Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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:
*Jeff Calareso*

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

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.

Meet Jason Burger and Jennifer Queen. They're not only married; they just started a business together: Burger Queen.

This is great. How great? So great that they now need to learn about proportions to help their business grow.

A **proportion** is a set of ratios that are equal to each other. What's a ratio? It's a comparison of one thing to another. For example, at Burger Queen, it takes one pound of beef to make four burgers. So the ratio of pounds of beef to burgers is 1 to 4, which we can write as 1/4.

A proportion is just two ratios that equal each other. So if Jennifer is ordering beef, and she wants to have enough for 500 burgers, she sets up an equation: 1/4 = *x*/500. Instead of four burgers, she wants 500. Instead of one pound of beef, she'll need, well, we don't know. So we use *x*.

To solve this proportion problem, we cross-multiply. So 1 * 500 = 4 * *x*. That's 4*x* = 500. 500 divided by 4 is 125. So Jennifer needs 125 pounds of beef for 500 burgers. Our final proportion looks like this: 1/4 = 125/500. In any proportion, you could simplify one side of the equation so that it's the exact same as the other. 125/500 can be simplified to 1/4.

That's pretty much all you need to know to solve proportion problems. Figure out your fractions, then cross-multiply. Let's try a sample problem.

In one hour, Burger Queen serves 35 customers. At that rate, how many customers will be served in eight hours?

We need to figure out our fractions. We're comparing hours to customers. Our first ratio is 1/35. That's one hour to serve 35 customers. Our second ratio is *x*/8. We want to know how many customers, or *x*, will be served in eight hours.

If we set them equal to each other, that's 1/35 = *x*/8. Wait, that's not right. Our numerator in the first ratio is one hour. In the second one, our hours are in the denominator. That won't do. That's like putting a piece of a bun between two burgers. Be sure that your ratios line up. If it's helpful, include the labels of what they describe.

We should have 1/35 = 8/*x*. That's hours to hours and people to people. Much better.

Now, let's cross-multiply. This is *x* = 35 * 8. So *x* is 280. In eight hours, Burger Queen serves 280 people. Not bad!

In fact, things are going very well for Burger Queen. First, they expand to three locations. After successfully avoiding a trademark lawsuit from a similarly-named competitor, they decide to ramp things up and expand to 15 total restaurants. Wow!

Expansion means proportion problems. If three restaurants require 46 employees, how many employees will be required at 15 restaurants?

Let's set up some ratios. We're going from three to 15 locations, so our first ratio is 3/15. And we had 46 employees, but we don't know how many we'll need, so our other ratio is 46/*x*. That makes our equation 3/15 = 46/*x*.

That gets us 3*x* = 15 * 46. 15 * 46 is 690. Divide that by 3 to get 230. So they'll need 230 people. That's a lot of fry cooks, burger flippers and the all-important multitasking drive-thru operator/soda filler/cash handler/bagpipe players. Did I mention Burger Queen has bagpipe players? And yet they still manage to draw in customers. Those burgers must be amazing.

But wait, did we have to solve this problem in this way? Could we have said three locations require 46 people, so 3/46 = 15/*x*? Yep, we could. As long as our ratios accurately represent the facts and are set equal to each other appropriately, then there's more than one way to peel this potato. For fries. It's a French fry reference. Oh, never mind. Let's move on.

One day, Jason launches a new promotion. All day Tuesday, burgers are 25% off. If a burger normally costs $4.50, what is the sale price?

Let's set up our proportion! Okay, let's see. We want a ratio of the sale price to the original price. That's going to be *x*/4.50.

But what's the other ratio? This is a percent problem. A percent is just a ratio, though it may not look like one. Kind of like how a veggie burger is still called a burger, but it doesn't look (or taste) like one. 25% is just 25/100.

So is our proportion *x*/4.50 = 25/100? No. Remember, the burgers are 25% off. The sale price will then be 75%, or 100 - 25, of the original price. That makes our proportion *x*/4.50 = 75/100.

It's cross-multiply time. 100*x* = 4.50 * 75. So 100*x* = 337.5. And x = 3.375. Let's round that to $3.38. That's our sale price on burgers.

To summarize, a **proportion** is a set of ratios that equal each other. For example, 2/3 = 4/6.

To solve proportion problems, determine what your sets of ratios, or fractions, look like and how they are equal. Make sure you don't reverse one. Then just cross-multiply!

With percent problems, take extra care to note which fraction to use. For example, if something is 70% off, the ratio for the percent that includes the sale price is 30/100.

Now where did I put those fries?

Following this lesson, you'll have the ability to:

- Define proportion
- Explain how to solve problems with proportions
- Identify the extra care that needs to be taken when solving percent problems

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
3 in chapter 3 of the course:

Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- Ratios & Rates: Definitions & Examples 6:37
- How to Solve Problems with Money 8:29
- Proportion: Definition, Application & Examples 6:05
- Percents: Definition, Application & Examples 6:20
- How to Solve Word Problems That Use Percents 6:30
- Math Combinations: Formula and Example Problems 7:14
- How to Calculate a Permutation 6:58
- How to Solve Problems with Time 6:18
- Distance Formulas: Calculations & Examples 6:31
- Go to High School Algebra: Calculations, Ratios, Percent & Proportions

- Data Science for Marketing
- Individual Creativity in the Workplace
- Leadership in Action for Coaches
- Introduction to the Internet of Things
- Adaptive Leadership for Agile Organizations
- Logical vs. Creative Thinking in the Workplace
- Adaptive Technology & Innovation
- Marketing Analytics
- World Music Overview
- Big Data Analytics & Application
- Average AFQT Scores
- ASVAB Test Day Preparation
- How To Pass the GED Reading Test
- What is the AFQT?
- What is the Highest ASVAB Score?
- ASVAB Scores for Marines
- Can You Retake the ASVAB?

- History of Photography Materials & Techniques
- Basketry: Materials, Techniques & Processes
- Surface Area of a Pentagonal Prism
- Displaying Three-Dimensional Art: Methods & Techniques
- The Role of the Trauma Nurse in Injury Prevention & Outreach
- Common Practice Style & Developing Tonal Harmony
- Flast v. Cohen: Case Brief, Decision & Dissent
- Leadership with Intention & Reflection
- Quiz & Worksheet - Native American Art History
- Quiz & Worksheet - Mrs. Van Daan in Diary of a Young Girl
- Quiz & Worksheet - Fiber Art Materials Terms
- Quiz & Worksheet - Processes in Sculpting
- Quiz & Worksheet - Inheritance in Java
- Introduction to Research Methods in Psychology Flashcards
- Clinical Assessment in Psychology Flashcards

- Nutrition 101: Science of Nutrition
- European History Study Guide
- AP Physics 1: Homeschool Curriculum
- College Biology Textbook
- MTTC Biology: Practice & Study Guide
- NMTA Middle Grades Math: Properties of Lines
- Laboratory Safety & Procedures
- Quiz & Worksheet - Gestalt Therapy
- Quiz & Worksheet - Heisenberg Uncertainty Principle
- Quiz & Worksheet - Impact of Highway & Canal Transportation on Ecosystems
- Quiz & Worksheet - Endotherms
- Quiz & Worksheet - Dehydration Synthesis

- What Is Gene Expression? - Regulation, Analysis & Definition
- How to Subtract Fractions from Whole Numbers
- US Geography Lesson Plan
- Oregon Science Standards for 5th Grade
- SBEC Technology Application Standards for Teachers
- Dolch Sight Words Games & Activities
- How to Learn English Quickly
- How to Pass the Series 7 Exam
- Tennessee Homeschool Laws
- Book Club Suggestions
- Homeschooling in Wyoming
- Kentucky Science Standards for 3rd Grade

Browse by subject