Rational+Numbers

 = =  Rational Numbers 

===**A rational number can be any __whole number __, __fraction __,  __mixed number __ or __decimal __.**===

=

 * Terminating or repeating decimals must be found when the fraction is divided. **======

**+ Repeating - a decimal with endlessly repeating digits. (for example: 88/33 = 2.6666666666666)**
= = =__Rational Numbers are important! They are used in the real world EVERYDAY!__  =

** Even though we are not thinking about if the number is rational or not, we still use them in our everyday lives. At school or in the kitchen. We even see them on T.V!

EXAMPLES: 1)Baking: Ingredients in recipes are often listed as fractions to show the measurements. For example, a 1/2 cup of flour going into a batch of cookie dough. 1/2 is a rational number.

2)Commercials: Many commercials use rational numbers as statistics to get you to buy their products. For example, 4/5 dentists approve this toothpaste, or 9/10 women like this lipstick best.

3)Medical Field: Medical journals use  st <span style="font-family: Verdana,Geneva,sans-serif;"><span style="color: rgb(73, 70, 119); font-size: 11pt; font-family: Verdana;">atistics to inform people about the risks of certain things. Such as 1/5 deaths in America are related to smoking <span style="color: rgb(73, 70, 119); font-size: 11pt;"> or 1/4 Americans are overweight.    <span style="font-size: 11pt; font-family: Verdana,Geneva,sans-serif;">

4) Math Class (of course): We use Rational numbers in math class absolutely EVERYDAY. **

There was once an ancient Greek mathematician named //Pythagoras//. He believed that all numbers were rational (could be written as a fraction). However, a very clever student of his, //Hippasus,// proved him wrong. He said that you could not represent the square root of 2 as a fraction and therefore, not all numbers were rational, but rather //irrational.// <span style="color: rgb(84, 184, 222); display: block; font-size: 12pt; text-align: left;"> **<span style="display: block; font-size: 12pt; color: rgb(0, 128, 0); text-align: left;"> <span style="color: rgb(84, 184, 222); display: block; font-size: 12pt; text-align: left;"> **<span style="display: block; font-size: 12pt; color: rgb(0, 128, 0); text-align: left;"> <span style="color: rgb(84, 184, 222); display: block; font-size: 12pt; text-align: left;"> <span style="display: block; font-size: 12pt; color: rgb(0, 128, 0); text-align: left;">Pythagoras had a hard time accepting this idea of irrational numbers. He stuck with his theory that all numbers had perfect values. In the end he could not prove Hippasus' theory of irrational numbers wrong, so he killed him. ** Rational Vs. Irrational __**
 * <span style="color: rgb(69, 114, 227); font-size: 18pt; text-align: left; display: block;">__Some Rational History__ <span style="display: block; font-size: 12pt; color: rgb(0, 128, 0); text-align: left;">
 * __<span style="color: rgb(117, 224, 62); font-size: 18pt;">

An **<span style="color: rgb(185, 34, 169); font-size: 12pt;">Irrational Number ** is a number that cannot be written as a simple fraction (the decimal goes on forever). For example, ** [|π] [| (Pi)]** is an Irrational Number. The value of ** [|π] [| (Pi)]** is " **<span style="color: rgb(242, 54, 54); font-size: 12pt;">3.1415926535897932384626433832795 ** (and more...)" Rational numbers can be written as a simple fraction (hence the term <span style="color: rgb(46, 165, 209); font-size: 12pt;"> **__<span style="color: rgb(84, 184, 222); font-size: 12pt;">//ratio// __** nal). You //**cannot**// write down a <span style="color: rgb(238, 17, 217); font-size: 12pt;">simple fraction to equal Pi. It is impossible. Therefore, Pi is an **Irrational Number**. Here is a chart to show you the difference:


 * ** Rational Numbers ** || ** Irrational Numbers ** ||
 * 8 || 9.33333333333333333-> ||
 * 4 || [[image:http://upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Pi-symbol.svg/600px-Pi-symbol.svg.png width="44" height="44"]] ||
 * 6 || 12.66666666666-> ||

<span style="color: rgb(144, 13, 217);"> __Fractions!__ <span style="font-size: 20pt; color: rgb(162, 0, 255);">

<span style="font-size: 11pt; color: rgb(41, 23, 232);"><span style="color: rgb(38, 26, 213);">__** Multiplying Fractions: **__ 1) Multiply the numerators 2) Multiply the denominators 3) *Reduce to lowest terms*  Examples: (2/5)(6/10) ^the numerators are '2' and '6' the denominators are '5' and '10' multiply them together =12/50 =6/25 ^the fraction 12/50 can be reduced into lower terms which is 6/25

(6/5)(3/4) ^the numerators are '6' and '3' the denominators are '5' and '4' multiply them together =18/20 =9/10 ^the fraction 18/20 can be reduced into lower terms which is 9/10  <span style="color: rgb(33, 67, 232);">

__** Dividing Fractions: **__ 1) Flip the second fraction to it's reciprocal. (Remember: <span style="color: rgb(239, 26, 26); font-size: 11pt; font-family: Verdana;">__**Divvy means Flippy**__ ) 2) Multiply the numerators 3) Multiply the denominators 4) *Reduce to lowest terms* Examples: (4/5)(2/3) = (4/5)(3/2) ^when dividing fractions, you must flip the second fraction than multiply the denominators and numerators together =12/10 =6/5 (improper) ^the fraction 12/10 can be reduced into lower terms which is 6/5 this type of fraction is called an improper fraction when the numerator is larger than the denominator you can change them into a proper fraction or keep it improper. =1 1/5 (proper)

(2/3)(1/4) =(2/3)(4/1) ^flip the second fraction multiply the denominators and numerators together =8/3 (improper) =2 2/3 (proper)

__** Adding Fractions: **__ <span style="color: rgb(46, 165, 209); font-size: 10pt; font-family: Verdana,Geneva,sans-serif;">1) Find a common denominator 2) Add the numerators (*NOT THE DENOMINATORS) 3) Reduce to lowest terms Examples: 3/4 + 2/3 = 9/12 + 8/12 (whatever you do to the denominator, you must do to the numerator) = 17/12 (improper) = 1 5/12 (proper)

- 4/7 + 1/3 (adding with integers is the same, you do not change anything) = -12/21 + 7/21 = - 5/21 ( -5/12 is lowest terms, they cannot both be divided evenly anymore)

<span style="color: rgb(160, 0, 255); font-size: 11pt;">__** Subtracting Fractions: **__ <span style="color: rgb(160, 0, 255);"> 1) Find a common denominator 2) Subtract the numerators (*// NOT THE DENOMINATORS //) 3) Reduced to lowest terms Examples: 5/6 - 1/2 = 10/12 - 6/12 (whatever you do to the denominator, you __must__ do to the numerator) = 4/12 = 1/3 (lowest terms)

= - 8/12 - ( - 9/12) = - 8/12 + 9/12 ( <span style="color: rgb(228, 17, 17); font-size: 11pt; font-family: Verdana;">** *NOTE: when there are there is a subtraction sign and a negative, change the signs to positive ** ) = 1/12 <span style="color: rgb(160, 0, 255);">
 * - ** 2/3 - (** - ** 3/4)

__** Adding AND Subtracting Mixed Numbers **__ *Convert both or the one mixed number to an improper fraction for BOTH adding and subtracting Examples: 2 1/4 + 1/2 = 9/4 + 1/2 = 9/4 + 2/4 = 11/4 (improper) = 2 3/4 (proper)

4 1/3 - 2 1/2 = 13/3 - 5/2 = 26/6 - 15/6 = 11/6 (improper) = 1 5/6 (proper)

=<span style="font-size: 11pt; color: rgb(162, 0, 255);">__ By; Rhys, Pat, Lilly and Brooke N. __ = =<span style="font-size: 11pt; color: rgb(162, 0, 255);"> = <span style="font-size: 11pt; color: rgb(162, 0, 255);"> <span style="font-family: Verdana,Geneva,sans-serif;">
 * __CITATIONS:__**

PICTURES- http://www.karlscalculus.org/rationals.gif http://en.wikipedia.org/wiki/File:Fracciones.gif

INFORMATION- Rational Number. 1 Dec. 2008 <http://en.wikipedia.org/wiki/Rational_number>. Math Page. 2001. 6 Dec. 2008 <http://www.themathpage.com/aPrecalc/rational-irrational-numbers.htm>. Pierce, Rod. Maths Fun. Ed. Rod Pierce. 2007. 10 Dec. 2008 <http://www.mathsisfun.com/rational-numbers.html>. Spector, L. 2007. //Multiplying Fractions Dividing Fractions//. 16 Dec. 2008 <http://www.themathpage.com/Arith/multiply-fractions-divide-fractions.htm>. Math Power 9 Ontario Edition. (1999). Toronto: McGraw-Hill Ryerson.