Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Derived copy of Fundamentals of Mathematics » Properties of Multiplication

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • CCQ display tagshide tags

    This module is included in aLens by: Community College of QatarAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Used as supplemental materials for developmental math courses."

    Click the "CCQ" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

  • College Open Textbooks display tagshide tags

    This module is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook CollaborativeAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Reviewer's Comments: 'I would recommend this text for a basic math course for students moving on to elementary algebra. The information in most chapters is useful, very clear, and easily […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • UniqU content

    This module is included inLens: UniqU's lens
    By: UniqU, LLCAs a part of collection: "Fundamentals of Mathematics"

    Click the "UniqU content" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Properties of Multiplication

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: 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

Example 1

Multiply the two whole numbers.

6 and 7.

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

7 ⋅ 6 = 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.

Practice Set A

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

Exercise 1

15 and 6.

Solution

15⋅6=9015⋅6=90 and 6⋅15=906⋅15=90

Exercise 2

432 and 428.

Solution

432⋅428=184,896432⋅428=184,896 and 428⋅432=184,896428⋅432=184,896

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

Example 2

Multiply the whole numbers.

8, 3, and 14.

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

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

Practice Set B

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

Exercise 4

73, 18, and 126.

Solution

165,564

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

Example 3

Multiply the whole numbers.

12 and 1.

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

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

Practice Set C

Multiply the whole numbers.

Exercises

For the following problems, multiply the numbers.

Exercise 7

18 and 41.

Exercise 9

132 and 6.

Exercise 10

1000 and 326.

Solution

326,000

Exercise 11

70 and 1400.

Exercise 13

16, 40, and 5.

Exercise 14

10, 97, and 22.

Solution

21,340

Exercise 15

110, 0, and 85.

Exercise 16

1, 462, and 18.

Solution

8,316

Exercise 17

3,178, 101, and 5.

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

Exercise 18

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

Solution

32⋅2=64=4⋅1632⋅2=64=4⋅16 size 12{"32" cdot 2="64"=4 cdot "16"} {}

Exercise 19

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

Exercise 20

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

Solution

23⋅1,166=26,818=253⋅10623⋅1,166=26,818=253⋅106 size 12{"23" cdot 1,"166"="26","818"="253" cdot "106"} {}

Exercise 21

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

Exercise 22

The fact that (a first number ⋅ a second number)⋅ a third number = a first number ⋅(a second number ⋅ a third number)(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.

Solution

associative

Exercise 23

The fact that 1 ⋅ any number = that particular number1 ⋅ any number = that particular number size 12{"1 " cdot " any number "=" that particular number"} {}is an example of the
property of mul­tiplication.

Exercise 24

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

Solution

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

Exercise 25

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

Exercises for Review

Exercise 26

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

Solution

6

Exercise 27

((Reference)) Replace the letter m with the whole number that makes the addition true. 85+  m̲9785+  m̲97alignr { stack { size 12{"85"} {} # size 12{ {underline {+m}} } {} # size 12{"97"} {} } } {}

Exercise 28

((Reference)) Use the numbers 4 and 15 to illustrate the commutative property of addition.

Solution

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

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

Exercise 29

((Reference)) Find the product. 8,000,000×1,0008,000,000×1,000 size 12{8,"000","000" times 1,"000"} {}.

Exercise 30

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

Solution

2, 3, 4, 6

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks