# Connexions

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

• Preface
• Acknowledgements

### 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.

Inside Collection (Textbook):

Textbook by: Ron Stewart. E-mail the author

# Summary of Key Concepts

Module by: Denny Burzynski, Wade Ellis. 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 "Measurement and Geometry."

## Summary of Key Concepts

### Measurement ((Reference))

Measurement is comparison to some standard.

### Standard Unit of Measure ((Reference))

A quantity that is used for comparison is called a standard unit of measure.

### Two Types of Measurement Systems ((Reference))

There are two major types of measurement systems in use today. They are the United States system and the metric system.

### Unit Fraction ((Reference))

A unit fraction is a fraction that has a value of 1. Unit fractions can be used to convert from one unit of measure to another.

### Meter, Liter, Gram, and associated prefixes ((Reference))

Common units of measure in the metric system are the meter (m), for length, the liter (L), for volume, and the gram (g), for mass. To each of these units, a prefix can be attached.

• kilo —  thousand
• deci —  tenth
• hecto —  hundred
• centi —  hundredth
• deka —  ten
• milli —  thousandth

### Metric Conversions ((Reference))

To convert from one metric unit to another:

1. Determine the location of the original number on the metric scale.
2. Move the decimal point of the original number in the same direction and the same number of places as is necessary to move to the metric unit you wish to convert to.

### Denominate Numbers ((Reference))

Numbers that have units of measure associated with them are denominate num­bers. The number 25 mg is a denominate number since the mg unit is associated with the pure number 25. The number 82 is not a denominate number since it has no unit of measure associated with it.

### Simplified Denominate Number ((Reference))

A denominate number is simplified when the number of standard units of measure associated with it does not exceed the next higher type of unit. 55 min is simplified, whereas 65 min is not simplified

### Addition and Subtraction of Denominate Numbers ((Reference))

Denominate numbers can be added or subtracted by

1. writing the numbers vertically so that the like units appear in the same column.
2. adding or subtracting the number parts, carrying along the unit.
3. simplifying the sum or difference.

### Multiplying a Denominate Number by a Whole Number ((Reference))

To multiply a denominate number by a whole number, multiply the number part of each unit by the whole number and affix the unit to the product.

### Dividing a Denominate Number by a Whole Number ((Reference))

To divide a denominate number by a whole number, divide the number part of each unit by the whole number beginning with the largest unit. Affix the unit to this quotient. Carry the remainder to the next unit.

### Polygon ((Reference))

A polygon is a closed plane (flat) figure whose sides are line segments (portions of straight lines).

### Perimeter ((Reference))

The perimeter of a polygon is the distance around the polygon.

The circumference of a circle is the distance around the circle. The diameter of a circle is any line segment that passes through the center of the circle and has its endpoints on the circle. The radius of a circle is one half the diameter of the circle.

### The number ππ ((Reference))

The symbol ππ, read "pi," represents the nonterminating, nonrepeating decimal number 3.14159... . For computational purposes, ππ is often approximated by the number 3.14.

### Formula ((Reference))

A formula is a rule for performing a task. In mathematics, a formula is a rule that directs us in computations.

### Circumference Formulas ((Reference))

C = π d C = π d size 12{C=π cdot d} {}


C ( 3 . 14 ) d C ( 3 . 14 ) d size 12{C approx $$3 "." "14"$$ d} {}
C = 2 π r C = 2 π r size 12{C=2 cdot π cdot r} {}

C 2 ( 3 . 14 ) r C 2 ( 3 . 14 ) r size 12{C approx 2 $$3 "." "14"$$ r} {}

### Area ((Reference))

The area of a surface is the amount of square length units contained in the surface.

### Volume ((Reference))

The volume of an object is a measure of the amount of cubic length units contained in the object.

### Area Formulas ((Reference))

Triangle: A=12bhA=12bh size 12{A= { {1} over {2} } cdot b cdot h} {}
Rectangle: A=lwA=lw size 12{A=1 cdot w} {}
Parallelogram: A=bhA=bh size 12{A=b cdot h} {}
Trapezoid: A=12(b1+b2)hA=12(b1+b2)h size 12{A= { {1} over {2} } cdot $$b rSub { size 8{1} } +b rSub { size 8{2} }$$ cdot h} {}
Circle: A=πr2A=πr2 size 12{A=π cdot r rSup { size 8{2} } } {}

### Volume Formulas ((Reference))

Rectangle solid: V=lwhV=lwh size 12{V=l cdot w cdot h} {}
Sphere: V=43πr3V=43πr3 size 12{V= { {4} over {3} } cdot π cdot r rSup { size 8{3} } } {}
Cylinder: V=πr2hV=πr2h size 12{V=π cdot r rSup { size 8{2} } cdot h} {}
Cone: V=13πr2hV=13πr2h size 12{V= { {1} over {3} } cdot π cdot r rSup { size 8{2} } cdot h} {}

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

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

PDF | EPUB (?)

### What is an EPUB file?

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

#### 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?

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?

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