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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses fractions of whole numbers. By the end of the module students should be able to understand the concept of fractions of whole numbers and recognize the parts of a fraction.

Section overview

  • More Numbers on the Number Line
  • Fractions of Whole Numbers
  • The Parts of a Fraction
  • Reading and Writing Fractions

More numbers on the number line

In Chapters [link] , [link] , and [link] , we studied the whole numbers and methods of combining them. We noted that we could visually display the whole numbers by drawing a number line and placing closed circles at whole number locations.

A number line with dots on the whole numbers.

By observing this number line, we can see that the whole numbers do not account for every point on the line. What numbers, if any, can be associated with these points? In this section we will see that many of the points on the number line, including the points already associated with whole numbers, can be associated with numbers called fractions .

Fractions of whole numbers

The nature of the positive fractions

We can extend our collection of numbers, which now contains only the whole numbers, by including fractions of whole numbers. We can determine the nature of these fractions using the number line.

If we place a pencil at some whole number and proceed to travel to the right to the next whole number, we see that our journey can be broken into different types of equal parts as shown in the following examples.

  1. 1 part.
    A number line. Two marks: one on the left, labeled, whole number, and one on the right, labeled next whole number. An arrow is drawn from the whole number to the next whole number.

  2. 2 equal parts.
    A number line. Two marks: one on the left, labeled, whole number, and one on the right, labeled next whole number.  In between the two marks is the midway point. An arrow is drawn from the whole number to the midway point, and then from the midway point to the next whole number.

  3. 3 equal parts.
    A number line. Two marks: one on the left, labeled, whole number, and one on the right, labeled next whole number. There are three arrows, connecting the two whole numbers and two evenly-spaced hash marks in between the whole numbers.

  4. 4 equal parts.
    A number line. Two marks: one on the left, labeled, whole number, and one on the right, labeled next whole number. There are four arrows, connecting the two whole numbers and three evenly-spaced hash marks in between the whole numbers.

The latin word fractio

Notice that the number of parts, 2, 3, and 4, that we are breaking the original quantity into is always a nonzero whole number . The idea of breaking up a whole quantity gives us the word fraction . The word fraction comes from the Latin word "fractio" which means a breaking, or fracture.

Suppose we break up the interval from some whole number to the next whole number into five equal parts.

A number line. Two marks: one on the left, labeled whole number, and one on the right, labeled next whole number. There are four hash marks in between the two whole numbers, creating five spaces of equal width, labeled Part 1 through Part 5.

After starting to move from one whole number to the next, we decide to stop after covering only two parts. We have covered 2 parts of 5 equal parts. This situation is described by writing 2 5 size 12{ { {2} over {5} } } {} .

A number line. Two marks: one on the left, labeled whole number, and one on the right, labeled next whole number. There are four evenly-spaced hash marks in between the two marks. There is an arrow from the whole number to the first hash mark, and an arrow from the first hash mark to the second hash mark.

Positive fraction

A number such as 2 5 size 12{ { {2} over {5} } } {} is called a positive fraction , or more simply, a fraction .

The parts of a fraction

A fraction has three parts .

  1. The fraction bar         .

    Fraction bar

    The fraction bar serves as a grouping symbol. It separates a quantity into individual groups. These groups have names, as noted in 2 and 3 below.

  2. The nonzero number below the fraction bar.

    Denominator

    This number is called the denominator of the fraction, and it indicates the number of parts the whole quantity has been divided into. Notice that the denominator must be a nonzero whole number since the least number of parts any quantity can have is one.

  3. The number above the fraction bar.

    Numerator

    This number is called the numerator of the fraction, and it indicates how many of the specified parts are being considered. Notice that the numerator can be any whole number (including zero) since any number of the specified parts can be considered.

    whole number nonzero whole number numerator denominator

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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