Chapter 2 Algebra 1 Flashcards

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Questions and Answers

What is the percent of change?

An equation that is always true for every value of the variable.

The change as a percent if the new number is greater than the original number.

A ratio of change in the amount to the original expressed as a percent. (correct)

A comparison of two numbers by division.

What does percent of increase/decrease represent?

The change as a percent if the new number is greater than the original (increase) or less (decrease).

What does it mean to solve an equation?

Finding the value for the variable that makes the sentence true.

What is an identity in algebra?

An equation that is true for every value of the variable. Signup and view all the answers

What is meant by 'no solution' in an equation?

An equation that is never true no matter what value is used for the variable. Signup and view all the answers

What are equivalent equations?

Equations that have the same solution. Signup and view all the answers

What is the subtraction property of equality?

If you subtract the same number from each side of an equation, the two sides remain equal. Signup and view all the answers

What is the addition property of equality?

If you add the same number to each side of an equation, the two sides remain equal. Signup and view all the answers

What is the multiplication property of equality?

You can multiply the same number on each side of an equation. Signup and view all the answers

What is the division property of equality?

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

What is a multi-step equation?

An equation that requires more than one step to solve because it has more than one operation. Signup and view all the answers

Define consecutive integers.

Integers in counting order, such as 4, 5, and 6 or n, n+1, and n+2. Signup and view all the answers

What are consecutive even integers?

Integers that can be represented as 2, 4, and 6, or n, n+2, and n+4. Signup and view all the answers

What defines consecutive odd integers?

Integers like 1, 3, and 5 or n, n+2, and n+2. Signup and view all the answers

What is the study of number theory?

The study of numbers and the relationships between them. Signup and view all the answers

Define a ratio.

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

What is a proportion?

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

What is a formula in mathematics?

A mathematical relationship or rule expressed as an equation. Signup and view all the answers

What is a unit rate?

How many of one item is being compared to 1 of another item. Signup and view all the answers

What are algebra tiles used for?

Tiles used to help model equations and expressions. Signup and view all the answers

What do properties of equality state?

What you do to one side of the equal sign, you must do to the other side. Signup and view all the answers

Define absolute value.

The distance from zero a number is. Signup and view all the answers

What are means in the context of proportions?

The middle terms of a proportion. Signup and view all the answers

What are extremes in the context of proportions?

The first and last terms of a proportion. Signup and view all the answers

What is a scale in mathematics?

A factor that shows the size differences of shapes. Signup and view all the answers

What is a scale model?

The figure that changed sizes by a certain factor. Signup and view all the answers

What is the debt to income ratio?

The amount owed per month divided by the amount earned per month. Signup and view all the answers

Define dimensional (unit) analysis.

The process of carrying units through a computation. Signup and view all the answers

What is a weighted average?

An average found by multiplying each data value by its weight and then finding the mean of the new data. Signup and view all the answers

What are mixture problems in mathematics?

Problems where 2 or more parts are combined into a whole. Signup and view all the answers

What are rate problems (uniform motion)?

Problems in which an object moves at a certain speed or rate. Signup and view all the answers

Define a rate in mathematics.

A ratio of two measurements having different units of measure. Signup and view all the answers

What does metric refer to in a mathematical context?

A rule for assigning a number to some characteristic. Signup and view all the answers

What is a literal equation?

An equation that involves several variables. Signup and view all the answers

Study Notes

Percent of Change

Defined as the ratio of change in amount to the original amount, expressed as a percentage; applicable for both increases and decreases.

Percent of Increase/Decrease

Indicates the change in percentage based on whether the new value is greater (increase) or less (decrease) than the original.

Solving Equations

Involves finding the variable's value that satisfies the equation, making it true.

Identity

An equation that holds true for all values of the variable, meaning the variable can equal all real numbers.

No Solution

Refers to an equation that has no possible variable value that will make it true.

Equivalent Equations

Equations that yield the same solution; they may appear different but result in identical outcomes.

Properties of Equality

Subtraction Property: Subtracting the same number from both sides of an equation maintains equality.
Addition Property: Adding the same number to both sides of an equation retains equality.
Multiplication Property: Multiplying both sides of an equation by the same number keeps the equation balanced.
Division Property: Dividing both sides of an equation by the same non-zero number results in an equivalent equation.

Multi-Step Equations

Equations requiring more than one operation to solve, necessitating multiple steps.

Consecutive Integers

Refers to integers in counting sequence, e.g., n, n+1, n+2.

Consecutive Even/Odd Integers

Even integers: n, n+2, n+4 (e.g., 2, 4, 6).
Odd integers: n, n+2, n+4 (e.g., 1, 3, 5).

Number Theory

The study focused on numbers and their relational dynamics.

Ratio and Proportion

Ratio: A comparison of two numbers indicated through division.
Proportion: An equation that asserts two ratios are equal.

Mathematical Relationships

Formula: A rule or equation expressing a mathematical relationship.
Unit Rate: Comparison of how many of one item is equivalent to one of another.

Algebra Tiles

Physical or visual tools used to model equations and expressions for better understanding.

Absolute Value

Represents the distance of a number from zero on a number line, disregarding the direction.

Proportion Terminology

Means: The middle terms in a proportion.
Extremes: The first and last terms in a proportion.

Scale and Scale Models

Scale: A factor indicating size differences of figures.
Scale Model: A representation of an object adjusted in size by a specific factor.

Debt to Income Ratio

Calculation derived from dividing monthly debt by monthly income.

Dimensional Analysis

Process of ensuring units are consistently applied during calculations, such as converting feet to miles.

Weighted Average

Computed by multiplying each data point by its corresponding weight and then finding the average of the results.

Mixture Problems

Situations where two or more components are combined to form a whole.

Rate and Rate Problems

Rate: A ratio comparing two different units of measurement.
Rate Problems: Focus on objects moving at a defined speed or rate.

Metric

A system or rule for designating a numeric value to some characteristic, such as grading metrics.

Literal Equations

Equations involving multiple variables, often used to express formulas.

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Description

Test your understanding of key concepts from Chapter 2 of Glencoe Algebra 1 with these flashcards. This quiz covers definitions of important terms such as percent of change and methods for solving equations. Perfect for review and study.