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.

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.

How'd you like to earn some money? Let's say I get paid $100 to wash the windows of a skyscraper. But, I'm afraid of heights, so I pay my buddy Larry 1/2 of what I'd get to do it for me. Larry then convinces his brother Darryl to do it for 1/2 of what he'd earn. Darryl convinces his other brother Darryl (whom we call Darryl 2) to do it for 1/2 of what he'd earn. Then, Darryl 2 comes to you and offers you 1/2 of what he'd earn. That's probably worth it, right?

Well, that's 1/2 of 1/2 of 1/2 of 1/2 of $100. 1/2 * 1/2 * 1/2 * 1/2 is 1/16, and 1/16 of $100 is $6.25.

Would you wash the windows of this building for $6.25?

I wouldn't. But, I wouldn't do it for $100, either. And, what did we just do to figure that out? We multiplied fractions! Let's learn more about it without the acrophobia.

To **multiply fractions**, we follow three steps. Step one: multiply the numerators; those are the top numbers. Step two: multiply the denominators; those are the bottom numbers. Step three: simplify the fraction, if necessary.

So, if we had 1/4 * 2/5, we start with 1 * 2, which is 2. Then we do 4 * 5, which is 20. Now we have 2/20. We can simplify that to 1/10. So, 1/4 * 2/5 is 1/10. This is just like what we did with the window washing example

Let's look at another one in context. Let's say we're in a band, and we're eating before our big gig. We get a mega-super-carnivore pizza. I'm super hungry, so I take 1/2 of it, which is 4 slices. But after eating just 1 slice, which is 1/4 of what I took, I can feel my arteries clogging, so I stop. How much did I eat? I ate 1/4 of 1/2, so let's do 1/4 * 1/2. 1 * 1 is 1. 4 * 2 is 8. So, I ate 1/8 of the pizza.

Okay, now I need to get over my illness, because we're going onstage soon. We're opening the gig for another group. It's a sold-out show at a 3,600-person club. If 5/9 of the total crowd is there early to hear us play, and 1/10 of them buy our t-shirts after being blown away by our awesome sound, how many shirts do we sell?

So, we do 5/9 * 1/10. 5 * 1 is 5, and 9 * 10 is 90. That's 5/90. We can simplify that to 1/18. What is 1/18 of 3,600? It's 200. That's a lot of shirts! Well, it is for us. And, it's enough gas money to get home.

On the way, our drummer spends 2/3 of the trip telling us about his fantasy kickball league. It's pretty boring, and you sleep through a good 7/8 of the story. How much of the trip did you spend sleeping? It's 2/3 * 7/8. 2 * 7 is 14, and 3 * 8 is 24. So, 14/24, which simplifies to 7/12. That's some good shuteye.

Okay, but what do we do if the fractions get more complicated? Let's talk about how we **multiply mixed numbers**. This is a four-step process. Step one: convert to improper fractions. Step two - well, really, we just follow the steps from earlier: multiply the top, multiply the bottom, then simplify.

If we have 3 1/2 * 2 1/4, first we convert to improper fractions. To convert 3 1/2, multiply the whole number times the denominator, that's 3 * 2, or 6, then add that to the numerator. So, that's 7/2. With 2 1/4, we do 2 * 4, or 8, and get 9/4. 7/2 * 9/4? 7 * 9 is 63, and 2 * 4 is 8. So, it's 63/8. That simplifies to 7 7/8.

How about one in context? Let's say I quit the band and start training to make the NBA. I run 3 1/4 miles on Tuesday. If I want to run 2 1/2 times as far on Wednesday, how far will I go?

First, convert to improper fractions. 3 1/4 becomes 13/4. 2 1/2 becomes 5/2. So, we have 13/4 * 5/2. 13 * 5 is 65. 4 * 2 is 8. So, 65/8. That simplifies to 8 1/8. Can I do 8 1/8 miles? I just multiplied mixed numbers, so I think so! Well, actually, there's no proven correlation between multiplying mixed numbers and distance running.

I have another problem. I'm 6'3' '. That's 6 3/12 feet. Tall? Sure, but not NBA tall. Then I meet an old wizard selling magic growing cookies. Magic and cookies? I'm all in. He says they'll make me grow 2 5/6 as tall as I am now. That seems like a random amount, but he's a wizard selling magic cookies, so I go with it. What is 6 3/12 * 2 5/6?

With 6 3/12, we do 6 * 12, which is 72, then add that to 3 to get 75/12. 2 5/6 becomes 17/6. With 75/12 * 17/6, we do 75 * 17, which is 1275. And then 12 * 6, which we know is 72. So, 1275/72. That simplifies to 17 51/72, then to 17 17/24. So, I'll be over 17 feet tall. I'll definitely make the NBA at that height.

Okay, let's do one more. After the magic cookies totally fail to make me even an inch taller, though they were tasty, I get a job feeding animals at the zoo. The lions get 12 2/5 pounds of meat at a time. The tigers get 1 2/3 times that. What do the tigers get? And why does the zoo write their instructions like this? I don't know, but I do know how to figure out the tigers' food. That's important, because no one wants hungry tigers.

12 2/5 converts to 62/5. 1 2/3 converts to 5/3. 62 * 5 is 310. 5 * 3 is 15. So, 310/15. That simplifies to 20 10/15, or 20 2/3. That's a lot of meat, but they're big cats.

In summary, to **multiply fractions**, we follow three steps: first, multiply the numerators; second, multiply the denominators; finally, simplify as needed. With mixed numbers, we start by converting them to improper fractions, then we just multiply the fractions!

You should be able to multiply fractions and mixed numbers after watching this video lesson.

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
7 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
- Practice with Fraction and Mixed Number Arithmetic 7:50
- 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

- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Computer Science 203: Defensive Security
- JavaScript Language Basics
- Forms & JavaScript
- JavaScript & HTML
- Error Handling, Debugging & Events in JavaScript
- HTML Elements & Lists
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP
- MEGA Exam Registration Information
- MEGA & MoGEA Prep Product Comparison
- PERT Prep Product Comparison

- Human Experience in Texts: Literary Features & Analysis
- System Calls: Function, Importance & Categories
- Multilingualism: Definition & Role in Education
- Supporting Adaptive Skills in Preschool
- Networking Components in Commercial Networks
- Managing Cybersecurity Risks through User Training, Awareness & Accountability
- Practical Application for C Programming: Recursive Functions
- Quiz & Worksheet - Stative Verbs
- Quiz & Worksheet - Significance of the Ganges River
- Quiz & Worksheet - Behavioral Theory & Learning Environments
- Quiz & Worksheet - Raising Reading Rate & Accuracy
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Common Core Math Worksheets & Printables
- 12th Grade Math Worksheets & Printables

- High School Trigonometry: Help and Review
- 11th Grade English: Help and Review
- MEGA Elementary Education Science Subtest: Practice & Study Guide
- MTEL Speech (44): Practice & Study Guide
- Principles of Business Ethics: Certificate Program
- SHSAT Math: Quadrilaterals
- Systems of Government
- Quiz & Worksheet - Method for Making a Dot Plot
- Quiz & Worksheet - Magnetic Storage Devices
- Quiz & Worksheet - Enantiomers vs. Diastereomers
- Quiz & Worksheet - Adding Two Numbers in Java
- Quiz & Worksheet - Practice Differentiating Logarithms

- Brain Ventricles: Definition & Function
- Avoidant Personality Disorder: Symptoms & Treatment
- Alternative Teacher Certification in Maryland
- Special Education Certification in Texas
- Common Core State Standards in Idaho
- Civil War Activities for Kids
- 5th Grade Math Centers
- Utah Science Standards for 4th Grade
- California Alternative Teacher Certification
- Common Core State Standards in Maryland
- 9th Grade Reading List
- Finding Summer Teaching Opportunities

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

Browse by subject