Use the following Media4Math resources with this Illustrative Math lesson.
Thumbnail Image | Title | Body | Curriculum Nodes |
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Math Example: Percents with Double Number Lines: Example 4 | Math Example: Percents with Double Number Lines: Example 4TopicRatios, Proportions, Percents DescriptionThis example illustrates how to calculate 40% of 105 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 105. By aligning 40% on the percentage line with its corresponding value on the numerical line, we can determine that 40% of 105 is 42. This method visually demonstrates that 40% is equivalent to two-fifths of a quantity. |
Ratios and Rates | |
Math Example: Percents with Double Number Lines: Example 5 | Math Example: Percents with Double Number Lines: Example 5TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to find 12.5% of 88 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 88. By aligning 12.5% on the percentage line with its corresponding value on the numerical line, we can see that 12.5% of 88 is 11. This method visually represents the concept that 12.5% is equivalent to one-eighth of a quantity. |
Ratios and Rates | |
Math Example: Percents with Double Number Lines: Example 6 | Math Example: Percents with Double Number Lines: Example 6TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to solve for an unknown value using a double number line when given a percentage. The image features two parallel number lines: one ranging from 0 to 100% and another from 0 to an unknown value x. It visually illustrates the process of determining x when 75 is 50% of x. |
Ratios and Rates | |
Math Example: Percents with Double Number Lines: Example 7 | Math Example: Percents with Double Number Lines: Example 7TopicRatios, Proportions, Percents DescriptionThis example illustrates how to determine an unknown value using a double number line when given a part and its corresponding percentage. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to an unknown value x. It visually demonstrates the process of finding x when 120 is 25% of x. |
Ratios and Rates | |
Math Example: Percents with Double Number Lines: Example 8 | Math Example: Percents with Double Number Lines: Example 8TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to find an unknown value using a double number line when given a part and its corresponding percentage, involving a fractional percentage. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to an unknown value x. It visually illustrates the process of determining x when 125 is 33 1/3% of x. |
Ratios and Rates | |
Math Example: Percents with Double Number Lines: Example 9 | Math Example: Percents with Double Number Lines: Example 9TopicRatios, Proportions, Percents DescriptionThis example illustrates how to solve for an unknown value using a double number line when given a part and its corresponding percentage. The image shows two horizontal number lines: the top line ranges from 0 to 100%, and the bottom line ranges from 0 to an unknown number x. The 40% mark on the top line aligns with 220 on the bottom line, visually demonstrating the process of finding x when 220 is 40% of x. |
Ratios and Rates | |
MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents | MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents
What Are Percents?Percents Are a Type of Fraction |
Solving Percent Equations | |
Math in the News: Issue 100--Late Night TV Ratings | Math in the News: Issue 100--Late Night TV Ratings
July 2014. In this issue of Math in the News we look at the mathematics of the Nielsen Ratings. This provides an excellent application of ratios, proportions, and percents. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis | |
Math in the News: Issue 21--Why Does Washington Spend So Much? | Math in the News: Issue 21--Why Does Washington Spend So Much?
8/8/11. In this issue we look at federal spending and the growth of such spending. Looking at data provided by the government, we calculate the annual rate of growth. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis and Percents | |
Math in the News: Issue 96--The California Drought | Math in the News: Issue 96--The California Drought
July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents and Proportions | |
Math in the News: Issue 96--The California Drought | Math in the News: Issue 96--The California Drought
July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents and Proportions | |
Paper-and-Pencil Quiz: Equations with Percents (Easy) | Paper-and-Pencil Quiz: Equations with Percents (Easy)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations | |
Paper-and-Pencil Quiz: Equations with Percents (Hard) | Paper-and-Pencil Quiz: Equations with Percents (Hard)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations | |
Paper-and-Pencil Quiz: Equations with Percents (Medium) | Paper-and-Pencil Quiz: Equations with Percents (Medium)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations | |
Video Transcript: Application of Ratios: Roofs and Ramps | Video Transcript: Application of Ratios: Roofs and Ramps
What Are Ratios?A ratio is the relationship between two or more quantities among a group of items. |
Applications of Ratios, Proportions, and Percents | |
Video Transcript: Percents: Applications of Percent -- Grade | Video Transcript: Percents: Applications of Percent -- Grade
This is the transcript that goes with the video segment entitled Video: Percents: Applications of Percent -- Grade. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Calculating Commissions and Tips | Video Transcript: Percents: Calculating Commissions and Tips
This is the transcript that goes with the video segment entitled Video: Percents: Calculating Commissions and Tips. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Calculating Tax | Video Transcript: Percents: Calculating Tax
This is the transcript that goes with the video segment entitled Video: Percents: Calculating Tax. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Calculating the Whole Given a Percent | Video Transcript: Percents: Calculating the Whole Given a Percent
This is the transcript that goes with the video segment entitled Video: Percents: Calculating the Whole Given a Percent. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Percents | |
Video Transcript: Percents: Estimating Percents | Video Transcript: Percents: Estimating Percents
This is the transcript that goes with the video segment entitled Video: Percents: Estimating Percents. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Fraction-Percent Conversion | Video Transcript: Percents: Fraction-Percent Conversion
This is the transcript that goes with the video segment entitled Video: Percents: Fraction-Percent Conversion. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Multiple Percents | Video Transcript: Percents: Multiple Percents
This is the transcript that goes with the video segment entitled Video: Percents: Multiple Percents. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Percent Decrease | Video Transcript: Percents: Percent Decrease
This is the transcript that goes with the video segment entitled Video: Percents: Percent Decrease. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Percent Increase | Video Transcript: Percents: Percent Increase
This is the transcript that goes with the video segment entitled Video: Percents: Percent Increase. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Percent of a Difference | Video Transcript: Percents: Percent of a Difference
This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Percent of a Difference. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Percent of a Number | Video Transcript: Percents: Percent of a Number
This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Percent of a Number. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Percents and Multiples of Numbers | Video Transcript: Percents: Percents and Multiples of Numbers
This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Percents and Multiples of Numbers. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Percents | |
Video Transcript: Percents: Probabilities and Percents | Video Transcript: Percents: Probabilities and Percents
This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Probabilities and Percents. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: Simple Interest | Video Transcript: Percents: Simple Interest
This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Simple Interest. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Percents: The Percent One Number is of Another | Video Transcript: Percents: The Percent One Number is of Another
This is the transcript that goes with the video segment entitled Video Tutorial: Percents: The Percent One Number is of Another. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Percents | |
Video Transcript: Percents: Visual Models for Percents | Video Transcript: Percents: Visual Models for Percents
This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Visual Models for Percents. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents | |
Video Transcript: Ratios, Proportions, and Percents: Calculating Percents | Video Transcript: Ratios, Proportions, and Percents: Calculating Percents
This is the transcript that goes with the video segment entitled Video Tutorials: Ratios, Proportions, and Percents: Calculating Percents. This is part of a collection of video transcripts for the video tutorial series on Ratios. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Ratios and Rates | |
Video Tutorial: Percents, Video 11 | Video Tutorial: Percents: Simple Interest
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. What Are Percents?Percents are a type of fraction. A fraction is part of a whole. |
Percents | |
Video Tutorial: Percents, Video 12 | Video Tutorial: Percents: Calculating Tax
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. What Are Percents?Percents are a type of fraction. A fraction is part of a whole. |
Percents | |
Video Tutorial: Percents, Video 9 | Video Tutorial: Percents: Percent Increase
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. What Are Percents?Percents are a type of fraction. A fraction is part of a whole. |
Percents | |
Video Tutorial: Percents, Video 1 | Video Tutorial: Percents: Percent of a Number
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. What Are Percents?Percents are a type of fraction. A fraction is part of a whole. |
Percents | |
Video Tutorial: Percents, Video 10 | Video Tutorial: Percents: Percent Decrease
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. What Are Percents?Percents are a type of fraction. A fraction is part of a whole. |
Percents | |
Video Tutorial: Percents, Video 13 | Video Tutorial: Percents: Calculating Commissions and Tips
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Percents, Video 14 | Video Tutorial: Percents: Multiple Percents
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. What Are Percents?Percents are a type of fraction. A fraction is part of a whole. |
Percents | |
Video Tutorial: Percents, Video 15 | Video Tutorial: Percents: Probabilities and Percents
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Percents, Video 16 | Video Tutorial: Percents: Percents and Multiples of Numbers
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Percents, Video 2 | Video Tutorial: Percents: Calculating the Whole Given a Percent
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Percents, Video 3 | Video Tutorial: Percents: Percent of a Difference
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Percents, Video 4 | Video Tutorial: Percents: The Percent One Number is of Another
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Percents, Video 5 | Video Tutorial: Percents: Visual Models for Percents
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Percents, Video 6 | Video Tutorial: Percents: Estimating Percents
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. What Are Percents?Percents are a type of fraction. A fraction is part of a whole. |
Percents | |
Video Tutorial: Percents, Video 7 | Video Tutorial: Percents: Fraction-Percent Conversion
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Percents, Video 8 | Video Tutorial: Percents: Applications of Percent -- Grade
This video is part of a series of videos that cover the topic of percents. This includes the definition of a percent, percent operations, and applications of percents. Each video includes real-world examples of using percents to solve specific problems. —CLICK ON PREVIEW TO VIEW THE VIDEO TUTORIAL— To see the complete collection of video tutorials on percents, click on this link.The following section provides background information on percents. Use this material to supplement the video series. You can also use the videos and this background material to fully review the topic of percents. |
Percents | |
Video Tutorial: Ratios, Video 16 | Video Tutorial: Ratios, Proportions, and Percents: Calculating Percents
This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos. What Are Ratios?A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection. Let's look at an example. |
Ratios and Rates | |
Video Tutorial: Ratios, Video 17 | Video Tutorial: Ratios: Visual Models for Ratios and Percents This is part of a collection of video tutorials on the topic of Ratios and Proportions. This series includes a complete overview of ratios, equivalent ratios, rates, unit rates, and proportions. The following section will provide additional background information for the complete series of videos. What Are Ratios?A ratio is the relationship between two or more quantities among a group of items. The purpose of a ratio is find the relationship between two or more items in the collection. Let's look at an example. |
Ratios and Rates |