Back To Course

Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

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:
*Jennifer Beddoe*

There are three basic number properties that help to form the backbone of algebra. One of those properties is the associative property. This lesson will define the associative property and give some examples of how it works.

How many times have you been out with friends and heard, or yelled, that statement: 'I call shotgun!'? The unquestioned right to sit in the front seat and have room to stretch your legs and de facto control of the radio. At the next stop, someone else may call out for their turn in the front seat.

I bet the thought never crossed your mind that sitting in different seats in the vehicle did not change the makeup of the people that were with you. They are all the same, no matter where they are sitting. Bob is still Bob wherever he is riding, and Jody is still herself, even if she's no longer in control of what music you are listening to.

So, who's in charge of the math radio? There is a mathematical rule governing that very question! OK, it's not presented in those terms, but it means the same. And the answer is the same as when you are out with your friends. But first, let's do a bit of background.

In mathematics, there are three basic principles for how equations work. They form the backbone of all higher math. These properties are:

â€¢ The commutative property

â€¢ The associative property

â€¢ The distributive property

They all govern different aspects of how you can manipulate and solve mathematical equations correctly.

The **associative property** is the focus for this lesson. It states that terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same. In other words, it doesn't matter which terms are in the back seat and which are in the front - the makeup of the equation is the same, just like it was in the car in the introduction.

Let's look a little bit at how that works. If you have an addition problem such as (3 + 6) + 13, you can also write it as 3 + (6 + 13), and, when you solve the problem, the answer will be the same either way: 22. Remember that the parenthesis signify the portion of the problem that should be completed first.

So, the associative property states that it doesn't matter which portion of the problem you do first, the answer will be the same. Again, this only works with addition and multiplication problems, and not if they are mixed. With mixed operations, you need to always follow the order of operations, which is: multiplication and division then addition and subtraction.

However, if your problem contains only addition or only multiplication, you can group them in any way and still get the same answer.

Look at this next example: (2 * 5) * 7 is the same as 2 * (5 * 7). It doesn't matter if you multiply the 2 and 5 first or the 5 and 7 first, the answer is still 70.

Let's try it both ways:

(2 * 5) * 7 = 10 * 7, or 70.

2 * (5 * 7) = 2 * 35, which is also 70.

The associative property can work with subtraction, but only if you convert your subtraction problem to an addition problem. If you remember, subtraction is the opposite of addition. Because of this, you can turn any subtraction problem into an addition problem. This means that 6 - 3 is equal to 6 + (-3).

When you turn your subtraction problem into an addition problem, you can use the associative property to rearrange the groupings.

With simple problems such as these, you might be scratching your head, wondering why mathematicians go to all this trouble; why is the associative property so important?

While these examples might seem simplistic, the associative property can be very useful when working with more complicated problems. When mathematicians or scientists or engineers are working with a complex equation, it can help them with the solution if they are sure that they can regroup the terms without negatively affecting the outcome of the problem.

The associative property states that in addition and multiplication problems, the grouping of the terms does not matter to the final outcome of the problem. You can group the terms in any order and still obtain the correct answer. The property is also true for subtraction if you convert your subtraction problem to an addition problem and are very careful to keep the negative with the correct number.

After you've completed this lesson, you should be able to:

- Understand what the associative property states and when you can use it
- Remember the order of operations
- Use the associative property with subtraction problems
- Determine when the associative property can be helpful

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
11 in chapter 1 of the course:

Back To Course

Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

- What Is a Number Line? 5:16
- Binary and Non-Binary Operations 5:34
- How to Perform Addition: Steps & Examples 4:07
- How to Perform Subtraction: Steps & Examples 3:46
- How to Perform Multiplication: Steps & Examples 5:22
- How to Multiply Large Numbers: Steps and Examples 7:43
- How to Perform Division: Steps & Examples 3:56
- Performing Long Division with Large Numbers: Steps and Examples 9:12
- Arithmetic Calculations with Signed Numbers 5:21
- The Commutative Property: Definition and Examples 3:53
- The Associative Property: Definition and Examples 4:28
- How to Find the Greatest Common Factor 4:56
- How to Find the Least Common Multiple 5:37
- What Are the Different Parts of a Graph? 6:21
- Parentheses in Math: Rules & Examples 4:01
- Algebra Vocabulary Terms 3:48
- What Is The Order of Operations in Math? - Definition & Examples 5:50
- Go to High School Algebra: Basic Arithmetic

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Early Civilizations & The Ancient Near East
- Fundamental Overview of World War I
- The Virginia Dynasty & Jacksonian America
- 1920's America and the Great Depression
- Building the United States After the American Revolution
- 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

- Subtraction in Java: Method, Code & Examples
- Hydrogen Chloride vs. Hydrochloric Acid
- Extraction of Aluminum, Copper, Zinc & Iron
- Iroquois Culture, Traditions & Facts
- Noun Clauses Lesson Plan
- Adverb of Manner Lesson Plan
- Timeline Project Ideas for High School
- Quiz & Worksheet - Multi-Dimensional Arrays in C
- Quiz & Worksheet - What is a Diastereoisomer?
- Quiz & Worksheet - Mauryan Empire Art & Culture
- Quiz & Worksheet - What is a Convergent Sequence?
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- History Essay Topics for Teachers
- What is Inquiry-Based Learning? | Definition & Resources for Teachers

- Praxis Physics (5265): Practice & Study Guide
- Social Psychology Textbook
- High School Algebra II: Homeschool Curriculum
- Major Eras in World History Study Guide
- Common Core Math Grade 8 - Statistics & Probability: Standards
- TExES Physical Science 6-12: Laboratory Equipment
- MTEL Middle School Math/Science: Area, Perimeter & Volume
- Quiz & Worksheet - Anthropomorphized Animals in Literature
- Quiz & Worksheet - The Exclusionary Rule
- Quiz & Worksheet - Square Matrix
- Quiz & Worksheet - Stream of Consciousness in Literature
- Quiz & Worksheet - Formula for Calculating Distance in Math

- Characterization in Lord of the Flies
- Parts of a Rocket: Lesson for Kids
- 8th Grade Math Games
- Finding Travel Grants for Teachers
- Oklahoma Alternative Teacher Certification
- Creative Writing Prompts
- What to Do When Studying Abroad
- Writing Prompts for Kids
- Next Generation Science Standards in California
- What is Micro Credentialing?
- Alcohol Awareness Activities
- Creative Writing Exercises for Middle School

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

Browse by subject