In this context, terms refer to individual components in an algebraic expression, contributing to the overall area.

Area

Area measures the number of square units required to fill a flat surface; this concept will extend to three-dimensional shapes in advanced studies.

Closed Sets

A set is closed under an operation if performing that operation on members of the set yields results still within the set, such as whole numbers under addition, but not under division.

Equation

An equation entails two equivalent expressions separated by an equals sign (=), representing relationships between quantities.
For example, 7x + 4.2 = -8 links the left expression to -8.

Expression

An expression combines terms using plus or minus signs without an equals sign.
An algebraic expression includes variables; for instance, 4 + (5 - 3) or 6xy² + 24.

Legal Moves

"Legal" moves with algebra tiles preserve the equality of expressions when manipulating an equation mat, allowing certain transformations as per algebraic properties.

Product

The product refers to the outcome of multiplication; for example, multiplying 4 and 5 yields 20.

Standard Form

Linear equations in standard form follow ax + by = c.
Quadratic expressions are in standard form as ax² + bx + c.

Base

In an exponential expression b^a, 'b' serves as the base, indicating the number being multiplied.

Dimensions

Dimensions specify the extent of a flat region in two directions; for instance, a rectangle's dimensions may be 16 cm by 7 cm.

Evaluate

Evaluating an expression involves substituting variable values and computing according to order of operations; for example, 2x + y - 10 evaluates to 1 with x = 4 and y = 3.

Generic Rectangles

Generic rectangles visually illustrate multiplying expressions. Each side length corresponds to an expression, with the area representing the product sum.

Length · Width

Represents the formula for calculating area in rectangular shapes.

Solution

A solution satisfies an equation or inequality. For instance, x = 4 is a solution for 3x - 2 = 10, represented as an ordered pair for two-variable equations.

Sum

The term sum indicates the result of addition within a mathematical context.

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Description

Test your knowledge of key concepts from Algebra Chapter 3 with these flashcards. This chapter focuses on algebra tiles, their definitions, and applications. Perfect for visual learners looking to solidify their understanding of algebraic concepts.