# OpenStax-CNX

You are here: Home » Content » Multiplication and Division of Whole Numbers: Summary of Key Concepts

### 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?

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

#### Endorsed by (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

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

"Used as supplemental materials for developmental math courses."

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

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

• College Open Textbooks

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

"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 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

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

"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 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.

# Multiplication and Division of Whole Numbers: Summary of Key Concepts

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 summarizes the concepts discussed in the chapter "Multiplication and Division of Whole Numbers."

## Summary of Key Concepts

### Multiplication ((Reference))

Multiplication is a description of repeated addition.
7+7+7+77 appears 4 times 7+7+7+77 appears 4 times
This expression is described by writing 4 X 7.

### Multiplicand/Multiplier/Product ((Reference))

In a multiplication of whole numbers, the repeated addend is called the multiplicand, and the number that records the number of times the multiplicand is used is the multiplier. The result of the multiplication is the product.

### Factors ((Reference))

In a multiplication, the numbers being multiplied are also called factors. Thus, the multiplicand and the multiplier can be called factors.

### Division ((Reference))

Division is a description of repeated subtraction.

### Dividend/Divisor/Quotient ((Reference))

In a division, the number divided into is called the dividend, and the number dividing into the dividend is called the divisor. The result of the division is called the quotient.
quotient divisor dividend quotient divisor dividend

### Division into Zero ((Reference))

Zero divided by any nonzero whole number is zero.

### Division by Zero ((Reference))

Division by zero does not name a whole number. It is, therefore, undefined. The quotient 0000 size 12{ { {0} over {0} } } {} is indeterminant.

### Division by 2, 3, 4, 5, 6, 8, 9, 10 ((Reference))

Division by the whole numbers 2, 3, 4, 5, 6, 8, 9, and 10 can be determined by noting some certain properties of the particular whole number.

### Commutative Property of Multiplication ((Reference))

The product of two whole numbers is the same regardless of the order of the factors. 3×5=5×33×5=5×3 size 12{3 times 5=5 times 3} {}

### Associative Property of Multiplication ((Reference))

If three whole numbers are to be 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 then that product is multiplied by the first.
(3×5)×2=3×(5×2)(3×5)×2=3×(5×2) size 12{ $$3 times 5$$ times 2=3 times $$5 times 2$$ } {}
Note that the order of the factors is maintained.

### Multiplicative Identity ((Reference))

The whole number 1 is called the multiplicative identity since any whole number multiplied by 1 is not changed.
4 × 1 = 4 4 × 1 = 4 size 12{4 times 1=4} {}
1 × 4 = 4 1 × 4 = 4 size 12{1 times 4=4} {}

## Content actions

### Give feedback:

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?

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