Algebra Class Key Concepts

Questions and Answers

What is the definition of 'equivalent'?

equal, equal in amount or value (correct)

greater than

not equal

less than

What are equivalent equations?

Equations that have different solutions

Only one equation

Equations that are equal to each other (correct)

Equations with no solutions

What does the Addition Property of Equality state?

Adding the same number to each side of an equation makes an equivalent equation.

What is the Subtraction Property of Equality?

Subtracting the same number from each side of an equation makes an equivalent equation. Signup and view all the answers

What does the Multiplication Property of Equality mean?

Multiplying each side of an equation by the same nonzero number makes an equivalent equation. Signup and view all the answers

Define the Division Property of Equality.

Dividing each side of an equation by the same nonzero number makes an equivalent equation. Signup and view all the answers

What does 'isolate' mean in mathematics?

To get alone. Signup and view all the answers

What is the meaning of 'inverse'?

Opposite. Signup and view all the answers

What is an inverse operation?

An operation that undoes another operation. Signup and view all the answers

What does 'combine' mean in math?

To join or bring together. Signup and view all the answers

What are like terms?

Groups of variables that have the same variables and the same powers. Signup and view all the answers

Define a literal equation.

An equation that involves 2 or more variables. Signup and view all the answers

What does 'quantity' refer to?

Amount, how much. Signup and view all the answers

What is a formula in mathematics?

An equation that states a relationship among quantities. Signup and view all the answers

What is a ratio?

A comparison of two numbers by division. Signup and view all the answers

What is rate?

A ratio that compares quantities measured in different units. Signup and view all the answers

Define unit rate.

A rate with a denominator of 1 unit. Signup and view all the answers

What does it mean to 'convert' in mathematics?

Changing from one thing/unit to another. Signup and view all the answers

What is unit analysis?

Calculations that show the units for each quantity. Signup and view all the answers

What is a proportion?

An equation that states that two ratios are equal. Signup and view all the answers

What is meant by a figure in mathematics?

A picture or shape. Signup and view all the answers

What are similar figures?

Two things that have similar shapes but different sizes. Signup and view all the answers

Define scale in mathematics.

A proportion between two sets of dimensions. Signup and view all the answers

What is a scale drawing?

A drawing that is similar to an actual object or place, but is not the same size. Signup and view all the answers

What is a scale model?

A three-dimensional model that is similar to an actual three-dimensional object. Signup and view all the answers

What does percent change express?

An amount of change as a percent of an original amount. Signup and view all the answers

What is percent increase?

A change in quantity that is greater than the original quantity shown as a percent. Signup and view all the answers

What does percent decrease indicate?

A change in quantity that is less than the original quantity shown as a percent. Signup and view all the answers

Define relative error.

The ratio of the absolute value of the difference between a measured value and an actual value compared to the actual value. Signup and view all the answers

What is percent error?

Relative error expressed as a percent. Signup and view all the answers

Study Notes

Key Algebraic Concepts

Equivalent: Indicates two expressions or values that are equal in amount or value.
Equivalent Equations: Equations that yield the same solution; they are equal to each other.

Properties of Equality

Addition Property of Equality: Adding the same number to both sides of an equation results in an equivalent equation (e.g., x - 3 = 2 becomes x = 5).
Subtraction Property of Equality: Subtracting the same number from both sides maintains equivalence (e.g., x - 3 = 2 becomes x = 5).
Multiplication Property of Equality: Multiplying both sides of an equation by a nonzero number yields an equivalent equation (e.g., x/3 = 2 becomes x = 6).
Division Property of Equality: Dividing both sides of an equation by the same nonzero number maintains equality (e.g., 5x = 20 becomes x = 4).

Key Terminology

Isolate: To separate a variable in an equation to solve for it.
Inverse: Refers to opposite operations, which can undo each other (e.g., addition and subtraction).
Inverse Operation: The operation that reverses or cancels another (e.g., multiplication vs. division).
Combine: To join different quantities together.

Like Terms: Terms containing the same variable and power (e.g., 12xy^5 and -5xy^5 are like terms; 12xy^5 and -5xy^3 are not).
Literal Equation: An equation involving two or more variables that is solved for one variable in terms of others.

Quantities and Relationships

Quantity: Refers to an amount or how much of something.
Formula: An equation that illustrates a relationship among different quantities or variables.
Ratio: A comparison of two quantities expressed through division (e.g., a/b, a:b).
Rate: A special type of ratio comparing quantities in different units.
Unit Rate: A ratio that has a denominator of one unit.

Conversion Concepts

Convert: The act of changing from one unit or form to another.
Unit Analysis: The process of checking units in calculations to ensure they make sense.

Proportions and Scale

Proportion: An equation showing that two ratios are equal (e.g., a/b = c/d).
Similar Figures: Shapes that have the same shape but different sizes, denoted with the symbol ~.
Scale: The ratio between two sets of dimensions, often used in models or drawings.
Scale Drawing: A representation of an object that is not to scale but maintains the same proportions.
Scale Model: A three-dimensional representation that is proportional to the actual object.

Percent Changes and Errors

Percent Change: The amount of change represented as a percentage of the original amount, calculated using: p% = (amount of change)/(original amount).
Percent Increase: A change that is greater than the original amount, expressed as a percentage.
Percent Decrease: A change that is less than the original amount, expressed as a percentage.
Relative Error: The absolute difference between a measured value and an actual value, compared to the actual value.
Percent Error: The relative error expressed as a percentage, providing insight into accuracy.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz covers key algebraic concepts and properties of equality, focusing on equivalent equations and their manipulation. You will encounter definitions and applications of addition, subtraction, multiplication, and division properties. Test your understanding of isolating variables and using inverse operations.