PROPERTIES OF REAL NUMBER:
Real numbers have the two basic properties of being an ordered field, and having the least upper bound property. The first says that real numbers comprise a field, with addition and multiplication as well as division by nonzero numbers, which can be totally ordered on a number line in a way compatible with addition and multiplication. The second says that if a nonempty set of real numbers has an upper bound, then it has a least upper bound. These two together define the real numbers completely, and allow its other properties to be deduced.

EXAMPLES: Closure Properties of Real Numbers
1) The sum of any two real numbers is a real number.
(In other words, if a and b are real, then so is a + b.)

2) The product of any two real numbers is a real number.
(In other words, if a and b are real, then so is ab.)

EXAMPLES OF PROPERTIES
#1. Commutative properties
The commutative property of addition says that we can add numbers in any order. The commutative property of multiplication is very similar. It says that we can multiply numbers in any order we want without changing the result.

addition
5a + 4 = 4 + 5a

multiplication
3 x 8 x 5b = 5b x 3 x 8

#2. Associative properties
Both addition and multiplication can actually be done with two numbers at a time. So if there are more numbers in the expression, how do we decide which two to "associate" first? The associative property of addition tells us that we can group numbers in a sum in any way we want and still get the same answer. The associative property of multiplication tells us that we can group numbers in a product in any way we want and still get the same answer.

addition
(4x + 2x) + 7x = 4x + (2x + 7x)

multiplication
2x2(3y) = 3y(2x2)

#3. Distributive property
The distributive property comes into play when an expression involves both addition and multiplication. A longer name for it is, "the distributive property of multiplication over addition." It tells...

...and laboratory practices is essential before allowing the learners to use it as their training ground during the application of the activities. These includes the good kitchen and laboratory practices, keeping the sanitation high in the laboratory,ang the proper way of keeping and handling the food.
GOOD KITCHEN AND LABORATORY PRACTICES
This means keeping things clean: and includes the following:
1. Maintain personal hygiene.
2. Keep and maintain the cleanliness...

...Pinoy Times, Lunes, Marso 5, 2001, p. 4
Maraming Pilipino ay nananatiling ”walang pakialam, walang interes, at walang komitment.” May pagkamanhid na nagaganap kaugnay ngmga usapin sa moralidad kaya madalas inuunawa na lamang yaong mga bagay na di dapat palagpasin;ang kasamaan ay hindi nasusugpo dahil lubhang abala angmga tao sa pagkayod ng ikabubuhay. Kung gusto nating tayo’y...

...Macro Environment Forces for Coffee
Socio-Cultural Environment
Wherever you may be in the world, you will find people looking forward to enjoying their morning pick me up cup of coffee. Coffee is as popular as a beverage that our consumption is said to account for a third of our total consumption of free tap water. For a lot more people, especially those in desk jobs, coffee may command an even bigger share of their liquid intake. It is the mildly stimulating effect of the caffeine in...

...Kaugalian NgMgaPilipino
Live Search Nais ngmgaPilipinoang Malusog na Puso Magkaroon ng Malusog na Pamumuhay-Ibigay ang Makikita ninyo sa talaan ng pagkain ang kaugalian tungkol sa pagkain. Special appreciation to Nais ngmgaPilipinoang Malusog na Puso Magkaroon...

...Listahan ngmga Pananaliksik
1. Pamagat : Information Technology and Firm Size
Patnugot : Albert Wenger
Posted November 2, 2012
continuations.com/post/3482468649/information-technology-and-firm-size-thesis
Anotasyon : Mayroong iba’t ibang pangangailangan ang isang tao, katulad ng physical at human assets mayroon ding information assets. Kaya ayroong tinatawag na customer information center, isang firm na nagbibigay impormasyon...

...Lustado, Thea Danizze M.
BSA-A3A
2 Leaders Who Practice True Democratic Styles
Corazon Aquino was the 11th president and first female president of the Philippines. She restored democracy after the long dictatorship of Ferdinand Marcos. She was known as the “Mother of Democracy” of the Philippines for she led the revolution, the culmination of a battle for freedom that was her husband's advocacy. It was a battle she won, and a victory that gave us back our nation's democracy. As President,...

...History of Quezon City
Quezon City was created on October 12, 1939 by virtue of Commonwealth Act 502. It became the capital of the Philippines with the enactment of Republic Act No. 333 on July 17, 1948. In 1975, Quezon City became part of the larger urban governance scheme that is Metro Manila, with the creation of the Metropolitan Manila Commission by virtue of Presidential Decree 824. On July 24, 1976, then President Ferdinand E, Marcos issued Presidential Decree No. 940, conferring the...

...Mga Pangyayari Matapos ang pagbagsak ng Kanlurang Imperyong Roman
Sa pagbagsak ng Kanlurang Imperyong Roman:
Naputol ang ugnayan ng Kanlurang Europe sa mayamang kalakalan ng Byzantine at Muslim.
Nawalan ng saysay angmga lungsod bilang sentro ng kalakalan.
Humina ang kalakalan dahil sa naging mapanganib ang...

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":true,"isPremiumCountry":false,"logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","essay":{"essayId":38219557,"categoryName":"Literature","categoryParentId":null,"currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":3,"pageRange":"1-3","totalPages":3}},"access":"premium","title":"Ang Katamaran Ng Mga Pilipino","additionalIds":[5,3,16,19,83],"additional":["Computer Science","Business \u0026 Economy","Law","Natural Sciences","Computer Science\/Domains"],"loadedPages":{"html":[],"text":[1,2,3]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Ang-Katamaran-Ng-Mga-Pilipino-1808101.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay\/100241","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.2","language":"en_US"},"analytics":{"googleId":"UA-32718321-1"}}

## Share this Document

Let your classmates know about this document and more at StudyMode.com