Skip to content Skip to navigation Skip to collection information

OpenStax-CNX

You are here: Home » Content » Derived copy of Fundamentals of Mathematics » Summary of Key Concepts

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.
 

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 reviews the key concepts from the chapter "Ratios and Rates."

Summary of Key Concepts

Denominate Numbers ((Reference))

Numbers that appear along with units are denominate numbers. The amounts 6 dollars and 4 pints are examples of denominate numbers.

Like and Unlike Denominate Numbers ((Reference))

Like denominate numbers are denominate numbers with like units. If the units are not the same, the numbers are unlike denominate numbers.

Pure Numbers ((Reference))

Numbers appearing without a unit are pure numbers.

Comparing Numbers by Subtraction and Division ((Reference))

Comparison of two numbers by subtraction indicates how much more one number is than another. Comparison by division indicates how many times larger or smaller one number is than another.

Comparing Pure or Like Denominate Numbers by Subtraction ((Reference))

Numbers can be compared by subtraction if and only if they are pure numbers or like denominate numbers.

Ratio Rate ((Reference))

A comparison, by division, of two like denominate numbers is a ratio. A comparison, by division, of two unlike denominate numbers is a rate.

Proportion ((Reference))

A proportion is a statement that two ratios or rates are equal.

3  people2 jobs=6  people4 jobs3  people2 jobs=6  people4 jobs size 12{ { {3`"people"} over {"2 jobs"} } = { {6`"people"} over {"4 jobs"} } } {} is a proportion.

Solving a Proportion ((Reference))

To solve a proportion that contains three known numbers and a letter that repre­sents an unknown quantity, perform the cross multiplication, then divide the product of the two numbers by the number that multiplies the letter.

Proportions Involving Rates ((Reference))

When writing a proportion involving rates it is very important to write it so that the same type of units appears on the same side of either the equal sign or the fraction bar.

unit type 1 unit type 2 = unit type 1 unit type 2   or   unit type 1 unit type 1 = unit type 2 unit type 2 unit type 1 unit type 2 = unit type 1 unit type 2   or   unit type 1 unit type 1 = unit type 2 unit type 2 size 12{ { {"unit type 1"} over {"unit type 2"} } = { {"unit type 1"} over {"unit type 2"} } ```````` ital "or"`````` { {"unit type 1"} over {"unit type 1"} } = { {"unit type 2"} over {"unit type 2"} } } {}

Five-Step Method for Solving Proportions ((Reference))

  1. By careful reading, determine what the unknown quantity is and represent it with some letter. There will be only one unknown in a problem.
  2. Identify the three specified numbers.
  3. Determine which comparisons are to be made and set up the proportion.
  4. Solve the proportion.
  5. Interpret and write a conclusion.
When solving applied problems, ALWAYS begin by determining the unknown quantity and representing it with a letter.

Percents ((Reference))

A ratio in which one number is compared to 100 is a percent. Percent means "for each hundred."

Conversion of Fractions, Decimals, and Percents ((Reference))

It is possible to convert decimals to percents, fractions to percents, percents to decimals, and percents to fractions.

Applications of Percents:

The three basic types of percent problems involve a base, a percentage, and a percent.

Base ((Reference))

The base is the number used for comparison.

Percentage ((Reference))

The percentage is the number being compared to the base.

Percent ((Reference))

By its definition, percent means part of.

Solving Problems ((Reference))

Percentage = ( percent ) × ( base ) Percentage = ( percent ) × ( base ) size 12{"Percentage"= \( "percent" \) times \( "base" \) } {}
Percent = percentage base Percent = percentage base size 12{"Percent"= { {"percentage"} over {"base"} } } {}
Base = percentage percent Base = percentage percent size 12{"Base"= { {"percentage"} over {"percent"} } } {}

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 | 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