Back To Course

ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

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.

Let's talk about cookies. Baking cookies is a form of chemistry - tasty, sometimes chocolate chip chemistry. But, there also seems to be an awful lot of math involved. This is especially true if you're like me and you don't always have an unlimited supply of every ingredient.

For example, maybe you have only 1 1/2 cups of flour left and you need to modify your recipe so that you maximize your cookie potential. You're going to need to divide fractions. Let's learn more about this critical skill.

To **divide fractions**, we follow three steps. Step one: flip the second fraction. This gives you its reciprocal. Step two: multiply the fractions. This means you multiply the numerators, then the denominators. Finally, step three: simplify as needed.

So, with 9/10 divided by 4/5, we flip the 4/5 to get 5/4. That's its reciprocal. Then, we multiply. 9 * 5 is 45, and 10 * 4 is 40. So, 45/40. We simplify that to 9/8, or 1 1/8.

Let's try a few in context. Let's say you're throwing a party. You have a punch bowl that has 8/9 of a gallon of punch left. If your cups will hold one cup of punch, which is 1/16 of a gallon, how many cups can you fill?

We need to divide 8/9 by 1/16. Okay, first step? Flip the second fraction. So, 1/16 becomes 16/1. Then, multiply 8/9 by 16/1. That's 128/9. That simplifies to 14 2/9. So, you can fill 14 cups and then someone gets stuck with 2/9 of a cup, which isn't great, but 14 people get full cups.

Next up, you're dishing out pizza. Unfortunately, you didn't plan this well. You only have 7/8 of a pizza on hand. You somehow only ordered one pizza and then you ate one slice while filling punch cups. There are 21 people at your party. How much of the pizza will each person get?

This is 7/8 divided by 21. Remember, 21 is the same as 21/1, so to get its reciprocal, we do 1/21. Now, we multiply 7/8 by 1/21. That's 7/168. That simplifies to 1/24. So, everyone gets 1/24 of the pizza. I call the pepperoni slice!

Let's try one more of these. After the pizza debacle, you're rationing your other snacks. You turn to your guacamole, of which you have 4/5 of a pound. You've overanalyzed this a bit and determined that people use about a tablespoon, or 1/32 of a pound, on each chip. How many chips can dip in your guacamole?

This is 4/5 divided by 1/32. Let's flip 1/32 to get 32/1. Then, multiply 4/5 by 32/1. That's 128/5, or 25 3/5. Hmmmâ€¦ 25 chips. This isn't only a good lesson in dividing fractions; it's also a good lesson in party planning.

Rather than focus on effective party preparation tips, let's take our fraction division to the next level and discuss dividing mixed numbers. To **divide mixed numbers**, we follow four steps. Step one: convert to improper fractions. So, if we have 3 1/3, we multiply the whole number times the denominator. That's 3 * 3, or 9. Then, add that to the numerator. So, we get 10/3.

Next, we follow the steps to divide fractions. Flip the second one, then multiply, then simplify. So, with 3 1/3 divided by 5 1/2, we convert both to improper fractions. We know 3 1/3 is 10/3. With 5 1/2, 5 * 2 is 10. Add 10 and 1 and get 11/2. Then, we flip that one to get 2/11. So, 10/3 * 2/11. 10 * 2 is 20. 11 * 3 is 33. So, 20/33. That looks like it should simplify, but it actually doesn't. So, we're done!

Let's try some in context. We're going to leave the party behind and talk about flowers. Let's say you're building a raised flower bed out of some scrap lumber. You have a board that's 10 3/4 feet long. You want pieces that are 2 1/2 feet long for the flower bed. How many pieces can you get?

We divide 10 3/4 by 2 1/2. First, convert to improper fractions. 10 3/4 becomes 43/4. 2 1/2 becomes 5/2. Next, flip 5/2 to get 2/5. Now, multiply 43/4 times 2/5. That's 86/20. That simplifies to 4 3/10. You needed four sides, so you have enough wood!

Ok, now let's say you're planting flowers. You have 6 1/4 square feet of space, and your flowers need 1 1/8 square feet to flourish. How many flowers can you plant?

So, 6 1/4 divided by 1 1/8. 6 1/4 becomes 25/4. 1 1/8 becomes 9/8. We flip 9/8 to get 8/9. And 25/4 times 8/9? 25 * 8 is 200. 4 * 9 is 36. So, we get 200/36. That simplifies to 5 5/9. Well, you can't really plant 5/9 of a flower, but you know you have space for 5 flowers and a little spare room.

After planting your flowers, you decide to make some cookies. Remember when I mentioned those earlier? I haven't stopped thinking about them, and now it's time to solve that problem once and for all. Plus, all that building and planting earned you some cookies, right? You realize you're running a bit low on sugar, though. You have 2 1/5 cups of sugar. Your recipe says each batch requires 1 1/6 cups of sugar. How many batches can you make?

So, 2 1/5 divided by 1 1/6. 2 1/5 becomes 11/5. 1 1/6 becomes 7/6. We flip 7/6 to get 6/7. Then, we multiply 11/5 by 6/7. 11 * 6 is 66. 5 * 7 is 35. 66/35 simplifies to 1 31/35. Oh no! You can definitely make one batch. But then you only have 31/35 of what you need for a second batch. This was definitely a two batch kind of day, so it looks like you'll be asking a neighbor for 4/35 of a cup of sugar. Let's hope you have the 4/35 cups measuring cup handy.

In summary, there are three steps involved with **dividing fractions**. First, flip the second fraction to get its reciprocal. Next, multiply the fractions. Finally, simplify as needed. When you want to **divide mixed numbers**, you start by converting them to improper fractions, then follow the steps to divide fractions.

After you have finished with this lesson, you'll be able to:

- List the steps for dividing fractions
- Explain the additional step required when dividing mixed numbers

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

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 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
8 in chapter 2 of the course:

Back To Course

ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

- How to Build and Reduce Fractions 3:55
- How to Find Least Common Denominators 4:30
- Comparing and Ordering Fractions 7:33
- Changing Between Improper Fraction and Mixed Number Form 4:55
- How to Add and Subtract Like Fractions and Mixed Numbers 4:14
- How to Add and Subtract Unlike Fractions and Mixed Numbers 6:46
- Multiplying Fractions and Mixed Numbers 7:23
- Dividing Fractions and Mixed Numbers 7:12
- Estimation Problems using Fractions 7:37
- Solving Problems using Fractions and Mixed Numbers 7:08
- How to Solve Complex Fractions 5:20
- Calculations with Ratios and Proportions 5:35
- Using Proportions to Solve Ratio Problems
- Practice Problems for Calculating Ratios and Proportions 5:59
- Go to ELM Test - Numbers and Data: Rational Numbers

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Algorithmic Analysis, Sorting & Searching
- Computer Programming Basics
- Stacks & Queues for Data Structures
- Functions & Modules in Programming
- Built-In Data Types for Programming
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- The Lion of the Tribe of Judah: Symbol & Meaning
- Partial Fractions: Rules, Formula & Examples
- Risk Identification: Process & Analysis
- Design Constraints in Engineering: Definition & Example
- What is a VLAN? - Definition, Function & Implementation
- Room 101 Lesson Plan
- Story Quilt Lesson Plan
- Quiz & Worksheet - Difference Between Temple & Synagogue
- Quiz & Worksheet - Dorsiflexion vs. Plantar Flexion
- Quiz & Worksheet - Narrative of the Life of Frederick Douglass
- Quiz & Worksheet - A Midsummer Night's Dream Play Within a Play
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Social Awareness Teaching Resources
- What is Common Core? | Common Core Math & ELA Standards

- Strategic Management in Business
- MTTC Health (043): Practice & Study Guide
- Praxis Middle School English Language Arts (5047): Practice & Study Guide
- NES Essential Academic Skills Writing Subtest 2 (002): Practice & Study Guide
- MTEL Mathematics (Elementary) (53): Practice & Study Guide
- Factors that Affect Students and Schools
- 20th Century Wars, Cultures & Legacies
- Quiz & Worksheet - 18th Century Monarchs in Great Britain
- Quiz & Worksheet - The End of Apartheid
- Quiz & Worksheet - Advantages & Disadvantages of Direct Democracy
- Quiz & Worksheet - WWII Consequences
- Quiz & Worksheet - What Is Terrorism?

- How to Master Multiple Choice Questions on the AP Chemistry Exam
- Adrenal Fatigue: Symptoms, Treatment & Diet
- What is a Lexile Score?
- Is the FTCE Middle Grades English 5-9 Test Difficult to Take?
- Aerospace Engineering Scholarships for High School
- Essay Prompts, Rubric & Instructions for English Literature
- How to Pass a Chemistry Test
- Failed the USMLE Step 1: Next Steps
- Renaissance Lesson Plan
- TExES Music Exam Dates
- Mechanical Engineering Scholarships for High School Seniors
- Using an Online Tutor

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject