# Ch 35: NES Middle Grades Math: Rates, Ratios & Proportions

### About This Chapter

## NES Middle Grades Math: Rates, Ratios & Proportions - Chapter Summary

Here, our exceptional instructors bring to you a full treatment of math topics related to ratios, rates, and proportions to help you get ready for the National Evaluation Series (NES) Middle Grades Mathematics exam. The lessons work through definitions, formulas for calculations, and real-world examples with fun graphics to cement the information in your memory before the big test. The topics covered by these lessons include, among others:

- Defining of rates, proportions, and ratios
- Finding unit rates
- Solving one-step and multi-step problems
- Calculating problems with rates/ratios/proportions
- Working with time and money
- Graphing proportions
- Solving real-world problems through proportions

Our study system treats you to brief videos with excellent instruction set to entertaining graphics and examples to minimize the time requirement and stress of test preparation. Adding the transcripts and worksheets to your review process gives you a learning experience that includes visual, aural, and print material to help all types of learners find something useful. The self-assessments help you determine if you are ready for the exam or if you need to go back to specific topics.

### 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. How to Solve Problems with Money

Money matters, and knowing how much things cost will be useful no matter where you go. In this lesson, we'll learn the steps for solving word problems involving money.

### 6. 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.

### 7. 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.

### 8. How to Solve Problems with Time

It's amazing how much time can be saved when people work together. In this lesson, we'll practice figuring out just how much time we're talking about as we solve problems involving time.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

### 14. 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!

### 15. 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.

### 16. 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 NES Middle Grades Mathematics (203): Practice & Study Guide course

- NES Middle Grades Math: Basic Arithmetic Operations
- NES Middle Grades Math: Solving Word Problems
- NES Middle Grades Math: Properties of Numbers
- NES Middle Grades Math: Estimating & Rounding
- NES Middle Grades Math: Number Theory
- NES Middle Grades Math: Roots & Radical Expressions
- NES Middle Grades Math: Exponents & Exponential Expressions
- NES Middle Grades Math: Scientific Notation
- NES Middle Grades Math: Simplifying Expressions
- NES Middle Grades Math: Integers
- NES Middle Grades Math: Rational Numbers
- NES Middle Grades Math: Introduction to Fractions
- NES Middle Grades Math: Operations with Fractions
- NES Middle Grades Math: Introduction to Decimals
- NES Middle Grades Math: Operations with Decimals
- NES Middle Grades Math: Percents
- NES Middle Grades Math: Money & Consumer Math
- NES Middle Grades Math: Number Patterns & Sequences
- NES Middle Grades Math: Properties of Functions
- NES Middle Grades Math: Graphing Functions
- NES Middle Grades Math: Negative Numbers
- NES Middle Grades Math: Absolute Value
- NES Middle Grades Math: Inequalities
- NES Middle Grades Math: Factoring
- NES Middle Grades Math: Monomials & Polynomials
- NES Middle Grades Math: Writing Algebraic Expressions
- NES Middle Grades Math: Basic Algebraic Expressions
- NES Middle Grades Math: Algebraic Distribution
- NES Middle Grades Math: One-Step Equations
- NES Middle Grades Math: Two-Step Equations
- NES Middle Grades Math: Rational Expressions
- NES Middle Grades Math: The Coordinate Graph
- NES Middle Grades Math: Linear Equations
- NES Middle Grades Math: Systems of Linear Equations
- NES Middle Grades Math: Measurement
- NES Middle Grades Math: Perimeter & Area
- NES Middle Grades Math: Polyhedrons & Geometric Solids
- NES Middle Grades Math: Symmetry, Similarity & Congruence
- NES Middle Grades Math: Properties of Lines
- NES Middle Grades Math: Angles
- NES Middle Grades Math: Triangles
- NES Middle Grades Math: Triangle Theorems & Proofs
- NES Middle Grades Math: Similar Polygons
- NES Middle Grades Math: The Pythagorean Theorem
- NES Middle Grades Math: Quadrilaterals
- NES Middle Grades Math: Circles
- NES Middle Grades Math: Circular Arcs & Measurement
- NES Middle Grades Math: Transformations
- NES Middle Grades Math: Data & Graphs
- NES Middle Grades Math: Statistics
- NES Middle Grades Math: Data Collection
- NES Middle Grades Math: Samples & Populations
- NES Middle Grades Math: Probability
- NES Middle Grades Math: Sets
- NES Middle Grades Mathematics Flashcards