# Ch 50: 6th-8th Grade Math: Rates, Ratios & Proportions

### About This Chapter

## 6th-8th Grade Math: Rates, Ratios & Proportions - Chapter Summary

Use the video lessons in this chapter to demonstrate how proportions, rates, and ratios can help your middle school students solve equations related to distance and unit measurements. Easy and interactive videos provide step-by-step instructions about one-step ratio problems, graphing, and proportional relationships. In addition, these lessons can teach students how to write and solve their own example equations. You will also have access to short, multiple-choice quizzes that can help you measure your middle school students' level of comprehension for these types of mathematical problems, and using the chapter exams can also help you determine how much information your students are absorbing.

## Chapter Lessons and Objectives

Lesson | Objectives |
---|---|

Ratios & Rates: Definitions & Examples | Identify how to calculate both rates and ratios. |

How to Find the Unit Rate | Explore techniques to determine unit rates. |

How to Solve a One-Step Problem Involving Ratios | Provide a description of a ratio and show methods for solving one-step ratio problems. |

How to Solve a One-Step Problem Involving Rates | Describe a rate and investigate techniques for calculating the answers to one-step rate problems. |

How to Solve Problems with Money | Determine and show how to find the total cost by taking the number of units and multiplying it by the cost per each unit. |

Proportion: Definition, Application & Examples | Explain what a proportion is and identify ways to solve problems with proportions. |

Calculations with Ratios and Proportions | Go over formulas and include techniques for solving problems with both ratios and proportions. |

How to Solve Problems with Time | Examine methods for calculating the concept of time. |

Distance Formulas: Calculations & Examples | Identify techniques for determining distance, and discuss methods for figuring out distance in relation to fuel consumption. |

How to Find an Unknown in a Proportion | Point out the steps for solving proportions with unknown variables. |

Calculating Unit Rates Associated with Ratios of Fractions | Discuss the unit rates of area, length, and other measurements, and then show how those rates are described through ratios of fractions. |

Proportional Relationships Between Two Quantities | Define the proportional relationship between quantities, and then figure out if two quantities are in a proportional relationship by graphing on a coordinate plane or by equivalent ratio testing. |

Identifying the Constant of Proportionality | In regards to proportional relationships, calculate the constant of proportionality in equations, tables, diagrams, verbal descriptions, and graphs. |

Representing Proportional Relationships by Equations | Show the steps for solving proportions and for writing proportional relationship equations. |

Graphing Proportional Relationships | Discuss the connection between the X and Y axes on graphs to proportional relationships, and then address the following: (0, 0) and (1, r), where r is the unit rate. |

Proportional Relationships in Multistep Ratio & Percent Problems | Analyze multistep percent and ratio problems, and then use proportional relationships to solve these equations. |

Constructing Proportions to Solve Real World Problems | Investigate techniques for solving application problems through the use of constructed proportions. |

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

In mathematics, a ratio indicates the number of times that a smaller number is contained within a larger number, while a rate expresses a ratio for two quantities measured in different units. Explore the definitions and examples of ratios and rates, learn how to compare them, and solve practice problems.

### 2. How to Find the Unit Rate

Unit rates can be helpful for anyone trying to figure out miles per hour, earnings per year, or practically any other amount of one unit it takes for something to happen in other units. In this lesson, take a look at what a unit rate is, why people use unit rates, finding the unit rate, and an example of unit rates.

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

Ratios express the mathematical relationship between two quantities. Learn how ratios improve decision-making, and observe the mathematical process being applied to a one-step problem in a common real-life situation: ordering food.

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

Rates can be used to calculate anything from distance between destinations to how long it takes to fill a pool. Learn all about rates, including how they are used and how to solve a one-step problem with them, and explore some everyday examples.

### 5. How to Solve Problems with Money

Some mathematical word problems focus on money, using real-world situations to calculate how much money is on hand and how much is needed to make purchases. Learn how to solve problems with money, and see several sample problems.

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

A problem with a proportion, which is a set of ratios that equal each other, can be solved with cross-multiplication. Learn about proportions, see sample problems, and learn how to calculate percent problems.

### 7. Calculations with Ratios and Proportions

Ratios allow us a way to mathematically compare two or more items, and proportions can help us find out even more information. Learn the definition of ratios and proportions, and understand how to calculate ratio and proportion problems.

### 8. How to Solve Problems with Time

Teamwork can help save time on complex tasks. Explore the work-rate formula, and learn how to solve for the time it takes for one individual and multiple individuals to complete a task, in order to compare the results.

### 9. Distance Formulas: Calculations & Examples

Distance formulas are used to compute the distance between two points. Learn how to solve for distance, rate, and time using the given examples, and explore calculations of distance from 'distance plus distance' problems and 'distance and fuel' problems.

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

In a proportion, finding an unknown can be a challenge. In this lesson, explore how to find those unknowns in proportions, then look at what a proportion is, calculating proportions, and checking the results of those calculations.

### 11. 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.

### 12. Proportional Relationships Between Two Quantities

Explore proportional relationships between two quantities that occur when the quantities maintain the same ratio. Examine what proportional relationships are, view a taste test and a bike test for proportionality, and see how to find the other value.

### 13. Identifying the Constant of Proportionality

Discover how to identify of the constant of proportionality, the ratio between two directly proportional quantities. View the constant of proportionality equation, explore word problems, view diagrams and tables, and understand its use in graphs.

### 14. 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.

### 15. 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!

### 16. 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.

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

Uncover how to construct proportions to solve real world problems utilizing a three-step process. Review what proportions are, understand cross multiplication, explore the use of proportions in solving real world problems, and view a quick example.

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### Other Chapters

Other chapters within the 6th-8th Grade Math: Practice & Review course

- 6th-8th Grade Math: Basic Arithmetic Operations
- 6th-8th Grade Math: Divisibility
- 6th-8th Grade Math: Properties of Numbers
- 6th-8th Grade Math: Number Theory
- 6th-8th Grade Math: Factoring
- 6th-8th Grade Math: Estimating & Rounding
- 6th-8th Grade Math: Whole Numbers
- 6th-8th Grade Math: Simplifying Whole Number Expressions
- 6th-8th Grade Math: 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 Decimals
- 6th-8th Grade Math: Operations with Decimals
- 6th-8th Grade Math: Introduction to Fractions
- 6th-8th Grade Math: Operations with Fractions
- 6th-8th Grade Math: Percents
- 6th-8th Grade Math: Exponents & Exponential Expressions
- 6th-8th Grade Math: Roots & Radical Expressions
- 6th-8th Grade Algebra: Writing Algebraic Expressions
- 6th-8th Grade Algebra: Basic Algebraic Expressions
- 6th-8th Grade Algebra: 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 Math: The Coordinate Graph
- 6th-8th Grade Algebra: Linear Equations
- 6th-8th Grade Algebra: Systems of Linear Equations
- 6th-8th Grade Math: Properties of Functions
- 6th-8th Grade Math: Graphing Functions
- 6th-8th Grade Math: Solving Math Word Problems
- 6th-8th Grade Measurement: Perimeter & Area
- 6th-8th Grade Geometry: Introduction to Geometric Figures
- 6th-8th Grade Geometry: Angles
- 6th-8th Grade Measurement: Units of Measurement
- 6th-8th Grade Geometry: Triangles
- 6th-8th Grade Geometry: Quadrilaterals
- 6th-8th Grade Geometry: Circles
- 6th-8th Grade Geometry: Circular Arcs & Measurement
- 6th-8th Grade Geometry: Polyhedrons & Geometric Solids
- 6th-8th Grade Geometry: Symmetry, Similarity & Congruence
- 6th-8th Grade Geometry: Transformations
- 6th-8th Grade Geometry: Triangle Theorems & Proofs
- 6th-8th Grade Geometry: Similar Polygons
- 6th-8th Grade Geometry: The Pythagorean Theorem
- 6th-8th Grade Math: Data & Graphs
- 6th-8th Grade Math: Probability
- 6th-8th Grade Math: Statistics
- 6th-8th Grade Math: Money
- 6th-8th Grade Math: Consumer Math
- 6th-8th Grade Math: Number Sequences
- 6th-8th Grade Math: Sets
- 6th-8th Grade Algebra: Monomials & Polynomials