# Ch 2: ELM Test - Numbers and Data: Rational Numbers

### About This Chapter

## ELM Numbers and Data: Rational Numbers - Chapter Summary

Prepare for the ELM math exam with our help. Interactive quizzes follow the short video lessons so you can get immediate feedback on your progress. This chapter's lessons include the following concepts:

- Building and reducing fractions
- Least common denominators
- Ordering and comparing fractions
- Mixed numbers and improper fractions
- Adding, subtracting, multiplying and dividing fractions and mixed numbers
- Estimating with fractions
- Complex fractions
- Ratios and proportions

These lessons explain strategies for comparing and ordering fractions in addition to giving you ample practice solving problems with fractions. After you take the quizzes, you can revisit any lessons that might need more attention.

### ELM Numbers and Data Objectives

The ELM math proficiency exam is required if you plan to attend a school in the California State University system. Your school will use the results to determine which math classes are appropriate for you.

The lessons in this chapter about rational numbers are part of the larger section of Numbers and Data on the ELM. The Numbers and Data portion of the exam constitutes about 35% of the 50-question test. You can expect your exam to test the following objectives:

- Solve problems using fractions, percents and decimals in context
- Order and compare rational numbers expressed as fraction or decimals
- Interpret and use proportion and ratio
- Use estimation
- Understand data presented in tables, charts and graphs
- Interpret and calculate mean and median

The videos and quizzes in this chapter and the others related to Numbers and Data can help you prepare for test day.

### 1. How to Build and Reduce Fractions

Fractions are a fundamental part of everyday life. Fractions represent a comparison of a part to the whole. To reduce fractions, we will divide by the greatest common factor, or the GCF.

### 2. How to Find Least Common Denominators

Finding a Least Common Denominator is an important tool when working with fractions. To find least common denominators, we will use multiples of our numbers.

### 3. Comparing and Ordering Fractions

Comparing and ordering fractions is way to examine fractions that contain different-sized sets. In order to compare these fractions, you must find a common denominator and make equivalent fractions.

### 4. Changing Between Improper Fraction and Mixed Number Form

Improper fractions and mixed numbers are two different types of fractions. They both have different purposes when using fractions in a problem. In this lesson, you will learn how to convert between these two different forms.

### 5. How to Add and Subtract Like Fractions and Mixed Numbers

When adding and subtracting fractions, you must be sure to have a common denominator. Once you have a common denominator, you just add or subtract your numerators and then your whole numbers. Learn how in this lesson.

### 6. How to Add and Subtract Unlike Fractions and Mixed Numbers

Simple fraction arithmetic gets a little more complicated when our denominators don't match. In this lesson, we'll learn how to add and subtract unlike fractions. Then, we'll do the same with mixed numbers.

### 7. Multiplying Fractions and Mixed Numbers

Multiplying fractions is much more straightforward than adding, subtracting or dividing fractions. In this lesson, learn how it works. We'll also learn how to multiply mixed numbers.

### 8. Dividing Fractions and Mixed Numbers

Dividing fractions and mixed numbers? It sounds daunting, but it's not as tricky as it sounds. In this lesson, we'll learn how to divide fractions and mixed numbers.

### 9. Practice with Fraction and Mixed Number Arithmetic

Adding whole numbers is one thing. But adding fractions and mixed numbers? That's not so simple. Or is it? In this lesson, we'll practice arithmetic with both fractions and mixed numbers.

### 10. Estimation Problems using Fractions

When working with fractions, estimating can save time and effort while getting you very close to the correct answer. In this lesson, we'll learn how to use estimation to quickly solve problems involving fractions.

### 11. Solving Problems using Fractions and Mixed Numbers

Fractions don't just live in math problems. They're all around us, helping us through our lives. In this lesson, we'll look at real scenarios where your ability to work with fractions can save the day.

### 12. How to Solve Complex Fractions

Did you know fractions can nest within fractions? In this lesson, we'll learn about complex fractions and look at two different methods for solving them.

### 13. 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.

### 14. Using Proportions to Solve Ratio Problems

Proportions allow many different real-world estimations and calculations, and can be done using a straightforward process. In this lesson, learn how to use proportions to solve ratio problems.

### 15. Practice Problems for Calculating Ratios and Proportions

In this lesson, you'll get a quick review of a type of math problem that shows up on the SAT: ratios and proportions. We'll walk through some problems in the video, and you can test your skills in the quiz questions.

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### Other Chapters

Other chapters within the ELM: CSU Math Study Guide course

- ELM Test - Numbers and Data: Basic Arithmetic Calculations
- ELM Test - Numbers and Data: Decimals and Percents
- ELM Test - Numbers and Data: Irrational Numbers
- ELM Test - Numbers and Data: Data & Statistics
- ELM Test - Algebra: Basic Expressions
- ELM Test - Algebra: Exponents
- ELM Test - Algebra: Linear Equations & Inequalities
- ELM Test - Algebra: Absolute Value Equations & Inequalities
- ELM Test - Algebra: Polynomials
- ELM Test - Algebra: Rational Expressions
- ELM Test - Geometry: Perimeter, Area & Volume
- ELM Test - Geometry: Properties of Objects
- ELM Test - Geometry: Graphing Basics
- ELM Test - Geometry: Graphing Functions
- About the ELM Test
- ELM Flashcards