<< Chapter < Page Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses properties of multiplication of whole numbers. By the end of the module students should be able to understand and appreciate the commutative and associative properties of multiplication and understand why 1 is the multiplicative identity.

Section overview

  • The Commutative Property of Multiplication
  • The Associative Property of Multiplication
  • The Multiplicative Identity

We will now examine three simple but very important properties of multiplication.

The commutative property of multiplication

Commutative property of multiplication

The product of two whole numbers is the same regardless of the order of the factors.

Sample set a

Multiply the two whole numbers.

6 and 7.

6 7 = 42 size 12{6 cdot 7="42"} {}

7 6 = 42 size 12{7 cdot 6="42"} {}

The numbers 6 and 7 can be multiplied in any order. Regardless of the order they are multiplied, the product is 42.

Got questions? Get instant answers now!

Practice set a

Use the commutative property of multiplication to find the products in two ways.

15 and 6.

15 6 = 90 and 6 15 = 90

Got questions? Get instant answers now!

432 and 428.

432 428 = 184,896 and 428 432 = 184,896

Got questions? Get instant answers now!

The associative property of multiplication

Associative property of multiplication

If three whole numbers are multiplied, the product will be the same if the first two are multiplied first and then that product is multiplied by the third, or if the second two are multiplied first and that product is multiplied by the first. Note that the order of the factors is maintained.

It is a common mathematical practice to use parentheses to show which pair of numbers is to be combined first.

Sample set b

Multiply the whole numbers.

8, 3, and 14.

( 8 3 ) 14 = 24 14 = 336 size 12{ \( 8 cdot 3 \) cdot "14"="24" cdot "14"="336"} {}

8 ( 3 14 ) = 8 42 = 336 size 12{8 cdot \( 3 cdot "14" \) =8 cdot "42"="336"} {}

Got questions? Get instant answers now!

Practice set b

Use the associative property of multiplication to find the products in two ways.

The multiplicative identity

The multiplicative identity is 1

The whole number 1 is called the multiplicative identity , since any whole num­ber multiplied by 1 is not changed.

Sample set c

Multiply the whole numbers.

12 and 1.

12 1 = 12 size 12{"12" cdot 1="12"} {}

1 12 = 12 size 12{1 cdot "12"="12"} {}

Got questions? Get instant answers now!

Practice set c

Multiply the whole numbers.

Exercises

For the following problems, multiply the numbers.

For the following 4 problems, show that the quantities yield the same products by performing the multiplications.

( 4 8 ) 2 size 12{ \( 4 cdot 8 \) cdot 2} {} and 4 ( 8 2 ) size 12{4 cdot \( 8 cdot 2 \) } {}

32 2 = 64 = 4 16 size 12{"32" cdot 2="64"=4 cdot "16"} {}

Got questions? Get instant answers now!

( 100 62 ) 4 size 12{ \( "100" cdot "62" \) cdot 4} {} and 100 ( 62 4 ) size 12{"100" cdot \( "62" cdot 4 \) } {}

Got questions? Get instant answers now!

23 ( 11 106 ) size 12{"23" cdot \( "11" cdot "106" \) } {} and ( 23 11 ) 106 size 12{ \( "23" cdot "11" \) cdot "106"} {}

23 1, 166 = 26 , 818 = 253 106 size 12{"23" cdot 1,"166"="26","818"="253" cdot "106"} {}

Got questions? Get instant answers now!

1 ( 5 2 ) size 12{1 cdot \( 5 cdot 2 \) } {} and ( 1 5 ) 2 size 12{ \( 1 cdot 5 \) cdot 2} {}

Got questions? Get instant answers now!

The fact that ( a first number a second number ) a third number = a first number ( a second number a third number ) size 12{ \( "a first number " cdot " a second number" \) cdot " a third number "=" a first number " cdot \( "a second number " cdot " a third number" \) } {} is an example of the property of mul­tiplication.

associative

Got questions? Get instant answers now!

The fact that 1 any number = that particular number size 12{"1 " cdot " any number "=" that particular number"} {} is an example of the property of mul­tiplication.

Got questions? Get instant answers now!

Use the numbers 7 and 9 to illustrate the com­mutative property of multiplication.

7 9 = 63 = 9 7 size 12{"7 " cdot " 9 "=" 63 "=" 9 " cdot " 7"} {}

Got questions? Get instant answers now!

Use the numbers 6, 4, and 7 to illustrate the asso­ciative property of multiplication.

Got questions? Get instant answers now!

Exercises for review

( [link] ) In the number 84,526,098,441, how many millions are there?

6

Got questions? Get instant answers now!

( [link] ) Replace the letter m with the whole number that makes the addition true. 85 +   m ̲ 97 alignr { stack { size 12{"85"} {} #size 12{ {underline {+m}} } {} # size 12{"97"} {}} } {}

Got questions? Get instant answers now!

( [link] ) Use the numbers 4 and 15 to illustrate the commutative property of addition.

4 + 15 = 19 size 12{"4 "+" 15 "=" 19"} {}

15 + 4 = 19 size 12{"15 "+" 4 "=" 19"} {}

Got questions? Get instant answers now!

( [link] ) Find the product. 8, 000 , 000 × 1, 000 size 12{8,"000","000" times 1,"000"} {} .

Got questions? Get instant answers now!

( [link] ) Specify which of the digits 2, 3, 4, 5, 6, 8,10 are divisors of the number 2,244.

2, 3, 4, 6

Got questions? Get instant answers now!

Questions & Answers

what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask