Ratios and Proportional Reasoning: Course 2 Chapter 1
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Questions and Answers

What is a complex fraction?

  • A fraction where both the numerator and denominator contain fractions (correct)
  • A fraction that is simplified
  • A fraction with a whole number in the numerator
  • A fraction with decimals

What is the constant of variation in the equation y = kx?

k

Define constant rate of change.

The rate of change in a linear relationship.

The coordinate plane is where the x-axis and y-axis intersect.

<p>True (A)</p> Signup and view all the answers

What is dimensional analysis?

<p>The process of carrying units throughout a computation.</p> Signup and view all the answers

What describes direct variation?

<p>An equation of the form y = kx (A)</p> Signup and view all the answers

What are equivalent ratios?

<p>Two ratios that have the same value.</p> Signup and view all the answers

A nonproportional relationship has a constant rate.

<p>False (B)</p> Signup and view all the answers

What is an ordered pair?

<p>(x-coordinate, y-coordinate)</p> Signup and view all the answers

What is the origin in a coordinate plane?

<p>(0, 0)</p> Signup and view all the answers

Define proportion.

<p>An equation stating that two ratios are equivalent.</p> Signup and view all the answers

What is a proportional relationship?

<p>The relationship between two ratios with a constant rate.</p> Signup and view all the answers

What is a quadrant?

<p>One of four regions in the coordinate plane.</p> Signup and view all the answers

Define rate.

<p>The ratio of two measurements having different units of measure.</p> Signup and view all the answers

What is the rate of change?

<p>The change in a quantity over time.</p> Signup and view all the answers

What is slope?

<p>The ratio of the change in the y-coordinates to the change in the x-coordinates.</p> Signup and view all the answers

Define unit rate.

<p>A rate with a denominator of 1.</p> Signup and view all the answers

What is a unit ratio?

<p>A unit rate where the denominator is one unit.</p> Signup and view all the answers

What is the x-axis?

<p>The horizontal number line on a coordinate plane.</p> Signup and view all the answers

What is the x-coordinate?

<p>The first number in an ordered pair.</p> Signup and view all the answers

Define the y-axis.

<p>The vertical number line on a coordinate plane.</p> Signup and view all the answers

What is the y-coordinate?

<p>The second number in an ordered pair.</p> Signup and view all the answers

Flashcards

Complex Fraction

A fraction that contains one or more fractions in its numerator or denominator.

Constant of Variation

The constant factor k in the equation y = kx, showing direct variation.

Constant Rate of Change

A consistent change rate in linear relationships between two variables.

Coordinate Plane

A two-dimensional space with a horizontal (x-axis) and vertical (y-axis) number line.

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Dimensional Analysis

A method involving tracking units during calculations for consistency.

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Direct Variation

A relationship where y = kx indicates a direct proportionality between x and y.

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Equivalent Ratios

Ratios that express the same relationship, like 5:4 and 10:8.

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Nonproportional

Describes ratios that don’t maintain a constant rate or relationship.

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Ordered Pair

A pair of numbers (x, y) that identifies a point on the coordinate plane.

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Origin

The point (0,0) where the x-axis and y-axis intersect in the coordinate plane.

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Proportion

An equation stating two ratios are equivalent, used to solve for unknowns.

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Proportional

Characteristics of ratios with a consistent rate of change.

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Quadrant

Each of the four sections of the coordinate plane created by the axes.

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Rate

A type of ratio comparing two measurements with different units.

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Rate of Change

Variation of one quantity with respect to time, often expressed as a difference.

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Slope

The steepness of a line, calculated as rise over run between two points.

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Unit Rate

A rate where the denominator is one unit, facilitating comparisons.

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Unit Ratio

A type of unit rate with one unit in the denominator, simplifying relationships.

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X-axis

The horizontal line in the coordinate plane, holding y constant.

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X-coordinate

The first value in an ordered pair, indicating horizontal position.

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Y-axis

The vertical line in the coordinate plane, holding x constant.

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Y-coordinate

The second value in an ordered pair, representing vertical position.

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Study Notes

Key Vocabulary in Ratios and Proportional Reasoning

  • Complex Fraction: A fraction that includes one or more fractions in either its numerator, denominator, or both.
  • Constant of Variation: Denoted as k in the equation y = kx, indicating the constant factor in a direct variation.
  • Constant Rate of Change: Refers to the consistent change rate in linear relationships, illustrating how one variable changes with another.
  • Coordinate Plane: A two-dimensional space formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis), used for graphing points and equations.
  • Dimensional Analysis: A method that involves tracking units throughout calculations to ensure proper dimensional consistency and conversion.
  • Direct Variation: A relationship represented by the equation y = kx, where k is a non-zero constant, indicating a direct proportional relationship between x and y.
  • Equivalent Ratios: Ratios that express the same relationship or proportion, such as 5:4 being equivalent to 10:8.
  • Nonproportional: Describes the relationship between two ratios that do not maintain a constant ratio or rate of change.
  • Ordered Pair: A pair of numbers (x-coordinate, y-coordinate) that identifies a specific point on the coordinate plane.
  • Origin: The central point (0, 0) within the coordinate plane where the x-axis and y-axis intersect.
  • Proportion: An equation that states two ratios are equivalent, often used to solve for unknown variables in ratio problems.
  • Proportional: A characteristic of two ratios that have a consistent or constant rate of change.
  • Quadrant: Each of the four sections created by the x-axis and y-axis on a coordinate plane, with each quadrant representing different sign combinations of coordinates.
  • Rate: A specific kind of ratio that compares two measurements with different units, such as 60 miles per hour.
  • Rate of Change: Reflects the variation of one quantity with respect to time, often expressed as a difference over a specific time period.
  • Slope: The measure of steepness of a line, calculated as the ratio of the rise (change in y-coordinates) over the run (change in x-coordinates) between two points.
  • Unit Rate: A special case of rate where the denominator simplifies to one unit, facilitating comparisons between different rates.
  • Unit Ratio: A specific type of unit rate where the denominator is defined as one unit, simplifying the relationship between two quantities.
  • X-axis: The horizontal component of the coordinate plane, where the y-coordinate is held constant.
  • X-coordinate: The first value in an ordered pair, indicating the horizontal positioning in the coordinate plane.
  • Y-axis: The vertical component of the coordinate plane, where the x-coordinate is held constant.
  • Y-coordinate: The second value in an ordered pair, representing the vertical positioning in the coordinate plane.

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This quiz covers key vocabulary from McGraw-Hill's Course 2 Chapter 1 on Ratios and Proportional Reasoning. Test your understanding of terms like 'complex fraction' and 'constant of variation' through flashcards. Perfect for students looking to enhance their math vocabulary and concepts.

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