# Ch 17: Working with Rates, Ratios & Proportions

### About This Chapter

## Working with Rates, Ratios & Proportions - Chapter Summary

As you go through these lessons on working with rates, ratios and proportions, you can get a better understanding of how to solve real-world math problems. Experienced instructors explain the meaning of a point on a graph in a proportional relationship and how to solve multistep percent problems. They also discuss applications of proportion, including how they are constructed. By the end of the chapter, you should be ready to:

- Explain how to calculate ratios and rates
- Discuss using a denominator of one to find the unit rate
- Describe how a one-step problem is solved
- Provide an explanation for how an unknown in a proportion is found
- Recall how unit rates associated with ratios of fractions are calculated
- Decide if two quantities are in proportional relationships
- Find constant proportionality in graphs
- Develop an equation for a proportional relationship

The engaging teaching style used by our instructors can help to improve your knowledge of working with rates, ratios and proportions. A brief quiz is available to test your understanding of each lesson, and the quizzes can be printed for use as a helpful study tool. You can also use your personal Dashboard to keep track of the lessons you've completed, along with your quiz results.

### 1. Ratios & Rates: Definitions & Examples

If we have two items, or two numbers, and we want to compare them, what language can we use? How do we write the comparison? Find out as we learn about ratios and rates in this lesson.

### 2. How to Find the Unit Rate

If we are going to use math to predict outcomes, one of the most useful measures we can establish is the unit rate of change. In this lesson, you'll learn how to find the rate of change and apply the formula to real-life examples.

### 3. How to Solve a One-Step Problem Involving Ratios

Ratios show the relationship between different things. They can be very useful in math and everyday life. Learn how you can quickly and easily solve one-step ratio problems.

### 4. How to Solve a One-Step Problem Involving Rates

One of the most useful aspects of math is the ability to take a rate and use it to solve questions of time or quantity. In this lesson, we'll learn how to use rates, time, and quantity to solve for each other.

### 5. Proportion: Definition, Application & Examples

When we want to compare one ratio, or fraction, to another equivalent ratio, it's a proportion. Learn all about proportions and practice solving proportion problems in this lesson.

### 6. Calculations with Ratios and Proportions

Even if only 99 out of 100 people need to know how to work with ratios, the odds that they'll be useful to you are very high. In this lesson, we'll practice performing calculations with ratios and proportions.

### 7. How to Find an Unknown in a Proportion

Artists, engineers, athletes, and accountants all use proportions in their daily lives, and setting them up is really quite easy, once you know the rules. In this lesson, you'll learn how to solve proportions when there is an unknown value and work on some practice problems.

### 8. Calculating Unit Rates Associated with Ratios of Fractions

This lesson demonstrates a few different ways to calculate unit rates. We use them to solve problem such as how many beats per minute, or how many miles per hour. To master this lesson, you must understand how ratios and fractions will help to find the unit rate based off of a higher ratio of values.

### 9. Proportional Relationships Between Two Quantities

When two values always maintain the same ratio, forming the same fraction when you divide them, they have a proportional relationship. In this lesson, you can learn about proportional relationships between two quantities.

### 10. Identifying the Constant of Proportionality

Constants of proportionality might sound like something complicated, but chances are, you've encountered them before. In this lesson, we'll explore the constant of proportionality and how to find it.

### 11. Representing Proportional Relationships by Equations

After you read this lesson, you'll see just how easy it is to find an equation that represents your proportional relationship. You'll learn the formula you can use to find your equation for any proportion you have.

### 12. Graphing Proportional Relationships

Two values are proportional if they maintain the same ratio and their graph will always be a straight line that goes through the origin (0,0). In this lesson we'll explore how to draw proportional graphs and use them to solve desperate situations!

### 13. Proportional Relationships in Multistep Ratio & Percent Problems

This lesson introduces the concepts of ratios, rates, and proportions. It will show you how to use rates and ratios to develop proportional relationships. Using proportions to solve problems is very common in mathematics, because oftentimes many rates and ratios are constant.

### 14. Constructing Proportions to Solve Real World Problems

In this lesson, we will concentrate on proportions. Through definition and example, we will learn how to construct proportions and how to use proportions to solve real world problems.

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### Other Chapters

Other chapters within the MTLE Middle Level Mathematics: Practice & Study Guide course

- 6th-8th Grade Math: Basic Arithmetic Operations
- 6th-8th Grade Math: Properties of Numbers
- Number Theory & Factoring
- 6th-8th Grade Math: Estimating & Rounding
- 6th-8th Grade Math: Whole Numbers
- 5th Grade Math: Simplifying Whole Number Expressions
- Negative Numbers
- 6th-8th Grade Math: Absolute Value
- 6th-8th Grade Math: Integers
- 6th-8th Grade Math: Rational Numbers
- 6th-8th Grade Math: Inequalities
- 6th-8th Grade Math: Introduction to Fractions
- 6th-8th Grade Math: Operations with Fractions
- 6th-8th Grade Math: Introduction to Decimals
- 6th-8th Grade Math: Operations with Decimals
- 6th-8th Grade Math: Percents
- Practical Applications of Rates, Ratios & Proportions
- Introduction to Exponents
- Working with Exponential Expressions
- Understanding Square Roots & Radical Expressions
- Radical Expressions & Equations
- Imaginary & Complex Numbers
- 6th-8th Grade Algebra: Writing Algebraic Expressions
- Basic Algebraic Expressions & Factoring
- Algebraic Distribution
- 6th-8th Grade Algebra: Writing & Solving One-Step Equations
- 6th-8th Grade Algebra: Writing & Solving Two-Step Equations
- 6th-8th Grade Algebra: Simplifying & Solving Rational Expressions
- 6th-8th Grade Algebra: Linear Equations
- 6th-8th Grade Algebra: Systems of Linear Equations
- 6th-8th Grade Algebra: Monomials & Polynomials
- 6th-8th Grade Math: Properties of Functions
- 6th-8th Grade Math: Graphing Functions
- Rate of Change Basics
- Notation, Sequences & Series
- 6th-8th Grade Measurement: Units of Measurement
- Fundamentals of Geometric Figures & Angles
- Two-Dimensional Shapes
- Circle Geometry
- The Pythagorean Theorem & Trigonometry
- 6th-8th Grade Measurement: Perimeter & Area
- 6th-8th Grade Geometry: Polyhedrons & Geometric Solids
- Congruence & Similarity in Geometry
- 6th-8th Grade Math: The Coordinate Graph
- 6th-8th Grade Geometry: Transformations
- Modeling to Solve Problems
- Basic Probability
- Statistics & Sampling Basics
- MTLE Middle Level Mathematics Flashcards