Back To Course

College Algebra: Help and Review27 chapters | 228 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn how to divide and take the reciprocal of any rational expression. Learn the one easy step you take to be able to find your answer quickly and easily.

In this video lesson, we talk about **rational numbers**. What are they? They are numbers that can be written as the fraction of two integers. Remember that integers are whole numbers, both positive and negative. One way to think about rational numbers is when you want to share a certain number of things with a group of people, you have to divide what you have by the number of people. The math you get is a rational number.

For example, splitting 4 donuts among 3 people gives you 4/3, which is a rational number. Rational numbers include both fractions and your whole numbers because you can rewrite your whole numbers as a fraction being divided by 1. Your **rational expressions**, then, are math statements with rational numbers in them. So 4/3 by itself is both a rational number and a rational expression. (4/3) / (2/3) is a rational expression because it is a math statement with rational numbers in it.

You might be looking at that last rational expression and wondering how in the world you would evaluate that kind of problem. What you are seeing is the division of two rational numbers. In this case, we see a fraction being divided by another fraction.

How do we evaluate this kind of problem? We evaluate it by turning our division problem into a multiplication by applying the one easy step of flipping the fraction we are dividing by. In our problem, the fraction we are dividing by is 2/3. We flip it by moving the denominator to the numerator and moving the numerator to the denominator. So 2/3 flipped becomes 3/2.

Now we can change our division into multiplication. So (4/3) / (2/3) turns into (4/3) * (3/2). Do we know how to multiply fractions? Yes, we simply multiply across. We multiply the numerators together, and we multiply our denominators together. So (4/3) * (3/2) becomes 12/6. Now we look at what we got and see if we can simplify it more. Yes, we can. 12/6 simplifies to 2. Our final answer is 2.

How can we remember this process? Well, if you think of a division problem as having an upper part and a lower part, then you can think of the lower part as being opposite the upper part. If the lower part is opposite, then to fix it, we just flip everything around. What is on top goes on the bottom, and what is on the bottom goes on the top. We only do the flipping on the lower part of our division problem. After we flip, there is no need for the division because we've made things right. We can now multiply.

Taking the **reciprocal** is very closely related to division because it is 1 divided by our number. For example, the reciprocal of 4 is 1/4. This is easy to do when we have whole numbers. But what if we have a rational number that is a fraction? How do we take the reciprocal of one of these? For example, how do we take the reciprocal of (4/3)? We use the definition of reciprocal and we do 1 divided by our number. We get 1 / (4/3).

Now what? Well, we use what we know about dividing rational numbers and we flip the bottom rational number so that we can turn our problem into a multiplication problem. We get 1 * (3/4). Our answer, then, is 3/4. The reciprocal of 4/3 is 3/4. Do you notice something interesting here? Yes; the reciprocal of our rational number is simply the flipped version. To make it easy on yourself, just remember that the reciprocal of any rational number is simply the flipped version.

Let's look at some examples. The reciprocal of 5/4 is 4/5, the flipped version. Notice that the denominator is now in the numerator and the numerator is in the denominator.

What do you think the reciprocal of 6/7 is? That's right; it is 7/6.

What about division? How would you divide 9 by 1/3? 9 / (1/3). We flip the fraction in the denominator so we can turn it into a multiplication problem. We get 9 * (3/1). Our answer, then, is 27.

One more. (1/5) / (1/4). What do we do? Yes, we flip the bottom fraction and then turn the division into multiplication. (1/5) * (4/1). What does this equal? Multiplying straight across, we get 4/5. Our answer is 4/5.

Let's review what we've learned now. We learned that a **rational number** is a number that can be written as the fraction of two integers. A **rational expression** is a math statement with a rational number in it.

If we are dividing a rational number that happens to be a fraction, we flip the bottom fraction, the fraction we are dividing by so we can turn the problem into a multiplication problem. We then go ahead and multiply straight across. Since the **reciprocal** of a number is 1 divided by the number, the reciprocal of a rational number that is a fraction is simply the flipped version of it.

By successfully finishing this lesson, you can expand your ability to:

- Identify a rational expression
- Solve a division problem that includes rational numbers
- Find the reciprocal of a fraction

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
4 in chapter 16 of the course:

Back To Course

College Algebra: Help and Review27 chapters | 228 lessons

- Multiplying and Dividing Rational Expressions: Practice Problems 4:40
- Practice Adding and Subtracting Rational Expressions 9:12
- Rational Equations: Practice Problems 13:15
- Division and Reciprocals of Rational Expressions 5:09
- Solving Equations of Direct Variation 5:12
- Solving Equations of Inverse Variation 5:13
- Go to Working with Rational Expressions

- Go to Fractions

- Go to Factoring

- Psychology 316: Advanced Social Psychology
- Hiring & Developing Employees
- Accounting 305: Auditing & Assurance Services
- MTEL Physical Education (22): Study Guide & Test Prep
- Praxis Art - Content Knowledge (5134): Practice & Study Guide
- The Victim Movement
- Consequences of Crime Victimization
- The Nature of Violence
- Measuring Criminal Victimization
- Prejudice, Stereotyping & Discrimination
- Study.com CLEP Scholarship for Military Members
- Study.com Scholarship for Texas Students & Prospective Teachers
- Study.com Scholarship for Florida Students & Prospective Teachers
- What are TExMaT Exams?
- What is the Florida Teacher Certification Examination (FTCE)?
- Study.com TExES Scholarship: Application Form & Information
- Study.com FTCE Scholarship: Application Form & Information

- Forensic Evidence: Types, Definition & Cases
- Who is Candy in Of Mice and Men? - Description & Quotes
- Hills Like White Elephants: Summary, Characters & Setting
- How to Teach Math Facts to Kids
- Goal Setting for Reducing Organizational Stress
- Comparing ELD & SDAIE in English Learner Education
- Trauma Registry: Definition, Function & Components
- Independence Movements in Southeast Asia
- Quiz & Worksheet - Legal Self-Defense
- Quiz & Worksheet - Drugs, Violence & Crime
- Quiz & Worksheet - Agile Organization Traits
- Quiz & Worksheet - False Imprisonment: Meaning & Examples
- Quiz & Worksheet - Communication Techniques for Call Center Agents
- International Law & Global Issues Flashcards
- Foreign Policy, Defense Policy & Government Flashcards

- NES Essential Academic Skills Mathematics Subtest 3 (003): Practice & Study Guide
- Economics: High School
- Guide to Career Planning and Development
- ScienceFusion Earth's Water & Atmosphere: Online Textbook Help
- Advanced Excel Training: Help & Tutorials
- Invertebrates for High School Biology Lesson Plans
- Graph Symmetry Lesson Plans
- Quiz & Worksheet - Consistent System of Equations
- Quiz & Worksheet - Prime Factorization
- Quiz & Worksheet - Human Resource Management vs. Personnel Management
- Quiz & Worksheet - Stages of Meiosis
- Quiz & Worksheet - Executive Order 10988 of 1962 & the Civil Service Reform Act of 1978

- Harlem By Langston Hughes: Analysis & Overview
- Horatio Alger: Biography, Myth & Stories
- Sink or Float Lesson Plan
- Goal Setting Lesson Plan
- Scientific Notation Lesson Plan
- Scoring Changes on the New SAT
- How to Find an AP Environmental Science Released Exam
- How Many Questions are on the TABE Test?
- Free LSAT Prep
- Narrative Writing Prompts
- How to Ace a Panel Interview
- Scarcity Lesson Plan

Browse by subject