Home  Previous  Next 

MAT081 :: Lecture Note :: Week 03
Assessments

Handouts

Math Resources
{MathBabbler:
Email

Facebook

Twitter}
GDT::Bits::
Time

Weather

Populations

Special Dates
Instructor to class: How do we define fraction?
Instructor to class: Have you ever defined fraction as follows? A fraction is an unsolved division problem (i.e. it is a quotient of two numbers).
[humor]
Five out of every four people have difficulty understanding fractions.Fractions are used to represent partofawhole of something. Examples: Zelmo ate 1/2 of the whole pie. Edith spent 3/4 of a full hour sending an email message to Zelmo. Truman completed only 2/9 of the nine part exercise.
x x ÷ y is also the fraction  (also written x/y) y 'x' (dividend) is the numerator 'y' (divisor) is the denominatorSince the divisor divides into the dividend, the denominator divides into the numerator.
[terminology exercise: No or Yes: Dividing the denominator into the numerator results in a terminator.]A fraction can never have a denominator of zero because division by zero is undefined.
Ignoring negative numbers... A proper fraction is a fraction having a numerator that is less than the denominator. An improper fraction is a fraction having a numerator greater than or equal to the denominator.
2/3  proper fraction (2 < 3) 7/4  improper fraction (7 > 4) 5/5  improper fraction; equals 1 0/8  proper fraction (0 < 8) 9/0  undefined fraction (denominator is 0)Although improper fractions are called improper, there is nothing improper about them (i.e. they are not "bad" fractions).
A unit fraction is a fraction that has one as its numerator.
Every whole number 'n' can be written as a fraction by using 'n' in the numerator and one in the denominator.
A mixed number is a whole number plus a fraction.
1/8  unit fraction 5/1  the value 5 7 1/4  mixed number; 7 is a whole number; 1/4 is a fraction 7 1/4 is 7 + 1/4; most of the time the fractional part of mixed number is a proper fractionA fraction consisting of two integers is called a rational number. [Observe how the word rational contains the word ratio. Fractions are ratios.]
A fraction is negative if either the numerator is negative or the denominator is negative. If both the numerator and denominator are negative, then the fraction is positive.
GDT::BAB:: About the Fraction Five DividedBy Eight
Multiplication
Multiply the numerators to get the numerator of the product. Multiply the denominators to get the denominator of the product.
2 4 8 2 * 4 is 8  *  =  3 5 15 3 * 5 is 15Division
To divide one fraction by another one, multiply the top fraction by the reciprocal of the bottom fraction.
If dividing mixed numbers, then convert the mixed numbers to improper fractions and then perform the division.
Reciprocal is the multiplicative inverse of a number. For a fraction, it's obtained by "flipping the fraction."
2 1  ÷  5 7 rewritten 2 2 7 14 4   *  =  = 2  5 5 1 5 5  1  7Equivalent Fractions
Given a fraction, both the numerator and denominator can be multiplied or divided by the same number and the result is an equivalent fraction.
3 5 15  *  =  4 5 20Addition/Subtraction
Fractions can be added or subtracted only if they are like fractions (i.e. have common denominators). Typically we want the common denominator to be the smallest common denominator, but to help get started we will obtain a common denominator by using the product of the two denominators. Once a common denominator has been determined and the numerators adjusted (i.e. equivalent fractions calculated), then the numerators are added or subtracted.
Example
1 1  +  5 4 multiply the two denominators to get a common denominator 5 * 4 equals 20 1(n) 1(n)  +  20 20 adjust the numerators finding equivalent fractions given the common denominator 1(4) 1(5) 9  +  =  20 20 20 A + B _ _ _ _ _ _ _ _ _ _  _ _ _ _ _ _ _ _ _ _ 0/20 A A A A B B B B B _  _ _ _ _ _ _ _ _ _ _ 9/20Some Older Related BABs
 Cheap Gas Prices Along Route 66 In Illinois [07 February 2005]
 Learning About Fractions In The Early Days [01 February 2006]
 Mile Markers on Camelback Mountain [19 July 2005]
 BARS:: Incrementing Fractions on Northbound Loop 101 in Scottsdale, Arizona [24 May 2005]
 BARS:: Pima Road and Cave Creek Road Junction in Carefree, Arizona [05 January 2006]
 BARS:: Southbound Loop 101 in Tempe, Arizona [10 February 2006]
 BARS:: Superstition Springs Exit on US Hwy60 in Mesa, Arizona [12 February 2007]
 BARS:: Fractions on Yavapai County Road 10 Near Prescott, Arizona [24 September 2006]
 BARS:: Heading East on I40 To Winslow, Arizona [18 March 2006]
External Hyperlinks
 Math.com:: Homework Help Hot Subject: Fractions
 Wikipedia.org:: Fraction (mathematics)
{TopOfPage}
{MathWords}
{PurpleMath}
{KhanAcademy}
{SCC math resources... MathAS::id 5778; key 5778 
OER::book 
playbook 
{classroom: quiet 
thinking 
speed eraser 
wave erase}
Home  Previous  Next 
