Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Commutative Property of Multiplication

Study concepts, example questions & explanations for Pre-Algebra

Create An Account

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Commutative Property Of Multiplication

Which property is illustrated by the example:

$4\times 3=3\times 4$

Possible Answers:

Associative property of multiplication

Distributive property

Multiplicative identity property

Commutative property of multiplication

Correct answer:

Commutative property of multiplication

Explanation:

The commutative property of mulitplication states that the order in which 2 numbers are multiplied does not affect the result:

$a\times b=b\times a$

Or in this case,

$4\times 3=3\times 4$

$4\times3=12$

$3\times 4=12$

Report an Error

Example Question #2 : Commutative Property Of Multiplication

Use the Commutative Property of Multiplication to write the below expression in a different way.

$6 \times x^{1/2}$

Possible Answers:

$6 / x^{1/2}$

$x \times 6^{1/2}$

$x^{2} \times 6$

$x^{1/2}\times 6$

$1 / 6x^{1/2}$

Correct answer:

$x^{1/2}\times 6$

Explanation:

The rule for Commutative Property of Multiplication is $a \times b = b \times a$

Using this rule, the expression $6 \times x^{1/2}$ can be written as $x^{1/2} \times 6$

Report an Error

Example Question #1 : Commutative Property Of Multiplication

Which of the following equations correctly shows the commutative property of multiplication?

Possible Answers:

$\small 4*3*2 = 6*2*2$

$\small \small 3*6*4=6*4*3$

$\small 2*3*6=9*4$

$\small 3*6*4=3*6*4$

Correct answer:

$\small \small 3*6*4=6*4*3$

Explanation:

The commutative property states that factors can be multiplied in any order and the product is always the same. While each of our answer choices are real equations, only one correctly displays this property:

$a\times b = b\times a$

$3\times6\times4 = 6\times4\times3$

Report an Error

Example Question #4 : Commutative Property Of Multiplication

Evaluate the following expression without using a calculator

$\frac{7}{13}*\frac{11}{8}*\frac{4}{17}*\frac{8}{11}*\frac{6}{19}*\frac{13}{7}*\frac{19}{6}*\frac{17}{4}$

Possible Answers:

$\frac{2542}{4579}$

$\frac{9874}{8567}$

$\frac{7}{13}$

Correct answer:

Explanation:

This problem could easily turn into some super heavy calculations, but nobody has time for that. Instead, we can make this problem very easy by utilizing the commutative property of multiplication, which in essence says that numbers can be multiplied in any order.

In other words, 2 * 3 = 3*2 and 5 * 7 * 9 = 7 *9*5

That means that rather multiplying our numbers in their orginal order, which can actually change the order of the numbers without affecting the final product. At this point we should notice that one of our numbers is $\frac{7}{13}$ while another is $\frac{13}{7}$ . Similarly the fractions $\frac{4}{17}, \frac{6}{19},$ and $\frac{11}{8}$ are each accompanied by their recripocals $\frac{17}{4}, \frac{19}{6},$ and $\frac{8}{11}$ respecitively. At this point we must also remember the multiplicative inverse property, which tells us that the product of a number and its reciprocal will always be 1. With that in mind, the strategic way to order the multiplication is as follows:

$\frac{7}{13}*\frac{13}{7}*\frac{4}{17}*\frac{17}{4}*\frac{6}{19}*\frac{19}{6}*\frac{11}{8}*\frac{8}{11}$

Doing this pairs each number up with its reciprocal. Finally, we can utlize the associative properpty of multiplication, which tells us that we can multiply any two numbers at a time.

In other words, (5*7)*9=5 *(7*9) . This allows us to pair off the multiplication as follows.

$\left(\frac{7}{13}*\frac{13}{7}\right)*\left(\frac{4}{17}*\frac{17}{4}\right)*\left(\frac{6}{19}*\frac{19}{6}\right)*\left(\frac{11}{8}*\frac{8}{11}\right)$

Within each parentheses we now have a number multiplied by its reciprocal. Remembering that this always equals 1, we can simplify, giving

(1)*(1)*(1)*(1)=1

Our answer is 1.

Report an Error

Example Question #2 : Identities And Properties

Which answer shows the communitive property of multiplication to the equation below?

(15 * 7) * 6 =

Possible Answers:

(7 * 6) * 15 =

(105 ) * 6 =

15 + (7 + 6) =

(15 + 7) + 6

(90) * 7 =

Correct answer:

(7 * 6) * 15 =

Explanation:

The communitive property of multiplication is a property that states that the numbers can be multiplied in any combination. To show which answer is correct simply regroup the numbers in a different or and you will have your answer.

(15 * 7) * 6 = (7 * 6) * 15

Report an Error

Example Question #2 : Commutative Property Of Multiplication

Which of the following displays the commutative property of multiplication?

Possible Answers:

$a \cdot 1 = a$

$a \cdot b = b \cdot a$

$a (b + c) = (a \cdot b) + (a \cdot c)$

$a \cdot 0 = 0$

$a \cdot(b \cdot c) = (a \cdot b) \cdot c$

Correct answer:

$a \cdot b = b \cdot a$

Explanation:

The commutative property of multiplication states that 2 numbers can be multiplied in any order. Therefore,

$a \cdot b = b \cdot a$

displays the commutative property of multiplication.

Report an Error

View Pre-Algebra Tutors

Jeffrey
Certified Tutor

View Pre-Algebra Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

View Pre-Algebra Tutors

Sharif
Certified Tutor

NCCU, Bachelors, Physics and Mathematics.

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Chicago, GRE Tutors in Houston, Reading Tutors in Dallas Fort Worth, GMAT Tutors in Atlanta, Reading Tutors in Miami, Calculus Tutors in San Diego, French Tutors in New York City, Physics Tutors in Chicago, SSAT Tutors in Washington DC, Statistics Tutors in San Francisco-Bay Area

Popular Courses & Classes

ISEE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Boston, GRE Courses & Classes in Phoenix, ISEE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Atlanta, GMAT Courses & Classes in Phoenix, LSAT Courses & Classes in San Diego, MCAT Courses & Classes in Washington DC, ISEE Courses & Classes in Houston, GMAT Courses & Classes in Seattle

Popular Test Prep

SAT Test Prep in New York City, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in Houston, GRE Test Prep in Atlanta, GMAT Test Prep in Phoenix, GMAT Test Prep in Chicago, LSAT Test Prep in Los Angeles, MCAT Test Prep in Denver, SAT Test Prep in Seattle, GRE Test Prep in Phoenix

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Pre-Algebra : Commutative Property of Multiplication

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Commutative Property Of Multiplication

Example Question #2 : Commutative Property Of Multiplication

Example Question #1 : Commutative Property Of Multiplication

Example Question #4 : Commutative Property Of Multiplication

Example Question #2 : Identities And Properties

Example Question #2 : Commutative Property Of Multiplication

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: