Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 469 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:
*Kevin Newton*

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

One of the most useful aspects of math is the ability to take a rate and use it to solve questions of time or quantity. In this lesson, we'll learn how to use rates, time, and quantity to solve for each other.

Surely you've seen speed limit signs before. In black, bold writing they proclaim that you cannot legally go faster than the speed listed. Speed limits are really rate limits, as they limit the pace at which you can drive. A **rate** is just that, it is a definition of pace between two quantities. If the speed limit is 45 miles per hour, you can only go 45 miles in one hour. There is no limit on how many hours you can drive, but instead, it is an expression of what you can do in that hour.

Still, it's not just while driving that you are likely to encounter rates. If you go to the deli counter at a supermarket, you order meat and cheese in terms of pounds with the price listed. The price per pound is a rate. Something that is really important to notice about rates, however, is that they are almost always in terms of one of something. Speed limit signs are not posted in terms of fours of hours, but in terms of one hour. Likewise, deli meat is sold at a price per one pound, not a price per nine pounds.

This means that rates are remarkably useful things. We can quickly calculate how long it will take us to reach a destination by just knowing the distance to the goal. In short, they can effectively put an end to the chorus of 'Are we there yet?' from the back seat. Not only can rates calculate distances, but they can calculate costs. We can calculate costs of multiple pounds of ham by simply knowing the cost per pound. In short, rates allow us to quickly relate two different quantities to each other because they provide a link between the two.

Not only are rates useful, but they are remarkably easy to use. Remember how I said that rates almost always were in terms of one of something? That means that you don't have to think about too much cross-multiplying when using rates, since you'll be multiplying by one. If that doesn't make sense yet, don't worry about it - we're almost there! For now, just remember that as long as you can make sure that the units match up properly, you're good to go.

Making sure that the units match up properly is where many people get tricked up when using rates. Remember, the units are there to help you. Sure, it may save you a little bit of paper space to not write down miles or miles per hour, but the units will really help you keep your thinking straight. So, how do you solve something using rates?

First, figure out what it is that you are trying to solve for. For example, if you are solving for how long it will take you to get to a destination, acknowledge that time is what you are trying to solve for. Then, write down the information you've got. If you're solving for time, for example, you should have the distance as well as the rate in terms of distance over time. Remember, miles per hour is just another way of saying distance over time. Ask yourself what you have to do to end up with only the desired unit left as time. In solving for hours, that means setting up the problem where you divide out the miles. As such, you'll have to flip the rate. From there, divide out the units for distance leaving only the unit for time, and solve the math.

That may have all sounded complicated, so let's use an example to help us understand it. Say that you were driving at a speed of 60 miles per hour, and you wanted to know how long it would take you to go 120 miles. First, what do you want to find? You want to find the time, so you're focusing on the hours. Right now, in our rate, the time is on the bottom, but you want to divide by the distance. As such, flip the equation to be 1 hour over 60 miles. Divide 120 miles by 60 miles, and you'll get the number of hours, 2.

Or, better yet, let's say that you reached your final destination where you had wanted to have a pool party and are met with an empty pool. It seems that the water had to be pumped out, so now your friend has to start all over again. Luckily, the local fire department has agreed to let you use a fire hydrant to get more water per minute. The fire hydrant provides water at a rate of 1,000 gallons per minute, and your friend has a pool that holds 30,000 gallons. How long will it take to fill the pool?

In this case, you want to solve for time, so you need to look at your formula and isolate time by itself. In this case, that means that time is equal to the capacity of the pool over the rate of the hose. That means that it is 30,000 gallons over 1,000 gallons per minute. Do the math, and you end up with 30 minutes.

In this lesson, we learned how to use **rates** to solve one-step problems. Rates are very useful since they let us figure out everything from how much meat to buy at the deli counter to how long we are from our final destination. When using rates, the easiest way to make sure that you are getting the right answer is to follow the units and let them lead you to the proper answer. That could mean flipping a rate, but it will help make sure that your math is correct.

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 50 of the course:

Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Ratios & Rates: Definitions & Examples 6:37
- How to Find the Unit Rate 3:57
- How to Solve a One-Step Problem Involving Ratios 4:32
- How to Solve a One-Step Problem Involving Rates 5:06
- Proportion: Definition, Application & Examples 6:05
- Calculations with Ratios and Proportions 5:35
- How to Solve Problems with Time 6:18
- Distance Formulas: Calculations & Examples 6:31
- How to Find an Unknown in a Proportion
- Calculating Unit Rates Associated with Ratios of Fractions
- Proportional Relationships Between Two Quantities
- Identifying the Constant of Proportionality 6:10
- Representing Proportional Relationships by Equations
- Graphing Proportional Relationships
- Proportional Relationships in Multistep Ratio & Percent Problems
- Constructing Proportions to Solve Real World Problems
- Go to 6th-8th Grade Math: Rates, Ratios & Proportions

- 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
- Prejudice, Stereotyping & Discrimination
- Aggression in Social Psychology
- Interviewing Job Candidates
- Adapting to Changes in Business as a Manager
- The Changing Work Environment
- 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
- Study.com CLEP Scholarship: Application Form & Information
- List of FTCE Tests
- CLEP Prep Product Comparison

- Common Financial Ratios: Terms & Use
- What is Petty Theft? - Definition, Consequences & Law
- Collaborative Negotiation: Definition, Strategy & Examples
- What Is Larceny? - Definition, Types & Examples
- Word Choice in an Informational Text
- Clothing Construction: Terms, Basics & Methods
- Mixtec Writing: Codex Zouche-Noutall & Codex Bodley
- Circularly Linked Lists in Java: Creation & Uses
- Quiz & Worksheet - LM Curve in Macroeconomics
- Quiz & Worksheet - Antoine Lavoisier & Chemistry
- Quiz & Worksheet - Action Plans for Teams
- Quiz & Worksheet - Adaptable Organizations
- International Law & Global Issues Flashcards
- Foreign Policy, Defense Policy & Government Flashcards

- Linear Algebra Syllabus & Lesson Plans
- Resources for Texas Educators
- Shiloh by Phyllis Reynolds Naylor Study Guide
- Building Customer Relationships
- 8th Grade US History: Enrichment Program
- Earth Materials
- Glencoe Chemistry - Matter And Change Chapter 23: The Chemistry of Life
- Quiz & Worksheet - LCM Method in Accounting
- Quiz & Worksheet - Reasons for Substance Use, Abuse & Dependence
- Quiz & Worksheet - Types of Laboratory Measurements & Their Units
- Quiz & Worksheet - About Voyeurism, Frotteurism & Pedophilia
- Quiz & Worksheet - Delusional Mental Health Disorders

- How to Write a Thank You Letter to a Teacher
- Chebyshev's Inequality: Definition, Formula & Examples
- Bacteria Experiments for Kids
- Veterans Day Lesson Plan
- Animal Farm Lesson Plan
- Mexican-American War Lesson Plan
- Digital Citizenship Lesson Plan
- Average PSAT Score for Sophomores
- Essay Prompts, Rubric & Instructions for Advanced Technical Writing
- PSAT Test Dates
- Companies That Offer Tuition Reimbursement
- Lyndon B. Johnson and the Vietnam War: Learning Objectives & Activities

Browse by subject