Magic Carpet Airlines Case Study - 1637 Words

Magic Carpet Airlines (MCA) was a regional airline company that established operations in 1961. Over a span of 26 years, MCA grew from servicing flights in two cities to 18 cities. In 1987, MCA purchased another regional airline, River City Airlines (RCA), and merged the two operations. With the merge of the two regional airlines, the company became a small â€Å"national† airline until 1988 when MCA entered into a marketing agreement with a major national carrier to become a â€Å"feeder† airline for the carrier. Prior to the merging of MCA and RCA, neither company’s flight attendants were unionized. Rising concerns starting emerging among both MCA and RCA flight attendants in regards to the unsystematic way MCA’s management resolved personnel†¦show more content†¦Flight Attendants were worried about the arbitrary process MCA’s management used to resolve issues, expressly the margining of the seniority list and working conditions. This was a concern of job security. The flight attendants explicitly requested their seniority carry over to any new company in the event of another merger or buyout of MCA, and protection from any layoffs that may result. The flight attendants also expressed concerns with regarding wages via duty rig, and requested the same provision as those provided to the pilot. As of current, MCA only paid flight attendants for the time they were in the aircraft with it moving, they were not compensated for time spent sitting in airports or waiting for flights. The flight attendants want to implement duty rigs, where they are compensated a fixed percentage for time spent on duty with the company. Prior to negotiations, MCA was in a state of transition which caused much confusion. The negotiation team for MCA consisted of a group of executive management. Bill Orleans, the director of labor relations, was recently demoted from director of human resources, which he resented. Orleans was responsible for previously negotiating most of the union contracts at MCA. Ross Irving, the new director of human resources, was hired from an outside firm. Since Irving was hired as Orleans replacement, this created tension between the two, as a result, Irving avoided the negotiating sessionsShow MoreRelatedEssay on Magic Carpet Airlines Case Study1191 Words   |  5 Pagesï » ¿ Case Study – Magic Carpet Airlines Week 4 September 22, 2013 1. What did the union do to prepare for negotiations? What additional sources of information might it have used? What were the unions primary objectives? The union began preparing by doing research to find out what other similar airline carriers were supplying for their flight attendants (i.e. average working conditions, benefits, and wage rates). They used government sources to compare wage,Read MoreAccounting for Airline Frequent Flyer Programs: Management Incentives and Financial Reporting Impacts8715 Words   |  35 PagesACCOUNTING FOR AIRLINE FREQUENT FLYER PROGRAMS: MANAGEMENT INCENTIVES AND FINANCIAL REPORTING IMPACTS May 2012 Brian J. Franklin, BBA Accounting ‘12, College of Business and Public Policy, University of Alaska Anchorage, 3211 Providence Drive, Anchorage, AK 99508, 907-268-4233 Ext. 401, bfranklin@frontiertutoring.com ABSTRACT The obligation to provide free or reduced-fare travel to passengers who redeem their accrued frequent flyer program (FFP) benefits represents a significant liability onRead MoreHimachal Pradesh8795 Words   |  36 Pagespopulation in Himachal depend directly upon agriculture which provides direct employment to 71% of its people. The main cereals grown are wheat, maize, rice and barley. Himachal has a rich heritage of handicrafts. These include woolen and pashmina shawls, carpets, silver and metal ware, embroidered chappals, grass shoes, Kangra and Gompa style paintings, wood work, horse-hair bangles, wooden and metal utensils and various other house hold items. These aesthetic and tasteful handicrafts declined under competitionRead MoreCase Studies67624 Words   |  271 PagesCase Studies C-1 INTRODUCTION Preparing an effective case analysis C-3 CASE 1 CASE 2 CASE 3 CASE 4 CASE 5 CASE 6 CASE 7 ABB in China, 1998 C-16 Ansett Airlines and Air New Zealand: A flight to oblivion? C-31 BP–Mobil and the restructuring of the oil refining industry C-44 Compaq in crisis C-67 Gillette and the men’s wet-shaving market C-76 Incat Tasmania’s race for international success: Blue Riband strategies C-95 Kiwi Travel International Airlines Ltd C-105 CASE 8 Beefing up the beeflessRead MoreMarketing Mistakes and Successes175322 Words   |  702 Pages1-800-CALL WILEY (225-5945). 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No part of this publicationRead MoreScience and Technology13908 Words   |  56 Pages2009 Award Winning Essays Organized by Supported by T he Goi Peace Foundation U N ESC O Japan Airlines Foreword The International Essay Contest for Young People is one of the peace education programs organized by the Goi Peace Foundation. The annual contest, which started in the year 2000, is a UNESCO/Goi Peace Foundation joint program since 2007. The United Nations has designated 2001-2010 as the International Decade for a Culture of Peace and Non-Violence for the Children ofRead MoreInvestment and Economic Moats46074 Words   |  185 Pagesreader to pick and choose from the very best in investment advice today. 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In the words attributed to Socrates in Plato’s Apology,...

In the words attributed to Socrates in Plato’s Apology, â€Å"The unexamined life is not worth living.† David Foster Wallace expands on this idea in his â€Å"Kenyon College 2005 Commencement Address,† pointing out the importance of awareness and escaping the natural, default-setting of an unconscious, self-centred life. While commencement speeches are typically epideictic—celebratory—in nature, Wallace takes a deliberative rhetorical stance. According to Fahnestock, deliberative discourse is used in order to persuade in â€Å"the best possible course of future action† (1998, p. 333). Abizadeh argues that character and emotion are â€Å"constitutive features of deliberation,† and that deliberation cannot be â€Å"reduced to logical demonstration† (2002, p.†¦show more content†¦Connors (1979) argues the need for a lower complexity of the logical appeals in speech, stating that appeals â€Å"must be presented slowly a nd reiteratively† (1979, p. 288). Wallace uses multiple adjectives to describe an item or idea, and the scenarios in his examples are described extensively, which makes them more pertinent and comprehendible. For example, â€Å"the store is hideously, fluorescently lit, and infused with soul-killing Muzak or corporate pop.† (Wallace, 2008, para. 6) In his 1945 study, Ray Ehrensberger states an orator must â€Å"First tell ‘em what you’re gonna tell ‘em; then tell ‘em; finally, tell ‘em what you told ‘em† (p. 102). Wallace opens with an ironic analogy which, in itself, contains the â€Å"kernel of truth† he is trying to communicate. A young fish asks another â€Å"What the hell is water?† (Wallace, 2008, para. 1) This scenario is chosen purposefully because it is simple and relatable, which enables Wallace to present a new perspective on a familiar concept. Wallace later explains that point of the story is that â€Å"the most obvious, important realities are often the ones that are the hardest to see and talk about,† (Wallace, 2008, para. 2) and repeats this thesis throughout the speech. In the last few lines of his speech, Wallace again states his message in simple terms of the importance of awareness. He reminds the audience that awareness of what is â€Å"s o hidden in plain sight around us† (Wallace, 2008, para. 11) is essential and that weShow MoreRelatedSocrates : The Suicide Of Socrates1405 Words   |  6 PagesSocrates was born in 470 BCE in Athens, Greece. His father was Sophroniscus, a sculptor and stone mason from Athens and his mother was a midwife by the name of Phaenarete (30 Interesting Socrates Facts 2014). Socrates original profession was masonry and sculpting, before becoming a philosopher. On a day in 399 BC, Socrates ( roughly 71 years at the time) went to trial.Now why would anyone want to send an old man to court? Three answer is that Socrates was accused of refusing to recognize theRead MoreMachiavelli s The Prince And Plato s Apology1697 Words   |  7 PagesMachiavelli’s â€Å"The Prince† and Plato’s â€Å"Apology† Philosophers have unique and yet similar ways of interpreting life through a variety of different values and beliefs appointed to oneself. Some philosophers have the ability and courage to stand up to what they are trying to accomplish or for what they believe in, even if consequences follow their actions. Machiavelli and Plato have different perspectives and goals in their writing, however their stories also have some underlining similarities suchRead MoreEthics and Related Philosophies4468 Words   |  18 Pagesethics,  ethical theory,  moral theory, and  moral philosophy, is a branch ofphilosophy  that involves systematizing, defending and recommending concepts of right and wrong  conduct, often addressing disputes of  moral diversity.  The term comes from the Greek word á ¼  ÃŽ ¸ÃŽ ¹ÃŽ ºÃÅ'Ï‚Â  ethikos  from á ¼ ¦ÃŽ ¸ÃŽ ¿Ãâ€šÃ‚  ethos, which means custom, habit. The superfield within philosophy known as  axiology  includes both ethics and  aestheti cs  and is unified by each sub-branchs concern with value.  Philosophical ethics investigates what is theRead MoreSocrates : The Soul Man2954 Words   |  12 PagesSocrates: Soul Man Intro (245 words) How you have felt, O men of Athens, at hearing the speeches of my accusers, I cannot tell; but I know that their persuasive words almost made me forget who I was - such was the effect of them; and yet they have hardly spoken a word of truth.† - Apology, 17A So, as told by Plato, Socrates began his defence before an Athenian jury on charges of impiety and corrupting the youth of the city. However, the real aim of these accusations seems to have been toRead MorePolitical Philosophy and Plato Essay9254 Words   |  38 Pages SOCRATES Socrates 469 BC–399 BC, was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary Aristophanes. Many would claim that Platos dialogues are the most comprehensive accounts of Socrates to survive from antiquity. Through his portrayal in Platos dialogues,

Child Parent free essay sample

Child Parent by A. V., Old Orchard Beach, ME Ive become a 17-year-old mother of two boys. I didnt give birth to them or supply them with names yet now theyre mine, and I have no choice whether I want them or not. I worry when they cram their mouths with junk food. I gripe at them when they watch tasteless shows like Ricki Lake. I complain when they wrestle in the living room, pretending that theyre ninja warriors. Ive become overly protective of my brothers, half in love, half in obligation. Being the oldest, Ive been thrust into the spot of authority figure with a teenage attitude. Ive lost my interest in causing trouble and experimenting with my own freedom. Im the scowling older sister who yells and interferes when she has no such right. I cant raise children. I dont want that parental responsibility. We will write a custom essay sample on Child Parent or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page I watch my actions, maintain maturity and stifle my urge to go crazy, hoping that my examples will be noticed. Jordan sees me as a bossy jerk. Joey sees me as entertainment when I tickle him in his armpits and spider walk him across the kitchen, but he cant understand why I scowl at him when hes watching Power Rangers at 6 a.m. He doesnt know that I only want to keep his fragile brain from being scattered and distorted. Im choking my brothers with an urgency to save them from being hurt. It is quite evident that I am not happy with their obnoxious actions, but in caring for them, I am anxious and nervous. Parenting is too intense for me. Saturday night arrives. Jordan is at the dance, Joey is in bed, Mom, reading in her room with the music up loud, tells me to go out and do something for awhile. I know where they are and feel no need to worry. I let myself break away, going out to a friends house for a little excitement. Its 1: 30 and the party is breaking down. Everyone is slowly letting themselves slip into the dead unconsciousness following a rowdy night of brain-cell killing. Im sitting there, ice-cold sober, wondering how theyre all feeling, thinking What am I doing here? I laugh at their silliness, slurred mumbling, and woozy cavorting. Now theyre filled with unnatural substances, falling asleep like logs on the carpet. They had fun. I cant let go of my obligation. I like to come home and look Mom in the eye, knowing that she has nothing to hang over my head. My friends cant gossip about my embarrassing displays at last weeks party because there werent any. Im too responsible. Im so moral that Im probably abnormal. I know that there is nothing wrong with this seemingly unprecedented behavior, but balance, damnit! I feel like a moron, purposely scheduling screw-off time. Doesnt that happen naturally? This sudden change from teenager to adult has put me in turmoil. With Dad gone, the man of the house is missing. The father figure, husband, and security is gone. Now Mom and I share the household responsibility, but at different levels. She has been where Ive been. Ive never been in her place to see lifes unfolding trials. I want to be a child. I want to experience these years with curiosity and hope. Im too young to be a mom. Im too old to be innocent. I cant close my eyes to what lies ahead. I have emotionally adapted to lifes changes and I feel that I am stable enough to meet those tough challenges in these metamorphic years. I will not be shocked and disorientated when life throws me a curve ball. I feel that I am ready to overcome the harshness of growing up. The child parent within me is ready.

Tarenah Henriques Essays - Louis Armstrong, King Oliver,

Tarenah Henriques Dec. 10, 1998 Period 4 Louis Armstrong Born in August 1901 (not Independence Day 1900, as he was always told and believed), Louis Armstrong sang on the New Orleans streets in a boyhood quartet and in 1913 was admitted to the Colored Waifs' home for firing a gun into the air. In the home he learned the trumpet, and within four years was challenging every trumpet king in his home town, from Freddie Keppard to Joe Oliver, his first father-figure, whom he replaced in Kid Ory's band in 1919. In 1922 Oliver (by now King Oliver) invited Louis to join him in Chicago to play second trumpet. Tempting as it is to echo Nat Gonella's incredulous comment, I can't imagine Louis playing second trumpet to anyone, Oliver was able to teach Armstrong a little. The regular harmonic experience of playing second (his ear, even then, was faultless) and, above all, the importance of playing straight lead in whole notes, as Oliver did, were lessons that Armstrong was to remember for life. Experience was by now, however imperceptibly, toughening the young man up. His second wife Lil Hardin helped to focus his streak of ambition and he was learning that people could be devious - Oliver, it transpired, was creaming his sidemen's wages. Although he loved Oliver until the end, by 1924 Armstrong had made the jump to New York and Fletcher Henderson's orchestra. It was hot city company for a country boy, but he had the humor and talent to counter mockery (I thought that meant 'pound plenty'!, he quipped, when the stern Henderson ticked him off for a missed pp dynamic); somewhere along the way he decided he was the best, and got ready to defend his title if necessary. Louis played the Regal Theater in Chicago, remembers Danny Barker, and they had this fantastic trumpeter Reuben Reeves in the pit. So in the overture they put Reuben Reeves on stage doing some of Louis's tunes. Louis listened - then when he came on he said, Tiger Rag. Played about thirty choruses! The next show? No overture! In 1925 Armstrong, already a recording star, began OKEH dates with his Hot Five and Seven (featuring Johnny Dodds, Kid Ory and his wife Lil, until Earl Hines replaced her). The music on masterpieces such as Cornet Chop Suey, Potato Head Blues, Sol Blues and West End Blues turned jazz into a soloist's art form and set new standards for trumpeters world-wide. At the peak of his young form, Armstrong peeled off top Cs as easily as breathing (previously they were rare) and pulled out technical tours de force which never degenerated into notes for their own sake. His singing introduced individuality to popular vocals and, just for good measure, he also invented scat singing, when he dropped the music one day at a recording session. Best of all was his melodic inspiration: his creations were still being analyzed, harmonized and celebrated half a century later. Rather than playing ever higher and harder, Armstrong simplified his music, polishing each phrase to perfection, while keeping his strength for the knockout punch. By 1930 he was a New York star, with imitators all around him, but his business life was at a temporary impasse. Then he found his Godfather-figure, a powerful, often ruthless Mafia operator called Joe Glaser, who was to steer his client's fortunes for 35 years. In 1935, with Glaser's approval, Louis teamed with Luis Russell's orchestra, an aggregation of old New Orleans friends, and for five years he was to tour and record with them: the records are classics, and helped to get Armstrong into films such as Pennies from Heaven (1936) and Artists and Models (1937). In 1940, Glaser's office brusquely sacked the band and Louis put together another containing younger modernists such as John Brown (alto), Dexter Gordon (tenor) and Arvell Shaw (bass), a long Louis associate, with Velma Middleton sharing the singing. It lasted until summer 1947, but big bands were on a downward slide and Armstrong found leading a headache. In 1947 promoter Ernie Anderson presented him with a small band (directed by Bobby Hackett) at New York's Town Hall. The acclaim that greeted the move signaled the end of his big-band career, and for the last 24 years of

The Majesty Of Nuuanu Essay Research Paper free essay sample

The Majesty Of Nuuanu Essay, Research Paper On the island of Oahu, at the farthest ranges of emerald-garbed Nuuanu Valley is the Nuuanu Pali there # 8217 ; s a topographic point you can see to bask dense viridity forest, dramatic mountain-to-ocean positions, and a piece of Hawaiian history. Nuuanu is an country located on the southeasterly portion of the island and Pali is a Hawaiian word significance drop . Geting there is really simple if you # 8217 ; re coming from Honolulu. Get on H-1 expressway so take the Pali Highway off-ramp. Once on Pali Highway, follow the green marks alongside the route to make your finish. The drive should take about 15 to 20 proceedingss. Ladies, don # 8217 ; t have on a frock or skirt when sing the Pali because it # 8217 ; s really windy and you won # 8217 ; t bask yourself if you # 8217 ; re worrying about aliens seeing your underwear. Likewise, gentlemen, don # 8217 ; t wear chapeaus, loose dark glassess, or toupees to the site because when a strong blast of air current comes along, you may neer see your properties once more. We will write a custom essay sample on The Majesty Of Nuuanu Essay Research Paper or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Because of the air current, a jacket or jumper is recommended. Depending on the season, sporadic showers of rain are besides common. Make convey a camera, for the position is fabulous and you will non be disappointed. Nuuanu Pali is surrounded by dense forest heavy with wet. As you travel up Pali Highway, the houses begin to thin and the verdure begins to take over. During the winter and spring there are many waterfalls to be seen in the mountains. The trees, covered with moss and green writhing vines, block out the Sun and civilisation. The workss and vines seem to hold taken over everything except the asphalt route being driven on. All of a sudden, the forest terminals and a little unfastened parking batch appears. The sentinel is at the terminal of a paved paseo. On the sides of the paseo are a twosome of sellers. One seller sells Jerseies and custodies out booklets which educate people about the issue of Hawaiian Sovereignty. The other seller sells Polynesian humanistic disciplines and trades. As you stand at the sentinel, expression at the knife-edged ridges to your left and right. These cragged weaponries that embrace the win dward side as far north as Kualoa and as far south as Waimanalo are mere leftovers of Koolau mountain, they are landward wall of what once was a monolithic vent. Time and ocean tides have eroded and collapsed the offshore side of the vent. From the sentinel, many towns and topographic points of involvement can be seen. To the left is Kahaluu and the new H-3 expressway. Straight in front is Kaneohe and Kaneohe Bay. Olomana and Kailua are to the right. You can besides see Kaneohe Marine Corps Air Station, the Koolau and Pali golf classs, and Kapaa Quarry. The Koolau Mountains are amazing, olympian, and breathtaking. The blues of the ocean and sky blend together, doing it hard to state where the Earth ends and where the sky begins. Sometimes, the clouds and mist bead depression over the mountains and sheets of rain can be seen falling over the land and sea. Double and ternary rainbows are besides a familiar sight. The cold air current invariably blows and brings the aroma of rain, ferns, and moist Earth mixed together. Standing at that place, at the border of the drop, watching land, sea and sky semen together and feeling and hearing the tanning wind all about, it is easy to be transported back to a clip before concrete, cars, and pollution. More than 200 old ages ago, a great warrior head from the island of Hawaii named Kamehameha envisioned unifying all the Hawaiian islands. Many heads, including High Chief Kalanikupule from the island of Oahu did non portion in Kamehameha # 8217 ; s dream and decided to dispute him. In 1795, 1000s of Kamehameha # 8217 ; s warriors drove Kalanikupule and his ground forces up to Nuuanu Pali where many fell or fought to their deceases. Subsequently, in the early 1800s, the kamaaina would track the deadly Nuuanu Pali with kids, nutrient, and supplies tied to their dorsums. In 1897, a main road was built and during the building, workers found about 800 skulls and other castanetss at the underside of the drop # 8211 ; remains of the warriors who were defeated by Kamehameha. Many more betterments were made to the main road and now the old route is a boosting trail which branches off from the sentinel point.

Free Essays on Controversy Of 2008 Being, China Olympic Games

On July 13th 2001, China was chosen among several nations like Turkey, Japan, France and Canada to organize the Olympics. Whether or not China should have been granted this opportunity remains a sensitive issue for many. As for me, I totally agree with the selection of Beijing, China as the host city of the 2008 Summer Olympic Games. Many believe that China should not have been awarded the games based on alleged civil rights abuses on the part of the Chinese communist government towards its own dissidents. In this paper, I will talk about all the allegations put towards China as to why they should not have been awarded the games and explain why I believe that the decision to give Beijing the games was the right one. The allegations are well deserved. Due to communism, the preoccupation of the Chinese authorities is to maintain social stability in order to keep the power. Nowadays in China there is no freedom of association, no free speech and no press freedom. Journalists are not able to do their job freely because they could be prosecuted and jailed if their work is judged "against the Party". The most important repression of free speech concerns the Internet users. More than fifteen persons are in jail for having expressed themselves on the web and people continue to be arrested and charged with serious offences for using the Internet to spread information about human rights or other politically sensitive issues. From what I have found in my research, the human rights situation in China is particularly present in Tibet and in Xinjiang, areas that are located in west China. In 1950 this region was invaded by the Chinese forces. In 1959 Tibetan people tried to force the Chinese out but the army repressed this movement violently and the Dalaà ¯-Lama left Tibet. Since 1959, Tibetan people and particularly religious, Buddhist monks and nuns, have been victims of Chinese repression. At the end of 2000, hundreds of Buddhist monks and nun... Free Essays on Controversy Of 2008 Being, China Olympic Games Free Essays on Controversy Of 2008 Being, China Olympic Games On July 13th 2001, China was chosen among several nations like Turkey, Japan, France and Canada to organize the Olympics. Whether or not China should have been granted this opportunity remains a sensitive issue for many. As for me, I totally agree with the selection of Beijing, China as the host city of the 2008 Summer Olympic Games. Many believe that China should not have been awarded the games based on alleged civil rights abuses on the part of the Chinese communist government towards its own dissidents. In this paper, I will talk about all the allegations put towards China as to why they should not have been awarded the games and explain why I believe that the decision to give Beijing the games was the right one. The allegations are well deserved. Due to communism, the preoccupation of the Chinese authorities is to maintain social stability in order to keep the power. Nowadays in China there is no freedom of association, no free speech and no press freedom. Journalists are not able to do their job freely because they could be prosecuted and jailed if their work is judged "against the Party". The most important repression of free speech concerns the Internet users. More than fifteen persons are in jail for having expressed themselves on the web and people continue to be arrested and charged with serious offences for using the Internet to spread information about human rights or other politically sensitive issues. From what I have found in my research, the human rights situation in China is particularly present in Tibet and in Xinjiang, areas that are located in west China. In 1950 this region was invaded by the Chinese forces. In 1959 Tibetan people tried to force the Chinese out but the army repressed this movement violently and the Dalaà ¯-Lama left Tibet. Since 1959, Tibetan people and particularly religious, Buddhist monks and nuns, have been victims of Chinese repression. At the end of 2000, hundreds of Buddhist monks and nun...

THE TACTICS OF MAYA FARMERS Essay Example | Topics and Well Written Essays - 500 words

THE TACTICS OF MAYA FARMERS - Essay Example The classic Maya civilization flourished in the southern low lands of Mexico, Guatemala, and Honduras between the last four centuries before Christ and AD 900. Despite the conditions of prolonged dry spells caused by draught, constant brushfires that devastated the earth, and erratic rain patterns that wreaked havoc on agriculture, the Maya community’s survival for such a long period of time could be attributed to their farming tactics. The hot and humid conditions of the low lands, with no possibility for irrigation, posed the primary challenge to the Mayan existence as a farming community, but they seemed to have adapted to these adverse conditions by their innovative tactics. They moved to the dense forest area that mantled the southern lowlands, cleared the primordial forest and utilized it for agriculture. In order to overcome the infertility of their homeland, they adopted the slash-and-burn cultivation by cleaning the brush and trees, and burning them. This helped them to put to use even the barren lands. However, this had a shortcoming that the fertility would last for only about two years or so. The Mayans were again imaginative here by migrating to fresher meadows where they cultivated, and returned after several years to utilize the same land they earlier abandoned. Maintaining this process as a cycle, they were able to use a wider area of land. Thus they were able to circumvent, albeit temporarily, the c hallenges of nature.

Social Capital Essay Example | Topics and Well Written Essays - 3000 words

Social Capital - Essay Example nt methodologies that can be used to measure it, identify social concepts that can be addressed by social capital and lastly explain how social capital can solve problems in a specific organisation. The organisation chosen for analysis is the Environmental Protection Agency Queensland. This will be the focal point in the last portion of the essay as I work in this organisation. Many groups and individuals have attempted to define social capital. However, some of the statements passed of as definitions are in fact depictions of social capital and not the actual thing. Social capital may be defined as the informal and instantiated norm that acts as a means for promoting cooperation between individuals. Norms in this case may refer to the cases of reciprocation between two people or they may refer to complex doctrines from major religions such as Christianity. The most important aspect here is that these norms have to be engrained into a real human relationship. (Stayner, 1997: p7) The issue of reciprocation is something that potentially exists among all people but is usually evident when dealing with friends. In other words, other aspects such as civil society, trust and networks are only products of social capital but do not form part of the actual definition. It should be noted here that institutional norms do not just apply to any kind of norms. The norms under consideration in social capital are those ones that can cause an actual increase in the level of cooperation between certain groups. These norms must be linked to certain values that include honesty, reciprocity, performance of duties among others. This also means that other norms applicable in specific scenarios may not qualify as suitable ones in social capital. For instance, in some parts of Italy, there is great cohesion between members of the family but outside the family unit; individuals are allowed to take advantage of one another. Those norms are not acceptable in the definition of social

In a dark time Essay Example for Free

In a dark time Essay Reading and understanding poems is a creative process that goes on in time and from line to line even as the poet’s creation does. In the poem Roethke tries to break through the barriers of rational language with paradoxes and short, seemingly unrelated statements. In a sense, Roethke’s poem is also a commentary on the experience, and his essay is another attempt to record his mystical enlightenment. Each expression in turn becomes its own experience for the writer. â€Å"In a Dark Time,† was a dictated poem, something scarcely mine at all. The allegorical nature of his spiritual journey is clear from the phrase â€Å"A man goes far to find out what he is† that by is generality universalizes and distances the speaker’s quest. His search is less for personal identity than it is for defining characteristics of the human condition-man’s nature and the limits of his understanding. His mystical experience dissolves idiosyncrasies into ultimate concerns, yet we expect more of a union with the divine, a phase he saves for the last stanza. At the end of â€Å"In a Dark Time,† the speaker returns to the opening paradox that natural darkness is actually a spiritual light, but now the paradox has a more agonizing relevance. Instead of the general statement that â€Å"In a dark time, the eye begins to see,† he now confesses that â€Å"Dark, dark/my light, and darker my desire. † In mystical literature God remains the source of all light, although He may appear as darkness to man’s limited mind. Roethke, in the poem, would be restoring the original power of the One beyond God, and what is more, identifying himself with the greater of the two. While he is not the final authority on the meaning of â€Å"In a Dark Time,† Roethke’s interpretation demands the close attention: if only by the necessities of his art, he has lived with the poem longer and more intimately than his readers. Reference: Roethke, T. (1960). Roethke: Colleted Poems. Double-day Company, Inc.

Fostering Motivation by the Help of Neuroplasticity

Fostering Motivation by the Help of Neuroplasticity There are two types of mindset: fixed versus growth mindset. In fixed mindset, students (people) believe that their abilities is innate and they cannot change it, therefore a failure makes them start doubting in themselves and believing they are not smart/good enough to achieve their goals. On the other hand, those who have a growth mindset believe that they can improve their abilities by learning and practicing. They see failure as an opportunity to working on their mistakes and weaknesses; their perseverance and resilience makes them more motivated and work harder to improve their abilities. Moreover, one of the biggest difficulties that students face when they enter to a new stage of their academic life is lack of motivation. The main idea of this project is improving growth mindset as well as fostering intrinsic motivation among students by teaching them about the brain and neuroplasticity. For this purpose, a weekly workshop will be designed for five sessions. Below is the detai l of each session. Method This project is based on learning science approach with focus on embodiment and feedback which are explained in details. Participants In order to meet the goals of this project and having a sound base of interpretation of the results and eliminating some of the confound variables like method of learning and environmental differences, students from one class will be selected to participate in the workshop. Junior students are extremely vulnerable to fail to achieve an acceptable grade during their high school, because in general children in this age suffer from antisocial behavior, lack of self-esteem, school engagement and more importantly being motivated enough to continue their study. Having a positive or negative outcome in this age depends on students motivation and motivation is dependent on children core belief. In other words, the way students deal with their environment, indicate their future success and exactly here motivation comes to play an important role because if students are motivated enough to continue their study and like to challenge themselves, they can survive and even flourish during this peri od (Blackwell et al., 2007). For this reason, target group in this project will be high school students. Both male and female students with any ethnic background can participate in this study. It is ideal to have a balanced number of male and female participants in order to control for any potential gender differences in the study. Materials Prior to participating in the workshop, participants will be asked to answer to two questionnaires: one of them is a motivation questionnaire to examine students goal in the coming year and their view about the value of efforts and the other one is a mindset questionnaire. The mindset questionnaire will measure students core belief about their intelligence, goal orientation, belief about effort and attribution and strategies in response to failure. Teachers report on students level of engagement and motivation in classroom will be also collected. To investigate the impact of growth mindset on long term achievements (outcomes), the same questionnaire will be distributed at the end of semester, which will be two months after the workshop. The latest grade of students mathematic achievements (CAT) and students new math grade at the end of semester will be collected. Procedure Session 1: The Neurons: Structure and Function In this session, students will learn about concept of neuron and its structure and neurotransmitters by lecture and pictures (figure 1 and 2). The lesson plan for this session is as the following: Lesson Plan There are two types of cells in the brain: The first type is called glia, which comes from a word that means glue and they hold the brain together. Glia plays an important role in the processing and communication. The main brain cells are called neurons. They have a lipid bilayer as a cell membrane to keep everything inside. They have the fluidly cytosol, the liquid inside. Neurons have three main parts, the cell body, or the soma, is where we find the nucleus, the part that has DNA. And the other parts are the specialization that allows the neurons to communicate with other cells. Dendrites are branches around the soma. It integrates it in two ways, both spatially and temporally. Spatially means weve got all these inputs coming from different parts of the brain and temporally means that theres a time window over which the cell is looking at. Once the information has been summed up and the neuron decided how to process it, the neuron sends output down to the axon. Neurons shapes and sizes depend on their function within the neural circuit. The stereotypical one is called a multi-polar neuron which has more than one dendrites and only one axon. Bipolar neurons have one input and one output. Unipolar neurons have basically one long transmission wire with the cell body off to the side, so information just kind of flows down with, no real interference from the soma itself. Physiological properties of the neuron: The neuron is actually using electricity to send through the dendrites and then down the axon. Every cell has an electric membrane potential, or an electric resting potential, which is the difference between the electrical potential energy inside and outside the cell. By recording the electrical potential of cell membrane versus the electrical potential at an electrode outside the cell membrane we can have voltage difference. Most cells have a resting membrane potential of about -70 or -65 mV. The other property thats really important about the neurons is t hat they have Ion channels, which are like doorways in their cell membrane. When their membrane potential gets high and reaches the thresholds, these doors can open. Signal starts at this area at the juncture of the soma and the axon thats called the Axon Hillock. So, what happens is the membrane potential of the cell reaches a certain threshold, and that causes the door to open. When the door opens, positive ions start coming into the cell, which causes the membrane voltage to go up and opens more of these voltage sensitive doors. And eventually there would be a big influx of positive current, but the Ion Channels will be close very fast. That quick increase and decrease of the membrane potential, is called an action potential, which lasts for about one to two milliseconds. Action potential is an all-or-none event. As the positive ions are coming in from action potential that started at the Axon Hillock, its going to increase the memory voltage of the axon right next to it. Therefo re, more channels will be opened and more positive current flow in which will cause action potential to travel down the length of axon. What the neurons saying in the pattern of its spiking activity. In general, neuron does not directly talk to the next neuron via an electrical signal, instead when the electrical signal gets to the tip of the axon, the axon will release chemicals called neurotransmitters. Neurotransmitters are chemicals messengers that travel over a small gap between the neurons sending the information and the dendrites of the neuron receiving the information. That gap is called a synapse. The neuron receiving the information by their dendrites on that post synaptic side of this gap have special receptors for receiving the released chemicals by the presynaptic neuron. When the chemical binds to those special receptors, that causes changes in the membrane potential of the second neuron and then that neuron can collect that information and send its signal to its neigh bors. After this lecture, students will have time to ask any questions and discuss their thoughts and understanding of the concept of neurons within small groups. By the end of this session, students will learn about basic properties of neurons and how neurons communicate with each other.                Session 2: Brain structure and Function In this session, after a brief recalling of last session which was about neurons, few fact cards about brain will be given to students. Next, a brief introduction of brain anatomy and main areas of brains will be given by the help of pictures (figure 3 to 5). For avoiding boredom in students, instead of lecture given by the instructor, they will watch short videos explaining brains function. Videos are from an online course offered by University of Toronto Facts that are given after figure 3: Weight: 3 lbs 2% of total body weight Consumes 25% of the bodys oxygen supply Consumes 70% of the bodys glucose supply Consumers 25% of the bodys nutrients 100 Billion Neurons Facts that are given after figure 4: With matter is inside the brain and Gray matter is outside the brain Cerebral cortex is wrinkled. The grooves that make these wrinkles are called sulci and the ridges between them are called gyri Two hemispheres are connected by Corpus Callosum Facts that are given after figure 5: Brain has two main parts: cortex which has 4 parts: frontal, temporal, parietal and occipital lobe. and the other part is cerebellum After watching the videos, students will discuss their questions, any misconception that they might have about the brain and gained knowledge in small groups. The session will end by given pictures of brains structure and areas that students are required to name them. Session 3: Neuroplasticity In this session, the topic of neuroplasticity which is about the electrical and neural changes in the brain during learning will be thought. The lesson plan will be a brief explanation of neuroplasticity by summarizing some researches about this concept: Plasticity is one of the most essential functions of the human brain. According to Munte et al (2002) Neuroplasticity allows the brain to adapt to environmental factors that cannot be anticipated by genetic programming There are a vast majority of researchers that are interested in this topic and have been examining plasticity via different experiments both on animals and human. One of these researchers named Dr Norman Doidge who is author of The Brain that Changes Itself. In his book he talked about the brain as a modifiable, changeable, adaptable and plastic organism that is able to change its function and even structure without chemical reaction in the body, just based on our interaction with the brain. The interesting thing about the power of the brain is, its ability to change structurally even with imagination. Another discovery related to plasticity is the fact that learning changes the number of connection between neurons; even with hours of training the number of connection between two neurons can increase from 1300 to 2700 as an example. The reason how plasticity happen in our brain is: through activities and thoughts that people do with their brain, there are certain genes in nerve cells that become on and others off, this change causes producing protein and protein finally makes change in brain structure. This discovery made a strong proof for the role of learning and training in changing our brain and as a result changing our mind and behavior (Bush et al., 2004). People are able to change their behavior as a result of functional changing in their brain, for example depression is a severe disorder that causes 25% loose of gray matter in hippocampus. This is due to fact that chronic stress release cortisol which gradually weakens the role of left prefrontal cortex, a region that is known as a controller of negative emotion, and the weak activity of PFC causes 25% loose of gray matter in hippocampus. An experiment done in UK showed that the size and amount of gray matter would be the same again after 5 weeks of treatment in depressed people. Similarly, in article written by Draganski et al., (2004) the same finding was reported. Subjects of their experiments were d ivided into two groups: learner and non-learner. They scanned their subjects brain at the beginning of experiment and find that there is no difference between two groups. Then they taught the learner group how to juggle and when their subjects were professional enough to juggle in 1 minute, they had another FMRI scan for both group. For learners the amount of gray matter in the mid-temporal area and in the left posterior intraparietal was increased by 25% compared to non-learner and compared to the first scan. Finally they had third scan after 3 months without training for both group and they found that the amount of gray matter decreased again in learner group. Their finding was consistent with the finding about depression. Mà ¼nte et al., (2002) examined neuroplasticity in musicians that had begun their training in early age. They found musicians who began before the age of seven had a larger anterior midsagittal corpus callosum compared to others that started later. Therefore, they were able to have a bidirectional movement. In order to be able to control bidirectional movement, an enhanced interaction between two hemispheres is needed and since number of axons that can be transmitted to other hemisphere depends on size of midsagittal corpus callosum, therefore musicians with larger AMCC were able to have bidirectional movements. Elbert et al., (1995) showed that string players had a larger cortical representation of the digits finger in the left hand compared to non-musicians. They argued that even neuroplasticity was different among musicians depending on their interaction with music and their professional usage of music; for example a conductor is better in understanding non-adjacent and separatin g adjacent sound sources. Accordingly, there is an automatic movement in musicians body (fingers of hand or even leg) when they just listening to music and vice versa. This is because of co-activation of motor-audio regions in their brain. After this lecture, students will ask their questions (in case of any) and form small groups to share their ideas about neuroplasticity. During these sessions, students learned how their brain can be manipulated by practicing By the end of this session, knowledge creation about the brain will be ended. Therefore, in order to test the output of the sessions, they will be required to articulate their learning. They can either create an artifact (brain, neuron), or write a short essay related to neuroplasticity. As Chinn and Sherin (2005) mentioned one of the problem of team work would be more knowledgeable students will do the load of works and some students might be quiet and their learning process might be overestimated if they work in a group. To avoid this problem, each student is required to do articulation alone. They need to complete this task before last session. Understanding Goal: By the end of this session, students will understand that brains function and even structure can be changed. Session 4: Mindset Change This session consists of two parts. First part is the activity part in which students will discover more about brain and brain plasticity. This part is designed based on embodiment approach. Embodiment in a broad sense could be defined as the study of the subjective role of the body in making sense of life experiences (Kiverstein, 2012). In other words how our bodies influence and shape the way we speak, think, and behave with regard to environmental challenges we face in our daily lives (Gibbs, 2005). Following such a definition the idea of embodied cognition points out to the inter-connection of mind and body and how they both influence each other. Such an idea was raised as a counter-intuitive argument against the mind-body dualism proposed by Rene Descartes in the 17th century which supported a separation between human body and the external world in which body is completely divisible and mind is completely abstract and indivisible. However, this view was challenged by philosophers like Merleau-Ponty (1962) who viewed body as a primordial existence prior to the existence of a reflected world, and understanding of the external world as a reflection of the humans body. Pointing to the inter-relationship between body, environment, and peoples perception of the environment (i.e. the external world) Merleau-Ponty (1962; 235) writes that body is the fabric into which all objects are woven, and it is, at least in relation to the perceived world, the general instrument of comprehension (cited in Gibbs, 2005; p. ). Drawing from the definition of the embodiment, it can be concluded that acquiring and comprehending knowledge and solving problem are not solely manipulated in the brain. Conversely, it is influenced by the interaction we have with the external world and how our bodies manage to perceive them. According to Lakeoff and Johnson (1980) this relationship is highly represented in numerous metaphorical expressions in the language we use. For example we may say the something is beyond us when we cannot understand what a specific expression refers to. In this case we make a connection between our understanding of physical distance and mental concept of uncertainty in order to show how we feel about it. Using Lakeoff and Johnsons metaphorical representations, Barsalou (2008, p. 618) through exemplifying the act of sitting on a chair argues that embodied learning can take place through activating a perception-action-introspection complex. According to Barsalou (2008) this whole process is an i ntegrated and multimodal representation of current and past sensory experiences which results in comprehending an object. According to Abrahamson and Lindgren (2014)in order to place the embodiment theory in education there is need to have an embodied design in order for learners approach a problem in a subject matter through their natural body instinct and movements (p. 363). However, embodied designs could be challenged from three aspects of the types of activities, materials and artifacts, and facilitation of conceptual development. Accordingly they proposed that each of those challenges could be appropriately met through using initial simple activities which fall within the experiential domain of learners and then gradually move toward more symbolic one. Moreover, the types of materials and artifacts used to promote learning in such kinds of designs should be similar to ones found outside these designs and in unmediated environments. Finally, the movement and body engagement should be facilitated through providing real-time feedback by tutors and teachers to help learners develop their own conceptua l insights. Given this brief explanation of embodiment, students will participate in an activity that will result in understanding how their brain can be manipulated by practicing and how their intelligence could be increased through learning. During activity part, they will go through a Neural Network Maze spelling out the word SMARTER and saw how this network change when they learn something new. This activity is based on BNlackwell et al., (2007). In the second part students will see some examples of disabled people who were able to manage their disability and succeed in their life. The aim of this activity is showing students that even people who are suffering from major problems and lost their critical abilities (like walking) did not give up and challenge themselves to achieve their goals. An example of disabled people is Nicholas James Vujicic who is an Australian motivational speaker. He was born with tetra-amelia syndrome and has neither arms nor legs, but could graduate college with a bachelor degree in financing and is a successful writer. Understanding Goal: Everyone can be smart, because intelligence is not statistic and unchangeable Efforts is the most important factor in improving ability The way they think about their ability, can affect their behavior Session 5: Improving motivation by the help of feedback In the last session of workshop, students will summarize their learning and will explain how their misconceptions have changed (if changed) and the instructor will give each student the appropriate feedback. Depending on the number of students participated in this workshop, each student will have time to show their artifact or read their essay that was asked to complete it by the end of session 3. Instructor (experimenter) will give feedback for each students work because as we already know feedback is one type of reward and it can motivate students and even change extrinsic motivation to intrinsic motivation. Below is a summary of researches that support the effect of reward in increasing students motivation and their performance Harackiewicz (1979) was concerned about relation between feedback, motivation and the outcome and examined this relation among high school students. He found positive feedback increase motivation and motivation increase performance. However he claimed that positive feedback on the performance has different effect compared to reward effect. Positive feedback which is assessed as verbal rewards is known as an unexpected, competence improvement reward and has a significant positive influence on intrinsic motivation. In two studies that used positive feedback as a motivational resource, they tested how a slightly change in wording can bring a fundamental change in the motivation. In the first study, Ryan (1982) used a controlling feedback by saying: Excellent, you should keep up the good work, whereas in the other study, Pittman et al. (1980) used an informational feedback: Compared to most of my subjects, you are doing really well. The result of these two studies was in line with the claim; in the first statement subjects had less intrinsic motivation after few trials compared to second informational feedback. In conclusion, positive feedback can bring interest for receivers and will increase intrinsic motivation. ODohetry (2004) wrote an excellent review about the underlying mechanism of reward seeking and punishment avoidance in human behaviors. He discussed recent neuroimaging findings which gives insight into the reward representations and reward-related learning process that take place in the human brain. The author highlighted the involvement of ventromedial prefrontal cortex, amygdala, striatum, and dopaminergic midbrain in the reward-related learning process. Providing evidence from human neuroimaging, the author argues that specific reward-induced behaviors are subject to the function of different parts of the aforementioned network. However, no matter which component guides which specific reward-related behavior, the persistence of behavior is dependent on the value assigned to the reward and perhaps the punishment within this network. The importance of the findings reported in this paper is connecting them with goal-directed behavior which requires complex cognitive resources and fu nctionalities. In other words, the complexities involved in choosing between various behaviors and actions are based on evaluation of their representation of the predicted future rewards with the selected action having the highest predicted reward which varies depending on the its quality, frequency and variance in specific situations. As stated in the article, there are three main parts of the brain that is responsible for guiding our action. Therefore, our behavior is formed controlled as a response to a value of reward or punishment. The author also made a distinction between these parts and the role of each part in seeking the reward, evaluating the value of reward or punishment, predicting the future reward/punishment and deciding about a proper action based on the prediction of value. As a result becoming motivated in doing an action depends on the value of reward or punishment as well as its amount that is aligned with that action even in future. Our brain and even animals br ain is able to learn how to guide our action to receive rewards. It means, our brain tracks and analyses the process of gaining a reward for future use just like the classical conditioning situation. Better reward causes more motivation (ODohetry, 2004). Understanding Goal: By putting enough efforts, students can increase their performance on school Reference: Abrahamson, D., Lindgren, R. (2014). Embodiment and embodied design. In R. K. Sawyer (ed.)The Cambridge handbook of the learning sciences, pp. 358-376. Barsalou, L. W. (2008). Grounded cognition. Annual Review of Psychology, 59, 617-645. Blackwell, L. S., Trzesniewski, K. H., Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child development, 78(1), 246-263. Busch, V., Schuierer, G., Bogdahn, U., May, A. (2004). Changes in grey matter induced by training. Nature, 311-312. Doidge, N. (2007). The brain that changes itself: Stories of personal triumph from the frontiers of brain science. Penguin. Draganski, B., Gaser, C., Busch, V., Schuierer, G., Bogdahn, U., May, A. (2004, January 22). Changes in grey matter induced by training. Nature, pp. 247: 311-312. Elbert, T., Pantev, C., Wienbruch, C., Rockstroh, B., Taub, E. (1995). Increased cortical representation of the fingers of the left hand in string players. Science, 270(5234), 305. Galvà ¡n, A. (2010). Neural plasticity of development and learning. Human Brain Mapping, 31(6), 879-90. doi:10.1002/hbm.21029 Gibbs Jr, R. W. (2005). Embodiment and cognitive science. Cambridge University Press. Harackiewicz, J. M. (1979). The effects of reward contingency and performance feedback on intrinsic motivation. Journal of Personality and Social Psychology,37(8), 1352. Kiverstein, J. (2012). The meaning of embodiment. Topics in cognitive science, 4(4), 740-758. Lakoff, G., Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press. Merleau-Ponty, M. (1962). Phenomenology of perception. London: Routledge Kegan Paul. Mà ¼nte, T. F., Altenmà ¼ller, E., Jà ¤ncke, L. (2002). The musicians brain as a model of neuroplasticity. Nature Reviews. Neuroscience, 3(6), 473-8. doi:10.1038/nrn843 ODoherty, J. P. (2004). Reward representations and reward-related learning in the human brain: insights from neuroimaging. Current opinion in neurobiology,14(6), 769-776. Pittman, T. S., Davey, M. E., Alafat, K. A., Wetherill, K. V., Kramer, N. A. (1980). Informational versus controlling verbal rewards. Personality and Social Psychology Bulletin, 6(2), 228-233. Ryan, R. M. (1982). Control and information in the intrapersonal sphere: An extension of cognitive evaluation theory. Journal of personality and social psychology, 43(3), 450. Sawyer, R. K. (Ed.). (2005). The Cambridge handbook of the learning sciences. Cambridge University Press.

Makkah

Considered as perhaps one of the holiest cities in the whole world, Makkah or Mecca, is located in the historic Hejaz region of Saudi Arabia (Crone 231).   With a population of nearly two million (1,700,000 to be exact), this region is deeply revered by Muslims because it contains the Grand Mosque of Mecca.   From an etymological perspective, the word mecca means a location that is considered as the center of interest or a goal which religious adherents aspire for (Lapidus 43).   This is synonymous with the religious devotion that is associated with the area. One of the major events that occur in this area is the annual pilgrimage to Makkah which happens during the season of the Hajj.   This is very important for every Muslim since it is covered under the Five Pillars of Islam (Lapidus 43).   Given this relevance, every able bodied Muslim who has the means to must visit Mecca at least once in their lifetime.   This is a very strict rule (Lapidus 43).   During this time, nobody else is allowed to enter the holy city especially people belonging to other faiths. Historically, the Mecca has always been considered as one of the most important cities in the Arabian Peninsula (Crone 231).   Since the 6th century, it has always been the wealthiest of all the settlements in the area (Crone 231).   Due to the abundant water supply that it got from the Zamzam Well, Mecca soon grew in prosperity and became the site of the Kaaba, the holiest site in all of Islam (Crone 231).   Given this ideal location, it comes as no surprise then that this soon became one of the holiest areas in the world. The sacred mosque or the Al-Masjid al-Haram is the largest mosque in the entire world.   Its location in the city of Mecca is only appropriate given the fact that it surrounds what is the holiest place in the entire Islam, the Kaaba (Lapidus 43).   Also known as Haram or Haram Sharif, the mosque is capable of accommodating over four million (4,000,000) people during the great pilgrimage or the Hajj (Lapidus 43).   It covers a floor area of approximately three hundred and fifty-six thousand eight hundred (356,800) square meters. The Kaaba, is a large cubical shaped building that is currently surrounded by the Masjid al-Haram, which is the largest mosque in the world.   According to Islamic lore, the Kaaba was formerly the site where Abraham (Ibrahim) erected the Bait-ul-Allah (House of Allah) at the site of the well (Lapidus 43).   This was in turn supposedly created by Adam.   Currently, the Kaaba is the site for most of the religious practices of the Muslims.   During the Hajj, the Kaaba is the center of the ritual circumambulation that is practiced by Muslims.   It is also used during the Umrah or the lesser pilgrimage (Lapidus 43).   This is also the same direction that Muslims pray towards during prayer. The Well of Zamzam is located about twenty (20) meters away from the Kaaba (Hawting 47).   It was said that this was the site where the wife of the Prophet Ibrahim found water for her infant son (Hawting 44).   According to legend, the well was dug up by angel Jibril (Gabriel) who caused the spring to appear.   The name Zamzam comes from the phrase Zomà « Zomà « which literally means â€Å"stop flowing† in relation to the command that Hajar tried to issue to stop the spring water from flowing (Hawting 51).   This was also the site where tribes would frequent during their pilgrimage in order to settle disputes and settle debts as well as for other religious reasons (Hawting 47). Aside from the historical considerations, the religious ties that are connected to the holiest place in Islam, the Kaaba, make it the center of any Muslims faith.   The fact that the five pillars also require Muslims to visit this place makes it equally important for every Muslim to endeavor to visit this place at least once in their entire lifetime.   This is the reason why millions of Muslims make this pilgrimage every year. Works Cited: Crone, Patricia (1987). Meccan Trade and the Rise of Islam. Princeton University Press. Hawting, G. R. (1980). â€Å"The Disappearance and Rediscovery of Zamzam and the ‘Well of the Ka'ba'†. ‘Bulletin of the School of Oriental and African Studies, University of London 43 (1): 44-54. Lapidus, Ira M. (1988). A History of Islamic Societies. Cambridge University Press. ISBN 0 521 22552 5. Mecca IPA: /ˈmÉ›kÉ™/ or Makkah IPA: [ˈmà ¦kÉ™] (in full: Makkah Al-Mukarramah IPA: [(Arabic) mà ¦kË Ãƒ ¦(t) à ¦lmÊŠkarË‘amà ¦]; Arabic: Ù…ÙÆ'Ù‘Ø © Ø §Ã™â€žÃ™â€¦Ã™Æ'Ø ±Ã™â€¦Ã˜ ©Ã¢â‚¬Å½) is an Islamic holy city in Saudi Arabia's Makkah Province, in the historic Hejaz region. It has a population of 1,700,000 (2008 census). The city is located 73  kilometres (45  miles) inland from Jeddah, in a narrow valley, 277  metres (910  ft) above sea level. It is located 80  kilometres (50  miles) from the Red Sea. Historically, the city has also been called Becca[1][2]. The city is revered by Muslims for containing the holiest site of Islam, the Grand Mosque of Mecca. A pilgrimage to Mecca during the season of the Hajj is one of the Five Pillars of Islam, a sacred duty that is required of all able-bodied Muslims who can afford to go, at least once in their lifetime. People of other faiths are forbidden from entering the city. The English word mecca (uncapitalized), meaning â€Å"A place that is regarded as the center of an activity or interest† or â€Å"A goal to which adherents of a religious faith or practice fervently aspire.† [3] is borrowed from Mecca   

Sex Education in the School

In today's society there is an on going debate over sex education and its influence on our children. â€Å"The question is no longer should sex education be taught, but rather how it should be taught† (DeCarlo). With teenage pregnancy rates higher than ever and the imminent threat of the contraction of STD's, such as HIV, the role of sex education in the school is of greater importance now then ever before. By denying children sex education you are in a sense sheltering them from the harsh realities they are bound to encounter. Sex education has become an essential part of the curriculum and by removing the information provided by this class we'll be voluntarily putting our children in danger. During the teenage years every boy and girl undergo major changes in the body that most of the time need explaining. This underscores one of the most evident reasons for sexual education being taught to students. Sex education can help children to cope with the many changes caused by the onset of puberty. One such example is a female's first menstruation and the uneasiness they feel. If this girl had been informed of this change prior to its onset, then her ability to accept and understand it would be greatly enhanced. Hormonal and physical changes in the body begin without warning and a child needs to know why these changes are occurring. Students are taught about the anatomy of the human body and how and why it works the way it does. Knowing and understanding how ones body works is a fundamental part any persons life and ability to gain this knowledge should not be removed. At the beginning of puberty hormones start rushing and all teenagers begin to experience sexual urges. It's not something anyone, including a parent or teacher, can control. It's a natural function of the body and has been since the beginning of time. With this hormone rush comes experimentation among teenagers. They begin to explore their bodies along with the bodies of other people. â€Å"You can't prevent teenagers from having sex, no matter what you preach. If students are having sex they might as well do it the safe way. It's a way for schools to show that they actually care,† says Shauna Ling-Choung (qt. Richardson â€Å"When sex_† B1). Students need the support from schools to know they have somewhere to go for the good or bad. With sex education classes the students are taught about various methods of contraception, including abstinence. By teaching the students about the many types of contraception, the chance of contraceptives being used is greatly increased. Many schools have recently begun programs to distribute condoms to students in their schools in order to hopefully increase the use of condoms. A recent study shows that the availability of condoms in schools did in fact increase condom use. Condom access is a â€Å"low-cost harmless addition† to our current sex education programs (Richardson â€Å"Condoms in_† B8). When thinking of sex education for our children, the cliche‚ â€Å"better safe than sorry† should immediately come to mind. Along with teaching contraceptives to students the vital information of STD's are also taught. Currently, out of all age groups, teenagers have the highest rates of sexually transmitted diseases, with one in four young people contracting and STD by the age of twenty-one (DeCarlo). Included in the STD category is the HIV virus, which is spreading at alarming rates among our teenage population. It is believed that at least twenty percent of new patients with AIDS were infected during their teenage or early adult years. † And still some school leaders are trying to remove our best means of prevention of the disease: sex education (Roye 581) Teachers are able to educate students with the correct information on the many types of sexually transmitted diseases that exist in the world today. False information about ways of contracting diseases, symptoms of and treatments of STDs, and preventative measures are weeded out and students receive the accurate information about sexually transmitted diseases. Protection of our children from sexually transmitted diseases should start in the classroom where it can be assured that the correct and critical information will be provided to them. Nobody likes to be talked to like they are a child, and by denying teenagers sexual education, schools are in a sense talking down to them. By teaching them the facts about sex, teenagers feel a sense of maturity because it's a mature topic and they are fully aware of that. Students get the feeling that the adults in their lives feel that they are responsible enough to learn about this topic. Therefore bringing on more of a response from teenagers. They know they are being treated as adults so they are going to pay attention to what they are being taught and then act as adults and carry out what they were taught. Teenagers appreciate when adults treat them as equals, and anyone will see that children will always respond better to this than to being treated as a Much of the typical family structure in the United States and many other places in the world have deteriorated over the last century. A good portion of parents today are divorced and many of the families that haven't experienced divorce live with both parents working full time jobs. Families today aren't like the family on â€Å"Leave It to Beaver,† a sitcom that aired in the sixties; the mother isn't home all day baking and making sure that the house is clean. Since family structure has changed, so have the way children are being raised. Society cannot count on all parents to instill morals into their children and teach them the facts of life or even the difference between right and wrong these days. Parents just don't have the time for it. Recently the Vatican released a document stating that † parents alone cannot give children the positive sex education they need to develop healthy attitudes towards sex† (Euchner). Another view on the subject taken by the Nebraska Public School system is that sex education in today's society is to complicated to be left to â€Å"the varying influences of parental attitudes and haphazard environmental exposure† (Chaumont et al. ). Besides, even if the parent were around more often then not, the chances of a child approaching their parent about the â€Å"bird and the bees† is very unlikely. These children need to have a place were the information on this touchy subject is provided to them without them needing to ask. â€Å"Kids don't go asking their parents, this is the only way for them to find out answers because they are to embarrassed to ask anyone else,† says Pallodino, and eighteen-year-old from Virginia. (O'Hanlon B8). In order for children to grow up with the correct information regarding sex, it is necessary to have sex education provided to them in schools. Even though sex education seems as if it can do no wrong, there still remain many opponents, including many authors who clearly express their view, that are still against it in our schools. There are many reasons why people feel like this, two of which are they feel as if sex education does no good at all and another is that people feel that it is influencing students to have sex. Ellen Hopkins, author of â€Å"Sex is for Adults†, says that sex education does many great things , except for the one thing we want it to do, make our children more responsible. (Hopkins 589). She feels as though the information that students are receiving is not having any influence on them. The feeling that sex education classes are influencing teenagers to have sex is a feeling that is shared by William Kilpatrick. He states that â€Å"as the statistics show, American teenagers are living up to expectation. They are having more sex and using more condoms† (Kilpatrick 597). These two individuals, along with many others, feel that sex education is doing more harm then it is good. Teenage sexual activity has been raising steadily for more than two decades until now. A recent survey shows the first drop since the nineteen seventies. In 1990 girls that had engaged in sexual intercourse was at fifty-five percent, until 1995 when it dropped to fifty percent. The percentage of boys engaging in sexual intercourse also dropped by five percent. The use of condoms have tripled since the 1970's showing people are being safer about sex (Vobejda et al. A1). A poll done by Reuter's show that eighty-two percent of the people who participated in the survey supported sex education in schools (Yahoo). Studies obviously show that sex education courses are helping today's teenagers to become more responsible for their own actions. The information that sex education provides teenagers is indispensable. Schools are meant to educate our children in not just one topic but all topics. â€Å"Why would anyone on the state Board of Education not want to cover something comprehensively? Do we take that approach with history or math? † says Denice Bruce of Wichita, Kansas (Associated Press). Sexually educating our children is just important if not more important than math or history because sex education can mean the difference between life and death of your child.

Complete Guide to Fractions and Ratios in ACT Math

Complete Guide to Fractions and Ratios in ACT Math SAT / ACT Prep Online Guides and Tips Fractions and ratios (and by extension rational numbers) are all around us and, knowingly or not, we use them every day. If you wanted to brag over the fact that you ate half a pizza by yourself (and why not?) or you needed to know how many parts water to rice you need when making rice on the stove (two parts water to one part rice), then you need to communicate this using fractions and ratios. In essence, fractions and ratios represent pieces of a whole by comparing those pieces either to each other or to the whole itself. Don’t worry if that sentence makes no sense right now. We’ll break down all the rules and workings of these concepts throughout this guideboth how these mathematical concepts work in general and how they will be presented to you on the ACT. Whether you are an old hat at dealing with fractions, ratios, and rationals, or a novice, this guide is for you. This guide will break down what these terms mean, how to manipulate these kinds of problems, and how to answer the most difficult fraction, ratio, and rational number questions on the ACT. What are Fractions? $${\a\piece}/{\the\whole}$$ Fractions are pieces of a whole. They are expressed as the amount you have (the numerator) over the whole (the denominator). Amy’s cat gave birth to 8 kittens. 5 of the kittens had stripes and 3 had spots. What fraction of the litter had stripes? $5/8$ of the litter had stripes. 5 is the numerator (top number) because that was the amount of striped kittens, and 8 is the denominator (bottom number) because there are 8 kittens total in the litter (the whole). Kitten math is the best kind of math. Special Fractions There are several different kinds of "special fractions" that you must know in order to solve the more complex fraction problems. Let us go through each of these: A number over itself equals 1 $6/6 = 1$ $47/47 = 1$ ${xy}/{xy} = 1$ A whole number can be expressed as itself over 1 $17 = 17/1$ $108 = 108/1$ $xy = {xy}/1$ 0 divided by any number is 0 $0/0 = 0$ $0/5 = 0$ $0/{xy} = 0$ Any number divided by 0 is undefined Zero cannot act as a denominator. For more information on this check out our guide to advanced integers. But, for now, all that matters is that you know that 0 cannot act as a denominator. Now let's find out how to manipulate fractions until we unlock the answers we want. Reducing Fractions If you have a fraction in which both the numerator and the denominator can be divided by the same number (called a â€Å"common factor†), then the fraction can be reduced. Most of the time, your final answer will be presented in its most reduced form. In order to reduce a fraction, you must find the common factor between each piece of the fraction and divide both the numerator and the denominator by that same amount. By dividing both the numerator and the denominator by the same number, you are able to maintain the proper relationship between each piece of your fraction. So if your fraction is $5/25$, then it can be written as $1/5$. Why? Because both 5 and 25 are divisible by 5. $5/5 = 1$ And $25/5 = 5$. So your final fraction is $1/5$. Adding or Subtracting Fractions You can add or subtract fractions as long as their denominators are the same. To do so, you keep the denominator consistent and simply add the numerators. $2/ + 6/ = 8/$ But you CANNOT add or subtract fractions if your denominators are unequal. $2/ + 4/5 = ?$ So what can you do when your denominators are unequal? You must make them equal by finding a common multiple (number they can both multiply evenly into) of their denominators. $2/ + 4/5$ Here, a common multiple (a number they can both be multiplied evenly into) of the two denominators 5 is 55. To convert the fraction, you must multiply both the numerator and the denominator by the amount the denominator took to achieve the new denominator (the common multiple). Why multiply both? Just like when we reduced fractions and had to divide the numerator and denominator by the same amount, now we must multiply the numerator and denominator by the same amount. This process keeps the fraction (the relationship between numerator and denominator) consistent. To get to the common denominator of 55, $2/$ must be multiplied by $5/5$. Why? Because $ * 5 = 55$. $(2/)(5/5) = 10/55$. To get to the common denominator of 55, $4/5$ must be multiplied by $/$. Why? Because $5 * = 55$. $(4/5)(/) = 44/55$. Now we can add them, as they have the same denominator. $10/55 + 44/55 = 54/55$ We cannot reduce $54/55$ any further as the two numbers do not share a common factor. So our final answer is $54/55$. Here, we are not being asked to actually add the fractions, just to find the least common denominator so that we could add the fractions. Because we are being asked to find the least amount of something, we should start at the smallest number and work our way down (for more on using answer choices to help solve your problem in the quickest and easiest way, check out our article on plugging in answers). Answer choice A is eliminated, as 40 is not evenly divisible by 12. 120 is evenly divisible by 8, 12, and 15, so it is our least common denominator. So our final answer is B, 120. Multiplying Fractions Luckily it is much simpler to multiply fractions than it is to add or divide them. There is no need to find a common denominator when multiplyingyou can just multiply the fractions straight across. To multiply a fraction, first multiply the numerators. This product becomes your new numerator. Next, multiply your two denominators. This product becomes your new denominator. $2/3 * 3/4 = (2 * 3)/(3 * 4) = 6/12$ And again, we reduce our fraction. Both the numerator and the denominator are divisible by 6, so our final answer becomes: $1/2$ Special note: you can speed up the multiplication and reduction process by finding a common factor of your cross multiples before you multiply. $2/3 * 3/4$ = $1/1 * 1/2$ = $1/2$. Both 3’s are multiples of 3, so we can replace them with 1 ($3/3 = 1$). Our other cross multiples are 2 and 4, which are both multiples of 2, so we were able to replace them with 1 and 2, respectively ($2/2 = 1$ and $4/2 = 2$). Because our cross multiples had factors in common, we were able to reduce the cross multiples before we even began. This saved us time in reducing the final fraction at the end. Take note that we can only reduce cross multiples when multiplying fractions, never while adding or subtracting them! It is also a completely optional step, so do not feel obligated to reduce your cross multiplesyou can always simply reduce your fraction at the end. Dividing Fractions In order to divide fractions, we must first take the reciprocal (the reversal) of one of the fractions. Afterwards, we simply multiply the two fractions together as normal. Why do we do this? Because division is the opposite of multiplication, so we must reverse one of the fractions to turn it back into a multiplication question. ${1/3} à · {3/8} = {1/3} * {8/3}$ (we took the reciprocal of $3/8$, which means we flipped the fraction upside down to become $8/3$) ${1/3} * {8/3} = 8/9$ Now that we've seen how to solve a fraction problem the long way, let's talk short cuts. Decimal Points Because fractions are pieces of a whole, you can also express fractions as either a decimal point or a percentage. To convert a fraction into a decimal, simply divide the numerator by the denominator. (The $/$ symbol also acts as a division sign) $3/10 = 3 + 10 = 0.3$ Sometimes it is easier to convert a fraction to a decimal in order to work through a problem. This can save you time and effort trying to figure out how to divide or multiply fractions. This is a perfect example of a time when it might be easier to work with decimals than with fractions. We’ll go through this problem both ways. Fastest waywith decimals: Simply find the decimal form for each fraction and then compare their sizes. To find the decimals, divide the numerator by the denominator. $5/3 = 1.667$ $7/4 = 1.75$ $6/5 = 1.2$ $9/8 = 1.125$ We can clearly see which fractions are smaller and larger now that they are in decimal form. In ascending order, they would be: $1.125, 1.2, 1.667, 1.75$ Which, when converted back to their fraction form, is: $9/8, 6/5, 5/3, 7/4$ So our final answer is A. Slower waywith fractions: Alternatively, we could compare the fractions by finding a common denominator of each fraction and then comparing the sizes of their numerators. Our denominators are: 3, 4, 5, 8. We know that there are no multiples of 4 or 8 that end in an odd number (because an even number * an even number = an even number), so a common denominator for all must end in 0. (Why? Because all multiples of 5 end in 0 or 5.) Multiples of 8 that end in 0 are also multiples of 40 (because $8 * 5 = 40$). 40 is not divisible by 3 and neither is 80, but 120 is. 120 is divisible by all four digits, so it is a common denominator. Now we must find out how many times each denominator must be multiplied to equal 120. That number will then be the amount to which we multiply the numerator in order to keep the fraction consistent. $120/3 = 40$ $5/3$ = ${5(40)}/{3(40)}$ = $200/120$ $120/4 = 30$ $7/4$ = ${7(30)}/{4(30)}$= $210/120$ $120/5 = 24$ $6/5$ = ${6(24)}/{5(24)}$= $144/120$ $120/8 = 15$ $9/8$ = ${9(15)}/{8(15)}$= $135/120$ Now that they all share a common denominator, we can simply look to the size of their numerators and compare the smallest and the largest. So the order of the fractions from least to greatest would be: $135/120, 144/120, 200/120, 210/120$ Which, when converted back into their original fractions, is: $9/8, 6/5, 5/3, 7/4$ So once again, our final answer is A. As you can see, we were able to solve the problem using either fractions or decimals. How you chose to approach these types of problems is completely up to you and depends on how you work best, as well as your time management strategies. Percentages After you convert your fraction to a decimal, you can also turn it into a percentage (if the need arises). To get a percentage, multiply your decimal point by 100. So 0.3 can also be written as 30%, because $0.3 * 100 = 30$. 0.01 can be written as 1% because $0.01 * 100 = 1$, etc. Be mindful of your decimals and percentages and don't mix them up! 0.1 is NOTthe same thing as 0.1%. Mixed Fractions Sometimes you may be given a mixed fraction on the ACT. A mixed fraction is a combination of a whole number and a fraction. For example, $5{1/3}$ is a mixed fraction. We have a whole number, 5, and a fraction, $1/3$. You can turn a mixed fraction into an ordinary fraction by multiplying the whole number by the denominator and then adding that product to the numerator. The final answer will be ${\the \new \numerator}/{\the \original \denominator}$. $5{1/3}$ $(5)(3) = 15$ $15 + 1 = 16$ So your final answer = $16/3$ You must convert mixed fractions into non-mixed fractions in order to multiply, divide, add, or subtract them with other fractions. A cobbler charges a flat fee of 45 dollars plus 75 dollars per hour to make a pair of shoes. How many hours of labor was spent making the shoes if the total bill was $320? $3{2/15}$ $3{2/3}$ $4$ $4{4/15}$ $4{1/3}$ If the total bill was 320 dollars and the flat fee was 45 dollars, we must subtract the flat fee from the total bill in order to find the number of hours the cobbler worked. $320 - 45 = 275$ So the cobbler worked 275 dollars’ worth of hours. In order to find out how many hours that is, we must divide the earnings by the hourly fee. $275/75 = 3{50/75}$ 75 was able to go evenly into 225, leaving 50 out of 75 left over. Because 50 and 75 share a common denominator of 25, we can reduce $3{50/75}$ to: $3{2/3}$ So our final answer is B, $3{2/3}$ Now that we've broken down all there is to knowabout ACT fractions, let's take a look attheir close cousinthe ratio. What are Ratios? Ratios are used as a way to compare one thing to another (or multiple things to one another). If Piotr has exactly 2 grey scarves and 7 red scarves in a drawer, the ratio of grey scarves to red scarves is 2 to 7. Expressing Ratios Ratios can be written in three different ways: $A \to B$ $A:B$ $A/B$ No matter which way you write them, these are all ratios comparing A to B. Most all chemical molecules are namedfor their ratios. Here, one of our products iscarbon dioxide (one part carbon, two parts oxygen). Different Types of Ratios Just as a fraction represents a part of something out of a whole (written as: ${\a \part}/{\the \whole}$), a ratio can be expressed as either: ${\a \part}:{\a \different \part}$ OR $\a \part:\the \whole$ Ratios compare values, so they can either compare individual pieces to one another or an individual piece to the whole. If Piotr has exactly 2 grey scarves and 7 red scarves in a drawer, the ratio of grey scarves to all the scarves in the drawer is 2 to 9. (Why 9? Because there are 2 grey and 7 red scarves, so together they make $2 + 7 = 9$ scarves total.) Reducing Ratios Just as fractions can be reduced, so too can ratios. Danielle collects toy racecars. 12 of them are blue and 4 of them are yellow. What is the ratio of of blue cars to yellow cars in her collection? Right now, the ratio is $12:4$. But they have a common denominator of 4, so this ratio can be reduced. $12/4 = 3$ $4/4 = 1$ So the carshave a ratio of $3:2$ Increasing Ratios Because you can reduce ratios, you can also do the opposite and increase them. In order to do so, you must multiply each piece of the ratio by the same amount (just as you had to divide by the same amount on each side to reduce the ratio). So the ratio of $3:2$ can also be $3(2):2(2) = 6:4$ $3(3):2(3) = 9:6$ $3(4):2(4) = 12:8$ And so on. Though this presents itself as a geometry problem, we don’t need to know any geometry in order to solve itwe only need to know about ratios. We have two triangles in a ratio of 2:5 and the smaller triangle has a hypotenuse of 5 inches. This means that we need to increase each side of the ratio by the amount it takes 2 to go into 5. $5/2 = 2.5$ So we must increase each side of the ratio by a matter of 2.5 $2(2.5):5(2.5)$ $5:12.5$ Our new, increased ratio is 5:12.5, which means that the larger hypotenuse is 12.5. Our final answer is K. Expand ratios, reduce themgo wild! Finding the Whole If you are given a ratio comparing two parts ($\piece:\another \piece$), and you are told to find the whole amount, simply add all the pieces together. It may help you to think of this like an algebra problem wherein each side of the ratio is a certain multiple of x. Because each side of the ratio must always be divided or multiplied by the same amount to keep the ratio consistent, we can think of each side as having the same variable attached to it. For example, a ratio of $6:7$ can be: $6(1):7(1) = 6:7$ $6(2):7(2) = 12:14$ And so on, just as we did above. But this means we could also represent $6:7$ as: $6x:7x$ Why? Because each side must change at the same rate. And in this case, our rate is $x$. So if you were asked to find the total amount, you would add the pieces together. $6x + 7x = 13x$. The total amount is $13x$. In this case, we don’t have any more information, but we know that the total MUST beeither 13 or any number divisible by 13. So let’s take a look at another problem. Clarissa has a jewelry box with necklaces and bracelets. The necklaces and bracelets are in a ratio of 4:3. What is NOT a possible number of total pieces of jewelry Clarissa can have in the box? 12 28 84 2 140 In order to find out how many pieces of jewelry she may have total, we must add the two pieces of our ratio together. So $4x + 3x = 7x$ This means that the total number of jewelry items in the box has to either be 7 or any multiple of 7. Why? Because $4:3$ is the most reduced form of the ratio of jewelry items in the box. This means she could have: $4(1):3(1) = 7$ jewels in the box (7 jewelry pieces total) $4(2):3(2) = 8:6$ jewels in the box (14 jewelry pieces total) $4(3):3(3) = 12:9$ jewels in the box (21 jewelry pieces total) And so forth. We don’t know exactly how many jewelry items she has, but we know that it must be a multiple of 7. This means our answer is A, 12. There is no possible way that she can have 12 jewels in the box, because 12 is not a multiple of 7 and one cannot have half a bracelet (unless something has gone terribly wrong). You may also be asked to find the number of individual pieces in your ratio after you are given the whole. This is exactly the opposite of what we did above. The is the exact same process as finding the whole, but in reverse. We know we must add the pieces of our ratio to find our multiple of 30. And we also know our ratio is $2:3$. So let us add these together. $2x + 3x = 5x$ Together, our ratio components add up to $5x$. And there are 30 feet total. So: $30/5 = 6$ $x = 6$ This means that we must multiply each side of our ratio by 6 in order to get the exact amount of wood used. This means that each piece is: $2(6):3(6)$ $12:18$ Which means our shorter piece is 12 feet long. Our final answer is H, 12. And now we come to rational and irrational numbers. Rational and Irrational Numbers A rational number is any number that can be written as a fraction of two integers (where the denominator does NOT equal to 0). All other numbers are considered irrational. Rational Numbers: $7/2, 5, 1/212, 0.66666667$ Why is 5 a rational number? Because it can be expressed as the fraction $5/1$. Why is 0.6666667 a rational number? Because it can be expressed as the fraction $2/3$ Irrational Numbers: $Ï€, √2, √3$ Why is $Ï€$ irrational? Because there is no fraction of two integers that can properly express it (through 22/7 comes awfully close). (Hint: if the decimals continue on forever without repeating, the number is irrational) Here, we are being asked to find the single rational number. Even if you didn’t know what a rational number meant, you might be able to figure this problem out just by finding the answer choice that stands out the most. But since you DO know what rational and irrational numbers are, it makes the problem even easier. Many square roots are irrational (unless they are roots of perfect squares like $√16 = 4$). We can immediately eliminate answer choices A, B, and C, as they are not perfect squares and so are irrational. We can also eliminate answer choice D. When we reduce the fraction, we get $√{1/5}$, and this would also get us an irrational number. This leaves us with answer choice E. We can see that both the numerator and the denominator of the fraction $64/49$ inside the square root sign are perfect squares. Since the fraction is under the root sign, let us take the square root of each of these. So our final fraction would look like: $√{64/49}$ = $8/7$ Because our final fraction is represented as a fraction with two integers, this is a rational number. So our final answer is E. So let's break down how to solve these kinds of questions when they show up on the test. How to Solve Fraction, Ratio, and Rational Number Questions When you are presented with a fraction or ratio problem, take note of these steps to find your solution: 1) Identify whether the problem involves fractions or ratios A fraction will involve the comparison of a $\piece/\whole$. A ratio will almost always involve the comparison of a $\piece:\piece$ (or, very rarely, a $\piece:\whole$). You can tell when the problem is ratio specific as the question text will do one of three things: Use the : symbol, Use the phrase â€Å"___ to ___† Explicitly use the word â€Å"ratio† in the text. If the questions wants you to give an answer as a ratio comparing two pieces, make sure you don’t confuse it with a fraction comparing a piece to the whole! 2) If a ratio question asks you to change or identify values, first find the sum of your pieces In order to determine your total amount (or the non-reduced amount of your individual pieces), you must add all the parts of your ratio together. This sum will either be your complete whole or will be a factor of your whole, if your ratio has been reduced. 3) When in doubt try to use decimals Decimals can make it much easier to work out problems rather than using fractions. So do not be afraid to convert your fractions into decimals to get through a problem more quickly and easily. 4) Remember your special fractions Always remember that a number over 1 is the same thing as the original number, and that when you have a number over itself, it equals 1. Get ready, get set...GO! Test Your Knowledge 1) 2) 3) 4) How many irrational numbers are there between 1 and 8? Fewer than 3 3 6 7 More than 7 Answers: B, J, D, E Answer Explanations: 1) For this problem, we must combine our like terms in order to eventually isolate $k$ (for more on this, check out our guide to ACT single variable equations). We know that, when adding fractions, we must give them the same denominator, so we can manipulateour fractions to have matching denominators and solvefrom there. Alternatively, we could again use decimal points instead of fractions. We will go through both ways here. Method 1Fractions We have ${1/3}k$ and ${1/4}k$ that we must add. They share a common multiple of 12, so let us convert them to fractions out of 12. $1/3$ = ${1(4)}/{3(4)}$ = $4/12$ $1/4$ = ${1(3)}/{4(3)}$ = $3/12$ Now that they have the same numerator, we can combine them to be: $4/12 + 3/12 = 7/12$ So our equation is: ${7/12}k = 1$ Now we must divide both sides by $7/12$, which means that we must inverse and multiply. $k = 1(12/7)$ $k = 12/7$ So our final answer is B. Method 2Decimals Instead of using and converting fractions, we also could have used decimals instead. $1/3$ = $0.333$ $1/4$ = $0.25$ Because they are decimals, we can simply add them together to be: $0.333k + 0.25k = 0.583k$ $0.58k = 1$ $k = 1/0.583$ $k = 1.715$ Now, simply convert the answer choices to decimals tofind one that matches. In this case answer choice A would be far too small, and answers D and E are whole numbers, so they can all be eliminated. Answer choice C would be $7/2 = 3.5$. This leaves us with answer choice B: $12/7 = 1.714$ So our final answer is, again, B. 2) This question specifically asks for a rational number answer, but it is a bit deceptive, as a quick glance shows us that all the answer choices are rational numbers. This means you can ignore this stipulation for the time being. Again, we can solve this problem in one of two waysvia fractions or via decimals. We will go through both methods. Method 1Fractions We are trying to find a rational fraction halfway between $1/5$ and $1/3$, so let us convert them into fractions with the same denominator. A common multiple of 3 and 5 is 15, so let us make that their new denominator. $1/5$ = ${1(3)}/{5(3)}$ = $3/15$ $1/3$ =${1(5)}/{3(5)}$ = $5/15$ Well the rational number exactly halfway between $3/15$ and $5/15$ is $4/15$. So our answer is J, $4/15$. Method 2Decimals Again, if fractions aren't your favorite, you can always feel free to use decimals. First, convert $1/5$ and $1/3$ into decimals. $1/5 = 0.2$ $1/3 = 0.333$ Now, find the decimal halfway between them: ${0.2 + 0.333}/2 = 0.2665$ (For more on this process, check out our guide to ACT mean, median, and mode) Now, let us find the answer choice that, when converted into a decimal, matches our answer. If you know your decimals, then you know that $1/2 = 0.5$ and $1/4 = 0.25$, so these can be eliminated. We are now left with $2/15$, $4/15$, and $8/15$. The smart thing to do here is to pick the middle value and then go up or down if the mid value is too small or too large. So if we test $4/15$, we get: $4/15 = 0.2666$ Success! We nailed it at the mid value, no need to try the others. Our final answer is, again, J. 3) Even though this problem may, at first glance, look like a fraction problem, it is a ratio problem. We can tell because the question specifically asks for the ratios of the boys' sandwich consumption. If you're not paying attention, you can easily make a mistake and treat the questionas a fraction problem when ratios are written using the "/" symbol. So we have Jerome, who eats half the sandwich and Kevin, who eats one third, and Seth, who eats the rest. Now we can do this problem several ways, but let us pick two of the most straightforwardratio and fraction manipulation or plugging in your own numbers (for more on this strategy, check out guide to plugging in numbers). Method 1Ratio and Fraction Manipulation Because we are not told the portion of the sandwichthat Seth ate, we must find it. Fractions represent pieces of the whole and the whole is 1 (because anything over itself = 1). So let us add our two fractions and subtract that sum from 1 to find Seth's share of the sandwich. $1/2 + 1/3$. First, we must convert these fractions to ones with a shared denominator. Both 2 and 3 are multiples of 6, so we will use 6 as our new denominator. $1/2$ = ${1(3)}/{2(3)}$ = $3/6$ $1/3$ =${1(2)}/{3(2)}$ = $2/6$ Now, let us add them together and subtract their sum from 1. $3/6 + 2/6 = 5/6$ $1 - 5/6 = 1/6$ So Seth ate $1/6$ of the sandwich. And because these fractions now all share a common denominator, we can simply compare their numerators to find their ratio of sandwich shares (remember, ratios compare parts to other parts). So the sandwich eating fractions are: $3/6, 2/6,$ and $1/6$ When we just look at the numerators,the ratio is: $3:2:1$ Our final answer is D, $3:2:1$. Method 2Plugging in Numbers Instead of working exclusively with fractions and ratios, let's try the problem again using wholenumbers. We know that Jerome ate $1/2$ and sandwich and Kevin ate $1/3$, so let's give the sandwich an actual length value that is a shared multiple of those two numbers (note: our sandwich length does not have to be a multiple of 2 and 3it can be anything we want. It simply makes our lives easier to use a common multiple, as that way we can work with integers.) So let us say that the sandwich is 12 feet long. If Jerome ate half of it, then he ate: $12/2 = 6$ feet of sandwich. If Kevin ate one third of it, then he ate: $12/3 = 4$ feet of sandwich. If we add them together, they ate: $6 + 4 = 10$ feet of sandwich. Which means that Seth ate: $12 - 10 = 2$ feet of sandwich. Now let us compare their shares of 6, 4, and 2. $6:4:2$ We know that ratios can be reduced if each of the values shares a common factor. In this case, they can all be divided by 2, so let us reduce the ratio. $6:4:2$ = $3:2:1$ Again, our final answer is D, $3:2:1$ 4) This question asks you to find the amount of irrational numbers between two realnumbers, and the simple answer is that there are infinitely many. (Note: there isalso an infinite amount of rational numbers between any two realnumbers as well!). Why is this true? Think of it this way: The square root of 1 is rational, because it equals 1, which can be written as $1/1$. But the square root of 1.01 is irrational. And so is the square root of 1.02, and the square root of 1.03....None of these numbers can be written as ${\an \integer}/{\an \integer}$ (which you can tell because their decimals continue without repeating), and yet they all sitbetween 1 and 8 on a number line. So our final answer is E, more than 7 (and,in fact, infinite). Hurray and huzzah, you did it! The Take-Aways Don’t let fractions, ratios, and/or rational numbers intimidate you. Once you’ve mastered the basics behind how they behave, you’ll be able to work your way through many of the toughest fraction and ratio problems the ACT can put in your way The biggest point to look out for, when dealing with fractions and ratios, is not to mix them up! Always pay strict attention to times when you are comparing pieces to pieces or pieces to the whole. Though it can be easy to make a mistake during the test, don’t let yourself lose a point due to careless error. What’s Next? For you, fractions are a breeze, ratios were a snap, and rationals?Forget about it! Luckily for you, there is plenty more to tackle before test day.We have guides aplenty for the many math topics covered on the ACT, including trigonometry, integers, andsolid geometry. Running out of time duringACT Math practice? Check out our article on how to finish your math section before it's pencil's down. Don't know what score to aim for? Make sure you have a good grasp of whatkind of score would best suit your goals and current skill level, and how to improve it from there. Trying to push your score to the top? Look to our guide on how to get a perfect score, written by a 36 ACT-scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program.Along with more detailed lessons, you'll get thousands ofpractice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial: