Arithmetic tables for children, Lausanne, 1835

Arithmetic or arithmetics (from the Greek word ἀριθμός, arithmos “number”) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers. Professional mathematicians sometimes use the term (higher) arithmetic^[1] when referring to more advanced results related to number theory, but this should not be confused with elementary arithmetic.

History[link]

The prehistory of arithmetic is limited to a small number of artifacts which may indicate conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC although its interpretation is disputed.^[2]

The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system strongly influence the complexity of the methods. The hieroglyphic system for Egyptian numerals, like the later Roman numerals, descended from tally marks used for counting. In both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a counting board or the Roman abacus to obtain the results.

Early number systems that included positional notation were not decimal, including the sexagesimal (base 60) system for Babylonian numerals and the vigesimal(base 20) system that defined Maya numerals. Because of this place-value concept, the ability to reuse the same digits for different values contributed to simpler and more efficient methods of calculation.

The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, although it originated much later than the Babylonian and Egyptian examples. Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs. For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, and their relationships to each other, in his Introduction to Arithmetic.

Greek numerals, derived from the hieratic Egyptian system, also lacked positional notation, and therefore imposed the same complexity on the basic operations of arithmetic. For example, the ancient mathematician Archimedes devoted his entire work The Sand Reckoner merely to devising a notation for a certain large integer.

The gradual development of Hindu-Arabic numerals independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base and the use of a digit representing zero. This allowed the system to consistently represent both large and small integers. This approach eventually replaced all other systems. In the early 6th century AD, the Indian mathematician Aryabhata incorporated an existing version of this system in his work, and experimented with different notations. In the 7th century, Brahmagupta established the use of zero as a separate number and determined the results for multiplication, division, addition and subtraction of zero and all other numbers, except for the result of division by zero. His contemporary, the Syriac bishop Severus Sebokht described the excellence of this system as "...valuable methods of calculation which surpass description". The Arabs also learned this new method and called it hesab.

Leibniz's Stepped Reckoner was the first calculator that could perform all four arithmetic operations.

Although the Codex Vigilanus described an early form of Arabic numerals (omitting zero) by 976 AD, Fibonacci was primarily responsible for spreading their use throughout Europe after the publication of his book Liber Abaci in 1202. He considered the significance of this "new" representation of numbers, which he styled the "Method of the Indians" (Latin Modus Indorum), so fundamental that all related mathematical foundations, including the results of Pythagoras and the algorism describing the methods for performing actual calculations, were "almost a mistake" in comparison.

In the Middle Ages, arithmetic was one of the seven liberal arts taught in universities.

The flourishing of algebra in the medieval Islamic world and in Renaissance Europe was an outgrowth of the enormous simplification of computation through decimal notation.

Various types of tools exist to assist in numeric calculations. Examples include slide rules (for multiplication, division, and trigonometry) and nomographs in addition to the electrical calculator.

Arithmetic operations[link]

The basic arithmetic operations are addition, subtraction, multiplication and division, although this subject also includes more advanced operations, such as manipulations of percentages, square roots, exponentiation, and logarithmic functions. Arithmetic is performed according to an order of operations. Any set of objects upon which all four arithmetic operations (except division by zero) can be performed, and where these four operations obey the usual laws, is called a field.

Addition (+)[link]

Addition is the basic operation of arithmetic. In its simplest form, addition combines two numbers, the addends or terms, into a single number, the sum of the numbers.

Adding more than two numbers can be viewed as repeated addition; this procedure is known as summation and includes ways to add infinitely many numbers in an infinite series; repeated addition of the number one is the most basic form of counting.

Addition is commutative and associative so the order the terms are added in does not matter. The identity element of addition (the additive identity) is 0, that is, adding zero to any number yields that same number. Also, the inverse element of addition (the additive inverse) is the opposite of any number, that is, adding the opposite of any number to the number itself yields the additive identity, 0. For example, the opposite of 7 is −7, so 7 + (−7) = 0.

Addition can be given geometrically as in the following example:

If we have two sticks of lengths 2 and 5, then if we place the sticks one after the other, the length of the stick thus formed is 2 + 5 = 7.

Subtraction (−)[link]

Subtraction is the opposite of addition. Subtraction finds the difference between two numbers, the minuend minus the subtrahend. If the minuend is larger than the subtrahend, the difference is positive; if the minuend is smaller than the subtrahend, the difference is negative; if they are equal, the difference is zero.

Subtraction is neither commutative nor associative. For that reason, it is often helpful to look at subtraction as addition of the minuend and the opposite of the subtrahend, that is a − b = a + (−b). When written as a sum, all the properties of addition hold.

There are several methods for calculating results, some of which are particularly advantageous to machine calculation. For example, digital computers employ the method of two's complement. Of great importance is the counting up method by which change is made. Suppose an amount P is given to pay the required amount Q, with P greater than Q. Rather than performing the subtraction P − Q and counting out that amount in change, money is counted out starting at Q and continuing until reaching P. Although the amount counted out must equal the result of the subtraction P − Q, the subtraction was never really done and the value of P − Q might still be unknown to the change-maker.

Multiplication (× or · or *)[link]

Multiplication is the second basic operation of arithmetic. Multiplication also combines two numbers into a single number, the product. The two original numbers are called the multiplier and the multiplicand, sometimes both simply called factors.

Multiplication is best viewed as a scaling operation. If the numbers are imagined as lying in a line, multiplication by a number, say Failed to parse (Missing texvc executable; please see math/README to configure.): x , greater than 1 is the same as stretching everything away from zero uniformly, in such a way that the number 1 itself is stretched to where Failed to parse (Missing texvc executable; please see math/README to configure.): x

was. Similarly, multiplying by a number less than 1 can be imagined as squeezing towards zero. (Again, in such a way that 1 goes to the multiplicand.)

Multiplication is commutative and associative; further it is distributive over addition and subtraction. The multiplicative identity is 1, that is, multiplying any number by 1 yields that same number. Also, the multiplicative inverse is the reciprocal of any number (except zero; zero is the only number without a multiplicative inverse), that is, multiplying the reciprocal of any number by the number itself yields the multiplicative identity.

The product of a and b is written as a × b or a • b. When a or b are expressions not written simply with digits, it is also written by simple juxtaposition: ab. In computer programming languages and software packages in which one can only use characters normally found on a keyboard, it is often written with an asterisk: a * b.

Division (÷ or /)[link]

Division is essentially the opposite of multiplication. Division finds the quotient of two numbers, the dividend divided by the divisor. Any dividend divided by zero is undefined. For positive numbers, if the dividend is larger than the divisor, the quotient is greater than one, otherwise it is less than one (a similar rule applies for negative numbers). The quotient multiplied by the divisor always yields the dividend.

Division is neither commutative nor associative. As it is helpful to look at subtraction as addition, it is helpful to look at division as multiplication of the dividend times the reciprocal of the divisor, that is a ÷ b = a × ¹/_b. When written as a product, it obeys all the properties of multiplication.

Decimal arithmetic[link]

Decimal representation refers exclusively, in common use, to the written numeral system employing arabic numerals as the digits for a radix 10 ("decimal)" positional notation; however, any numeral system based on powers of ten, e.g., Greek, Cyrillic, roman, or Chinese numerals may conceptually be described as "decimal notation" or "decimal representation".

Modern methods for four fundamental operations (addition, subtraction. multiplication and division) were first devised by Brahmagupta of India. This was known during medieval Europe as "Modus Indoram" or Method of the Indians. Positional notation (also known as "place-value notation") refers to the representation or encoding of numbers using the same symbol for the different orders of magnitude (e.g., the "ones place", "tens place", "hundreds place") and, with a radix point, using those same symbols to represent fractions (e.g., the "tenths place", “hundredths place"). For example, 507.36 denotes 5 hundreds (10²), plus 0 tens (10¹), plus 7 units (10⁰), plus 3 tenths (10⁻¹) plus 6 hundredths (10⁻²).

Zero as a number comparable to the other basic digits is a concept that is essential to this notation, as is the concept of zero’s use as a placeholder, and as is the definition of multiplication and addition with zero. The use of zero as a placeholder and, therefore, the use of a positional notation is first attested to in the Jain text from India entitled the Lokavibhâga, dated 458 AD and it was only in the early 13th century that these concepts, transmitted via the scholarship of the Arabic world, were introduced into Europe by Fibonacci^[3] using the Hindu-Arabic numeral system.

Algorism comprises all of the rules for performing arithmetic computations using this type of written numeral. For example, addition produces the sum of two arbitrary numbers. The result is calculated by the repeated addition of single digits from each number that occupies the same position, proceeding from right to left. An addition table with ten rows and ten columns displays all possible values for each sum. If an individual sum exceeds the value nine, the result is represented with two digits. The rightmost digit is the value for the current position, and the result for the subsequent addition of the digits to the left increases by the value of the second (leftmost) digit, which is always one. This adjustment is termed a carry of the value one.

The process for multiplying two arbitrary numbers is similar to the process for addition. A multiplication table with ten rows and ten columns lists the results for each pair of digits. If an individual product of a pair of digits exceeds nine, the carry adjustment increases the result of any subsequent multiplication from digits to the left by a value equal to the second (leftmost) digit, which is any value from one to eight (9 × 9 = 81). Additional steps define the final result.

Similar techniques exist for subtraction and division.

The creation of a correct process for multiplication relies on the relationship between values of adjacent digits. The value for any single digit in a numeral depends on its position. Also, each position to the left represents a value ten times larger than the position to the right. In mathematical terms, the exponent for the radix (base) of ten increases by one (to the left) or decreases by one (to the right). Therefore, the value for any arbitrary digit is multiplied by a value of the form 10ⁿ with integer n. The list of values corresponding to all possible positions for a single digit is written as {..., 10², 10, 1, 10⁻¹, 10⁻², ...}.

Repeated multiplication of any value in this list by ten produces another value in the list. In mathematical terminology, this characteristic is defined as closure, and the previous list is described as closed under multiplication. It is the basis for correctly finding the results of multiplication using the previous technique. This outcome is one example of the uses of number theory.

Compound Unit Arithmetic[link]

Compound^[4] Unit Arithmetic is the application of arithmetic operations to mixed radix quantities such as feet and inches, gallons and pints, pounds shillings and pence and so on. Prior to the use of decimal-based systems of money and units of measure, the use of compound unit arithmetic formed a significant part of commerce and industry.

Basic arithmetic operations[link]

The techniques used for compound unit arithmetic was developed over many centuries and are well documented in many textbooks in many different languages.^{[5][6][7][8][9]} In addition to the basic arithmetic functions encountered in decimal arithmetic, compound unit arithmetic employs three more functions:

• Reduction where a compound quantity is reduced to a single quantity, for example conversion of a distance expressed in yards, feet and inches to one expressed in inches.^[10]
• Expansion, the inverse function to reduction, is the conversion of a quantity that is expressed as a single unit of measure to a compound unit, such as expanding 24 oz to 1 lb, 8 oz.
• Normalisation is the conversion of a set of compound units to a standard form - for example rewriting "1 ft 13 in" as "2 ft 1 in".

Knowledge of the relationship between the various units of measure, their multiples and their submultiples forms an essential part of compound unit arithmetic.

Principles of compound unit arithmetic[link]

There are two basic approaches to compound unit arithmetic:

• Reduction-Expansion Method where all the compound unit variables are reduced to single unit variables, the calculation performed and the result expanded back to compound units. This approach suited for automated calculations. A typical example is the handling of time by Microsoft Excel where all time intervals are processed internally as days and decimal fractions of a day.
• On going Normalisation Method in which each unit is treated separately and the problem is continuously normalised as the solution develops. This approach, which is widely described in classical texts, is best suited for manual calculations.

An example of the on-going normalisation method as applied to addition is shown below.

The addition operation is carried out from right to left; in this case, pence are processed first, then shillings followed by pounds. The numbers below the "answer line" are intermediate results.

The total in the pence column is 25. Since there are 12 pennies in a shilling, the number 24 is divided by 12 to give 2 with a remainder of 1. The value "1" is then written to the answer row and the value "2" carried forward to the shillings column. This operation is repeated using the values in the shillings column, with the additional step of adding the value that was carried forward from the pennies column. The intermediate total is divided by 20 rather than 12 as there are 20 shillings in a pound. The pound column is then processed, but as pounds are the largest unit that is being considered, no values are carried forward from the pounds column.

It should be noted that for the sake of simplicity, the example chosen did not have farthings.

Operations in practice[link]

A scale calibrated in imperial units with an associated cost display.

During the nineteenth and twentieth century various aids were developed to aid the manipulation of compound units, particularly in commercial applications. The most common aids were mechanical tills which were adapted in countries such as the United Kingdom to accommodate pounds, shillings, pennies and farthings and "Ready Reckoners" - books aimed at traders that catalogued the results of various routine calculations such as the percentages or multiples of various sums of money. One typical booklet^[11] that ran to 150 pages tabulated multiples "from one to ten thousand at the various prices from one farthing to one pound".

The cumbersome nature of compound unit arithmetic has been recognised for many years - in 1586, the Flemish mathematician Simon Stevin published a small pamphlet called De Thiende ("the tenth").^[12] in which he declared that the universal introduction of decimal coinage, measures, and weights to be merely a question of time while in the modern era, many conversion programs, such as that embedded in the calculator supplied as a standard part of the Microsoft Windows 7 operating system display compound units in a reduced decimal format rather than using an expanded format (ie "2.5 ft" is displayed rather than "2 ft, 6  in").

Number theory[link]

The term arithmetic also refers to number theory. This includes the properties of integers related to primality, divisibility, and the solution of equations in integers, as well as modern research that is an outgrowth of this study. It is in this context that one runs across the fundamental theorem of arithmetic and arithmetic functions. A Course in Arithmetic by Jean-Pierre Serre reflects this usage, as do such phrases as first order arithmetic or arithmetical algebraic geometry. Number theory is also referred to as the higher arithmetic, as in the title of Harold Davenport's book on the subject.

Arithmetic in education[link]

Primary education in mathematics often places a strong focus on algorithms for the arithmetic of natural numbers, integers, fractions, and decimals (using the decimal place-value system). This study is sometimes known as algorism.

The difficulty and unmotivated appearance of these algorithms has long led educators to question this curriculum, advocating the early teaching of more central and intuitive mathematical ideas. One notable movement in this direction was the New Math of the 1960s and 1970s, which attempted to teach arithmetic in the spirit of axiomatic development from set theory, an echo of the prevailing trend in higher mathematics.^[13]

See also[link]

• Lists of mathematics topics
• Mathematics
• Outline of arithmetic

Related topics[link]

Notes[link]

References[link]

External links[link]

Look up arithmetic in Wiktionary, the free dictionary.

Wikibooks has more on the topic of Arithmetic

Wikimedia Commons has media related to: Arithmetic

• What is arithmetic?
• MathWorld article about arithmetic
• Interactive Arithmetic Lessons and Practice
• Talking Math Game for kids
• The New Student's Reference Work/Arithmetic (historical)
• Arithmetic Game
• Math Games for kids and adults
• The Great Calculation According to the Indians, of Maximus Planudes – an early Western work on arithmetic at Convergence

Brooke Fraser
Background information
Birth name	Brooke Gabrielle Fraser
Born	(1983-12-15) 15 December 1983 (age 28) Wellington, New Zealand
Origin	Wellington, New Zealand
Genres	Pop, folk rock
Years active	2002–present
Labels	Sony Music, Wood + Bone
Associated acts	Hillsong
Website	www.brookefraser.com

Brooke Gabrielle Fraser Ligertwood, better known as Brooke Fraser (born 15 December 1983) is a New Zealand born award-winning folk-pop and Christian music^[1][2] artist. Her third studio album Flags has become the most successful album of her career, with the single "Something in the Water" reaching number one on the RIANZ singles chart in 2010.

Early life[link]

Fraser is the eldest of the three children born to former All Black Bernie Fraser,^[3] who was born in Lautoka, Fiji, and his wife Lynda Fraser.^[4] She grew up in Naenae, Lower Hutt and attended Dyer Street School, Naenae Intermediate School and Naenae College.^[5]

Fraser took piano lessons between the ages of seven and seventeen. She started writing songs at age twelve and taught herself the acoustic guitar at fifteen. Despite her skills as a singer she has never taken singing lessons.^[5]

She performed at Parachute, an annual New Zealand music festival in 2000 – including a special guest performance in 2007.^[5]

She began writing for the Soul Purpose magazine at age fifteen, and was later made editor in 2002. She gave up her job as editor shortly after moving to Auckland in late 2002 in order to pursue her music career.^[6]

Musical career[link]

In 2002, while Fraser was in Auckland, Scotty Pearson, the drummer for Elemeno P, organised a meeting with producer Matty J for her. Matty J became her manager, liaising with the major labels who had shown interest and compared their offers. Fraser had about five different labels offer her deals and chose to sign a multi-album deal with Sony Music at the age of 17.^[7]

[edit] What to Do With Daylight

Fraser's first album, What to Do with Daylight, was released in New Zealand in late 2003, debuting at number one and achieved gold status in the same week. The album eventually went seven times platinum,^[8] selling over 105,000 copies in New Zealand alone.^[9] It remained on the album charts for sixty-six weeks.^[10] All five singles from the album reached the top twenty in the New Zealand Singles Chart.^[11] Her album also topped the New Zealand Top 50 Albums of 2004.^[12]

Following the release of What to Do with Daylight, Fraser toured Australia and New Zealand with American artist John Mayer and then toured New Zealand with veteran U.K. rock artist David Bowie.^[13][14] Whilst on tour with John Mayer, she met with his guitarist and keyboardist Michael Chaves who, after recording Mayer's album Heavier Things, Fraser enlisted to play on her album and future concerts.^[15]

[edit] Albertine

In 2005, prior to writing and preparing her follow-up album, Fraser took a trip to Africa to immerse herself in Rwanda before visiting her sponsor children in Tanzania, as she is an advocate for child sponsorship. In this trip, she was so moved that she wrote the song Albertine about a young child (named Albertine), whom she met while in Rwanda. It was later decided to make this song the album's title track.^[16]

Fraser performing in Seattle, 8 December 2010

For the second album, Fraser decided to enlist a new band, primarily constructed from American musicians who'd worked with an array of notable artists, both live and recorded.^[17] In 2006, Fraser and the band went into the studio in Los Angeles to record the album. Later Fraser allowed her fans to listen to the album's first single Deciphering Me via her MySpace page. The single was later released initially to radio and ultimately to CD single, and achieved number four in the New Zealand single charts.

On 4 December 2006 Albertine was released in New Zealand, achieving double platinum status less than a month after its release and has remained, to date, in the top 20 every week since. The album was released in Australia and internationally on 31 March 2007. In Australia, it charted at number twenty-nine in its first week on 9 April and has thus far achieved Gold sales status.

On 6 April 2007, Fraser performed "Deciphering Me" for the Good Friday Appeal, an annual televised fundraising event to raise money for the Royal Children's Hospital in Melbourne.

In 2008, Fraser appeared on the Dave Barnes song "Believe" from his album Me + You + the World, performing backing vocals.

Albertine was also Fraser's U.S. debut, released 27 May 2008 and entered the Billboard 200 at number ninety on 19 July 2008. Her album propelled in success with online sales after being chosen as Editor's Choice on iTunes. On 4 July 2008 Fraser supported Canadian artist/U2 collaborator Daniel Lanois at the Montreal Jazz Festival. In August she toured the southern U.S.^[18] In September, she re-toured several major U.S. cities and completed the tour at the Shepherd's Bush Empire in London, UK.

[edit] Flags

Flags was recorded at East West Studios in Hollywood in the summer of 2010 ^[19] and released by Wood & Bone Records on 12 October 2010. Fraser celebrated with sold-out tours in the U.S., Australia and New Zealand. Flags reached the #1 spot on the New Zealand album chart,^[20] #3 in Australia,^[21] and entered at #59 on the Billboard 200 in the US,^[22] and climbed as high as #3 on the U.S iTunes album chart. "Flags" has been certified Gold in Australia and 3x Platinum in New Zealand where it was the 6th highest selling album of 2010.^[23] The first single, “Something in the Water,” has achieved extensive radio success across the globe, notably receiving BBC Radio 2 A-list rotation upon release.^[24] The single has gone on to achieve double platinum sales in NZ where it spent 21 weeks in the 2010 singles chart.^[25] The single has reached #2 in the Dutch airplay chart whilst residing in the top 5 singles chart for 6 consecutive weeks.^[26] The single has charted in Poland and Belgium at #15 and #23 respectively,^[27] as well as being certified Gold in both Germany and Italy.^[28] Flags was released in July 2011 in Germany, Austria and Switzerland and debuted in the following positions: #6 in Germany, #33 in Austria & #24 in Switzerland. One month on from release, "Flags" remained in the German top 20 at #13 and "Something in the Water" on the singles charts at #8. "Flags" was released in October 2011 in Hungary, reaching #15 on the national album chart by 2nd week of release.^[29] Flags is due to be released in Sweden, Norway, Denmark and Finland on 7 November 2011.^[27] Flags has received accolades from peers and press alike. Sara Bareilles announced to her 2 million followers on Twitter "If you don’t know her, you should. @brookefraser is a freakin gem. New album out now. Yay." and Women’s Wear Daily has called Brooke "The Kiwi Norah Jones."^[30][31]

In its review of Flags, Glide Magazine said: "Brooke Fraser’s third release, Flags, is a wonder. From the stunning lyrical imagery throughout to the impressive guest vocalists who join her (Cary Brothers, Jon Foreman and Aqualung among them), from Fraser’s ethereal and breathy performances to the wide-ranging soundscapes, this record is drenched in beauty and stands as one of the more remarkable achievements of 2010."^[32]

In support of "Flags" release in Switzerland, Brooke will be appearing in November 2011 at the “ENERGY STARS FOR FREE” event in Zurich alongside Lenny Kravitz and Snow Patrol.^[33]

Personal life[link]

After the success of her first album, Fraser moved to Sydney, where she has lived since 2004. On 17 March 2008 she married Scott Ligertwood, in Sydney, changing her name to Brooke Ligertwood.^[34] "Brooke Fraser" has remained her stage name for her activity as a Sony BMG recording/touring artist. She continues to write songs for Hillsong Church, now as "Brooke Ligertwood". Among her notable congregational songs are "Desert Song" and "Hosanna". After touring her second album Albertine for almost 4 years, Fraser returned home to Sydney. She took almost a year off from music-making. After attending the Coachella Valley Music and Arts Festival in the US and seeing Fleet Foxes ^[35] set she was inspired to work on her latest album Flags.^[36]

Fraser also runs a blog from her website where she comments on everything from touring, to fashion and food.^[37]

Philanthropy[link]

Fraser has enjoyed success in her career for many years, and she has always used her position to highlight many worthy causes and charity projects, and raising large amounts of money for them in the process. In late 2010 whilst on tour in the U.S. promoting her third album Flags, Fraser, in conjunction with charity: water ran a birthday campaign asking her fans to donate $27 in honor of her 27th birthday. The goal was to raise $50,000 to build clean water wells in Ethiopia.^[38] Joining the likes of Justin Bieber,^[39] Will Smith^[40] and Adam Lambert^[41] Fraser's birthday campaign was a success raising over $54,000. She has vowed to continue her work with charity: water on future projects.

Fraser has worked with World Vision as an Artist Associate since 2001. She has visited Cambodia and Tanzania with World Vision, the Philippines with Opportunity International and independently traveled to Rwanda in June 2005, in June 2006 as part of charity event "Hope Rwanda", and in May 2007 when she filmed the music video for the song "Albertine" off her second studio album of the same name. In 2006 she, along with Petra Bagust and Tau from Spacifix, appeared in an advertisement for the World Vision 40 Hour Famine; an event which raises funds for children in third world countries. She also sponsors eleven children through World Vision^[42] and makes child ways of contributing to the work of World Vision (i.e. fundraising t-shirts etc.).

Discography[link]

Studio albums

• What to Do with Daylight (2003)
• Albertine (2006)
• Flags (2010)

Awards and nominations[link]

APRA Awards

New Zealand Music Awards

GMA Dove Awards

References[link]

External links[link]

Wikimedia Commons has media related to: Brooke Fraser

• Official Brooke Fraser website
• Brooke Fraser at Allmusic
• Brooke Fraser on Myspace
• New Zealand Herald article

Lady Gaga
Lady Gaga performing on The Monster Ball Tour in 2010
Background information
Birth name	Stefani Joanne Angelina Germanotta
Born	(1986-03-28) March 28, 1986 (age 26) New York, New York, U.S.
Genres	Pop, dance, electronic
Occupations	Singer-songwriter, performance artist, record producer, dancer, businesswoman, activist
Instruments	Vocals, piano, keyboards
Years active	2005–present
Labels	Def Jam, Cherrytree, Streamline, Kon Live, Interscope
Website	LadyGaga.com Lady Gaga's signature

Stefani Joanne Angelina Germanotta (/ˈstɛfəniː dʒʌrməˈnɑːtə/ STE-fə-nee jurr-mə-NAH-tə; born March 28, 1986), known by her stage name Lady Gaga, is an American singer and songwriter. Born and raised in New York City, she primarily studied at the Convent of the Sacred Heart and briefly attended New York University's Tisch School of the Arts before withdrawing to focus on her musical career. She began performing in the rock music scene of Manhattan's Lower East Side, and was signed with Streamline Records by the end of 2007. During her employment as a songwriter for the record company, her vocal abilities captured the attention of recording artist Akon, who signed her to his label Kon Live Distribution.

Lady Gaga came to prominence as a recording artist following the release of her debut album The Fame (2008), which was a critical and commercial success that topped charts around the world and included the international number-one singles "Just Dance" and "Poker Face". After embarking on the The Fame Ball Tour, she followed the album with The Fame Monster (2009), which spawned the worldwide hit singles "Bad Romance", "Telephone" and "Alejandro". The album's success allowed her to embark on the eighteen-month long Monster Ball Tour, which later became one of the highest-grossing concert tours of all time. Her most recent album Born This Way (2011) topped the charts of most major markets and generated more international chart-topping singles, including "Born This Way", "Judas" and "The Edge of Glory". Besides her musical career, she involves herself with humanitarian causes and LGBT activism.

Influenced by David Bowie, Michael Jackson, Madonna and Queen, Lady Gaga is recognized for her flamboyant, diverse and outré contributions to the music industry through her fashion, performances and music videos. She has sold an estimated 23 million albums and 64 million singles worldwide, making her one of the best-selling music artists of all time and her singles are some of the best selling worldwide.^[1] Her achievements include five Grammy Awards and 13 MTV Video Music Awards. Lady Gaga has consecutively appeared on Billboard magazine's Artists of the Year (scoring the definitive title in 2010), ranked fourth in VH1's list of 100 Greatest Women in Music, is regularly placed on lists composed by Forbes magazine and was named one of the most influential people in the world by Time magazine.^[2][3] In 2012, Gaga was ranked at number four on Billboard's list of top moneymakers of 2011, grossing more than $25 million.^[4]

Biography[link]

1986–2004: Early life[link]

Manhattan's Upper West Side, where Gaga grew up, has been an inspiration for many of her songs.

Lady Gaga was born Stefani Joanne Angelina Germanotta on March 28, 1986 in New York City to parents Cynthia (née Bissett) and Joseph Germanotta, an Internet entrepreneur.^[5][6] Descending from Italian and more distant French-Canadian roots, Gaga is the elder of two children.^[7][8] Her sister, Natali, a fashion student, was born in 1992.^[9][10] Despite her seemingly affluent upbringing in the family home in Manhattan's Upper West Side, Gaga has stressed that she did not come from a wealthy background, stating that her parents "both came from lower-class families, so we've worked for everything—my mother worked eight to eight out of the house, in telecommunications, and so did my father."^[11][12]

From the age of 11, Gaga – who was raised Roman Catholic – attended the Convent of the Sacred Heart, a private all-girls Roman Catholic school on Manhattan's Upper East Side.^[13][14][15] She described her academic life in high school as "very dedicated, very studious, very disciplined" but also "a bit insecure": "I used to get made fun of for being either too provocative or too eccentric, so I started to tone it down. I didn't fit in, and I felt like a freak."^[16][17] Acquaintances dispute that she did not fit in at school. "She had a core group of friends; she was a good student. She liked boys a lot, but singing was No. 1," recalled a former high school classmate.^[18] Gaga began playing the piano at the age of 4, went on to write her first piano ballad at 13, and started to perform at open mike nights by the age of 14.^[19][20] Her passion for musical theatre brought her lead roles in high school productions, including Adelaide in Guys and Dolls and Philia in A Funny Thing Happened on the Way to the Forum.^[21] She also appeared in a very small role as a mischievous classmate in the television drama series The Sopranos in a 2001 episode titled "The Telltale Moozadell" in addition to unsuccessfully auditioning for parts in New York shows.^[11][22]

When her time at the Convent of the Sacred Heart came to an end, her mother encouraged her to apply for the Collaborative Arts Project 21 (CAP21), a musical theatre training conservatory at New York University's Tisch School of the Arts.^[11] After becoming one of twenty students to gain early admission, she eventually lived in an NYU dorm on 11th Street by the age of 17.^[21] CAP21 prepared her for her future career focus in "music, art, sex and celebrity" where, in addition to sharpening her songwriting skills, she composed essays and analytical papers on art, religion, social issues and politics, including a thesis on pop artists Spencer Tunick and Damien Hirst.^[20][23][24] With CAP21, she also tried out for and won auditions, including the part of an unsuspecting diner customer for MTV's Boiling Points, a prank reality television show.^[11][25] But Gaga felt more creative than some of her classmates. "Once you learn how to think about art, you can teach yourself," she said.

2005–07: Career beginnings[link]

Gaga (right) performing with Lady Starlight (left) at Lollapalooza 2007

Gaga withdrew from CAP21 at 19, in the second semester of her sophomore year, deciding to focus on her musical career.^[26] Her father agreed to pay her rent for a year, on the condition that she re-enroll at Tisch if unsuccessful. "I left my entire family, got the cheapest apartment I could find, and ate shit until somebody would listen," she remembers.^[21] Settled in a small apartment on Rivington Street towards the summer of 2005, Gaga recorded a couple of songs with hip-hop singer Grandmaster Melle Mel, for an audio book accompanying the children's book The Portal in the Park, by Cricket Casey.^[11][27] She also began a band called the Stefani Germanotta Band (SGBand) with some friends from NYU – guitarist Calvin Pia, bassist Eli Silverman, drummer Alex Beckham and booking manager Frank Fredericks – in September of that year.^[11][21] The band played a mixture of songs: some self-penned alongside classic rock numbers like Led Zeppelin's "D'yer Mak'er".^[11] Playing in bars like the Greenwich Village's The Bitter End and the Lower East Side's the Mercury Lounge, the band developed a small fan base and caught the eye of music producer Joe Vulpis.^[11] Soon after arranging time in Vulpis' studio in the months that followed, SGBand were selling their extended plays Words and Red and Blue (both 2005) at gigs around New York while becoming a local fixture of the downtown Lower East Side club scene.^[21]

SGBand reached their career peak at the 2006 Songwriters Hall of Fame New Songwriters Showcase at The Cutting Room in June where Wendy Starland, a musician, appeared as a talent scout for music producer Rob Fusari. Starland informed Fusari – who was searching for a female singer to front a new band – of Gaga's ability and contacted her. With SGBand disbanded, Gaga traveled daily to New Jersey to work on songs she had written and compose new material with the music producer.^[11] While in collaboration, Fusari compared some of her vocal harmonies to those of Freddie Mercury, lead singer of Queen.^[28] It was Fusari who helped create the moniker Gaga after the Queen song "Radio Ga Ga". Gaga was in the process of trying to come up with a stage name when she received a text message from Fusari that read "Lady Gaga."^[29] He explained, "Every day, when Stef came to the studio, instead of saying hello, I would start singing 'Radio Ga Ga'. That was her entrance song" and that the text message was the result of a predictive text glitch that changed "radio" to "lady". She texted back, "That's it," and declared, "Don't ever call me Stefani again."^[29][30] The New York Post, however, has reported that this story is incorrect, and that the name resulted from a marketing meeting.^[18]

Gaga performing in a bar, sporting one of her earlier looks (2008)

Although the musical relationship between Fusari and Gaga was unsuccessful at first, the pair soon set up a company titled Team Lovechild in which they recorded and produced electropop tracks and sent them to music industry bosses.^[11] Joshua Sarubin, the head of A&R at Def Jam Recordings, responded positively and vied for the record company to take a chance on her "unusual and provocative" performance. After having his boss Antonio "L.A." Reid in agreement, Gaga was signed to Def Jam in September 2006 with the intention of having an album ready in nine months.^[11] However, she was dropped by the label after only three months – an unfortunate period of her life that would later inspire her treatment for the music video for her 2011 single "Marry the Night".^[31][32] Devastated, Gaga returned to the solace of the family home for Christmas and the nightlife culture of the Lower East Side.^[11]

She became increasingly experimental: fascinating herself with emerging neo-burlesque shows, go-go dancing at bars dressed in little more than a bikini in addition to experimenting with drugs.^[11][14] Her father, however, did not understand the reason behind her drug intake and could not look at her for several months.^[14][30] "I was onstage in a thong, with a fringe hanging over my ass thinking that had covered it, lighting hairsprays on fire, go-go dancing to Black Sabbath and singing songs about oral sex. The kids would scream and cheer and then we'd all go grab a beer. It represented freedom to me. I went to a Catholic school but it was on the New York underground that I found myself."^[23] It was then when she became romantically involved with a heavy metal drummer in a relationship and break-up she likened to the musical film Grease: "I was his Sandy, and he was my Danny, and I just broke." He later became an inspiration behind some of her later songs.^[33]

During this time, she met performance artist Lady Starlight, who helped mold her on-stage persona.^[34] Starlight explained that, upon their first meeting, Gaga wanted to perform with her to songs she had recorded with Fusari. Like SGBand, the pair soon began performing at many of the downtown club venues like the Mercury Lounge, The Bitter End, and the Rockwood Music Hall. Their live performance art piece was known as "Lady Gaga and the Starlight Revue" and, billed as "The Ultimate Pop Burlesque Rockshow", was a low-fi tribute to 1970s variety acts.^[35][36] Soon after, the two were invited to play at the 2007 Lollapalooza music festival in August that year.^[37] The show was critically acclaimed, and their performance received positive reviews.^[20][35] Having initially focused on avant-garde electronic dance music, Gaga had found her musical niche when she began to incorporate pop melodies and the glam rock of David Bowie and Queen into her music.^[38]

While Gaga and Starlight were busy performing, producer Rob Fusari continued to work on the songs he had created with Gaga. Fusari sent these songs to his friend, producer and record executive Vincent Herbert.^[39] Herbert was quick to sign her to his label Streamline Records, an imprint of Interscope Records, upon its establishment in 2007.^[40] Gaga later credited Herbert as the man who discovered her, adding "I really feel like we made pop history, and we're gonna keep going."^[39] Having served as an apprentice songwriter under an internship at Famous Music Publishing, which was later acquired by Sony/ATV Music Publishing, Gaga subsequently struck a music publishing deal with Sony/ATV.^[41] As a result, she was hired to write songs for Britney Spears and labelmates New Kids on the Block, Fergie, and the Pussycat Dolls.^[41] At Interscope, singer-songwriter Akon recognized her vocal abilities when she sang a reference vocal for one of his tracks in studio.^[42] Akon then convinced Interscope-Geffen-A&M Chairman and CEO Jimmy Iovine to form a joint deal by having her also sign with his own label Kon Live, making her his "franchise player."^[31][43]

As 2007 came to a close, her former management company introduced her to songwriter and producer RedOne, whom they also managed.^[44] The first song she produced with RedOne was "Boys Boys Boys", a mash-up inspired by Mötley Crüe's "Girls, Girls, Girls" and AC/DC's "T.N.T.".^[30][44] Gaga continued her collaboration with RedOne in the recording studio for a week on her debut album and also joined the roster of Cherrytree Records, an Interscope imprint established by producer and songwriter Martin Kierszenbaum, after co-writing four songs with Kierszenbaum including the singles "Christmas Tree" and "Eh, Eh (Nothing Else I Can Say)".^[41] Despite her secure record deal, she admitted that there was fear about her being too "racy", "dance-orientated" and "underground" for the mainstream market. Her response: "My name is Lady Gaga, I've been on the music scene for years, and I'm telling you, this is what's next."^[15]

[edit] 2008–10: The Fame and The Fame Monster

Gaga performing at The Fame Ball Tour in 2009

By 2008, Gaga had relocated to Los Angeles in order to work extensively with her record label to complete her debut album and set up her own creative team Haus of Gaga, modeled on Andy Warhol's Factory.^[30][45] The Fame was first released on August 19, 2008 to slow radio play. Gaga supported it by performing around Europe and in small gay clubs around the US in addition to being billed as a supporting artist on the North American leg of New Kids on the Block's reunion concert tour.^[46][47] A sleeper hit, lead single "Just Dance" had preceded the album's release by four months but only hit the summit of the international charts in January 2009, provoking the instant success of the album, earning her first Grammy Award nomination (for Best Dance Recording) and becoming one of the best-selling singles worldwide.^[46][48] Gaga achieved a greater unexpected success when "Poker Face", another sleeper hit, reached number one in most major music markets worldwide in early 2009, selling 9.8 million singles worldwide.^[49][50] The follow-up single won the award for Best Dance Recording at the 52nd Grammy Awards over nominations for Song of the Year and Record of the Year.

The Fame itself was nominated for Album of the Year while winning Best Dance/Electronica Album at the same ceremony.^[51] Contemporary critics lauded the album, describing it as an exploration of her obsession with fame and the intricacies of a rich and famous lifestyle, noting its combination of genres "from Def Leppard drums and hand claps to metal drums on urban tracks", the inspiration drawn from 1980s synthpop and incorporation of dance music with clear hooks.^[31] The Fame went to number one in Austria, Canada, Germany, Ireland, Switzerland and the UK and appeared in the top five in Australia, the US and 15 other countries.^[52][53] It also stayed atop the Dance/Electronic Albums chart for 106 non-consecutive weeks and, since its release, has sold over 12 million copies worldwide.^[54] The album's success spawned many 2009 honors including Billboard magazine's Rising Star award and the accumulation of 3 of 9 MTV Video Music Awards nominations, winning Best New Artist with the video for her single "Paparazzi" gaining Best Art Direction and Best Special Effects.^[55][56] In addition to being an opening act on the Pussycat Dolls' Doll Domination Tour during the first half of 2009 in Europe and Oceania, she also embarked on her own six-month critically appreciated worldwide concert tour The Fame Ball Tour which ran from March to September 2009.^[57][58]

While she traveled the globe, she wrote The Fame Monster, an EP of eight songs released in November 2009. Each song, dealing with the darker side of fame from personal experience, is expressed through a monster metaphor. Making Gaga the first artist in digital history to have three singles (alongside "Just Dance" and "Poker Face") to pass the four million mark in digital sales, its lead single "Bad Romance" topped the charts in eighteen countries and reached the top two in the US, Australia and New Zealand while accruing the Grammy Awards for Best Female Pop Vocal Performance and Best Short Form Music Video.^[59] The second single "Telephone", which features singer Beyoncé, was nominated for the Grammy Award for Best Pop Collaboration with Vocals and became Gaga's fourth UK number one single; its accompanying music video, although controversial, received positive reception from contemporary critics who praised her for "the musicality and showmanship of Michael Jackson and the powerful sexuality and provocative instincts of Madonna."^[60][61] Her following single "Alejandro" paired Gaga with fashion photographer Steven Klein for a music video similarly as controversial – critics complimented its ideas and dark nature but the Catholic League attacked Gaga for her alleged use of blasphemy.^[62] Despite the controversy surrounding her music videos, they made Gaga the first artist to gain over one billion viral views on video-sharing website YouTube.^[63] At the 2010 MTV Video Music Awards, Gaga won 8 of her 13 nominations, including Video of the Year for "Bad Romance" (with "Telephone" also nominated), which made her the first female artist to be nominated twice for the award.^[64][65] In addition, The Fame Monster garnered a total of six nominations at the 53rd Grammy Awards – equating to the amount of Grammy nominations her debut received – winning Best Pop Vocal Album and earning her a second-consecutive nomination for Album of the Year.^[66][67]

Gaga performing at The Monster Ball Tour in 2010

The success of the album allowed Gaga to start her second worldwide concert tour, The Monster Ball Tour, just weeks after the release of The Fame Monster and months after having finished The Fame Ball Tour.^[68] Upon finishing in May 2011, the critically acclaimed and commercially accomplished tour ran for over one and a half years and grossed $227.4 million, making it one of the highest-grossing concert tours of all time and the highest-grossing for a debut headlining artist.^[69] Concerts performed at Madison Square Garden in New York City were filmed for a HBO television special titled Lady Gaga Presents the Monster Ball Tour: At Madison Square Garden. The special accrued one of its five Emmy Award nominations and has since been released on DVD and Blu-ray.^[70] Gaga also performed songs from the album at international events such as the 2009 Royal Variety Performance where she sang "Speechless", a power ballad, in the presence of Queen Elizabeth II; the 52nd Grammy Awards where her opening performance consisted of the song "Poker Face" and a piano duet of "Speechless" in a medley of "Your Song" with Elton John; and the 2010 BRIT Awards where a performance of an acoustic rendition of "Telephone" followed by "Dance in the Dark" dedicated to the late fashion designer and close friend, Alexander McQueen, supplemented her hat-trick win at the awards ceremony.^[71] Other performances may have included her participation in Michael Jackson's This Is It concert series at London's O2 Arena. "I was actually asked to open for Michael on his tour," she stated. "We were going to open for him at the O2 and we were working on making it happen. I believe there was some talk about us, lots of the openers, doing duets with Michael on stage."^[72]

In 2009 she collaborated with consumer electronic company Monster Cable Products to create a pair of in-ear jewel-encrusted headphones titled Heartbeats. "They are designed to be the first ever fashion accessories that double as the absolute best sonically sounding headphones in the world," she commented.^[73] Gaga also partnered with Polaroid in January 2010 as their Creative Director.^[74] Excited about "blending the iconic history of Polaroid and instant film with the digital era," Gaga unveiled the first trio of new products called Grey Label: a pair of picture-taking sunglasses, a paperback-sized mobile printing unit and an updated version of the traditional Polaroid camera at the 2011 Consumer Electronics Show.^[75] But her collaboration with past producer Rob Fusari led to her production team, Mermaid Music LLC, being sued in March 2010 when he claimed that he was entitled to a 20% share of the company's earnings. Gaga's lawyer, Charles Ortner, described the agreement with Fusari as "unlawful" and declined to comment, but five months later, the New York Supreme Court dismissed both the lawsuit and a countersuit by Gaga.^[76][77] In addition to such strife, Gaga was tested borderline positive for lupus, but claimed not to be affected by the symptoms. The revelations caused considerable dismay among fans, leading to Gaga addressing the matter in an interview with Larry King, saying she hopes to avoid symptoms by maintaining a healthy lifestyle.^[78][79]

[edit] 2011–present: Born This Way

Gaga performing on the 2011 Good Morning America Summer Concert Series

Gaga released her second studio album and third major release, Born This Way, on May 23, 2011. Described as a marriage of electronic music with metal, rock 'n' roll, pop and anthemic style melodies with sledge-hammering dance beats and referred to as an album "about what what keeps us up at night and what makes us afraid," Gaga characterized it as "something so much deeper than a wig or lipstick or a fucking meat dress" and, upon hearing it, Akon remarked that she is taking music to the "next level."^[80][81] Upon release, the album received generally positive reviews from music critics, who praised its range of different styles and her vocals.^[82][83] Born This Way sold 1.108 million copies in its first week in the US, debuted atop the Billboard 200, and topped the charts in more than 20 other countries.^[84] In addition to exceeding 8 million copies in worldwide sales, Born This Way received 3 Grammy Award nominations, including her third consecutive for Album of the Year.^[85]

In the months prior to its unveiling, Gaga released the singles "Born This Way", "Judas" and "The Edge of Glory" alongside promotional single "Hair". The eponymous lead single, first sung live at the 53rd Grammy Awards in a performance that saw Gaga emerge from an egg-like vessel, deals with self-acceptance regardless of race or sexual orientation. The single debuted atop the Billboard Hot 100, becoming the 19th number-one debut and the 1,000th number-one single in the history of the charts.^[86] It sold more than 3 million digital copies in the US by October 2011, becoming her eighth consecutive single to exceed sales of 2 million and, with worldwide sales of 8.2 million copies by November 2011, one of her five best-selling singles worldwide.^[87] Critics noted artistic and cultural references and praised the concept of the song's accompanying music video, in which Gaga gives birth to a new race amidst surrealistic images.^[88][89] The video for "Judas", in which Gaga portrays Mary Magdalene, and Biblical figures such as Jesus Christ and Judas Iscariot are also featured, was criticized for its religious references but received acclaim for its overall delivery and praise from others who claimed that there was nothing offensive about it.^[90] "Judas" also peaked within the top ten in several major musical markets, while "The Edge of Glory", first a commercial success in digital outlets, was later released as a single to critical appreciation, accompanied by a video which was notably stripped down from her usually "extravagant" efforts.^[91][92] She released "You and I" and "Marry the Night" as the following singles from Born This Way. Although their "crazy and ambitious" videos were praised for their audacity, both songs failed to match the similar international success that their predecessors achieved.^[93]

Gaga continued her musical endeavors by pairing with veteran artists like Tony Bennett to record a jazz version of "The Lady Is a Tramp".^[94] She also recorded a duet with Cher on a "massive" and "beautiful" track, which Gaga "wrote a long time ago, and I've never put it on one of my own albums for, really, no particular reason."^[95] Gaga also lent her vocals to an original duet with Elton John for the animated feature film Gnomeo & Juliet. The song, "Hello, Hello", was released without Gaga's vocals but the duet version features in the film.^[96][97] She also continued her live appearances throughout 2011, performing a one-of-a-kind concert at the Sydney Town Hall on July 13 in promotion of Born This Way and at the celebration of former US president Bill Clinton's 65th birthday, wearing a blond wig as a nod to the famous performance of Marilyn Monroe for John F. Kennedy and changing the lyrics to "You and I" specifically for the performance.^[98] Televised appearances comprised her own Thanksgiving Day television special entitled A Very Gaga Thanksgiving which was critically lauded, attained 5.749 million American viewers, and spawned the release of her fourth extended play A Very Gaga Holiday.^[99] Her second performance on Saturday Night Live saw her singing a selection of Born This Way songs alongside appearing in number of sketches with Justin Timberlake and Andy Samberg.^[100] In March 2012, Gaga was ranked at number four on Billboard's list of top moneymakers of 2011, grossing $25,353,039 dollars, which includes sales from Born This Way and her Monster Ball Tour.^[4]

In early 2012, Gaga stated that songs for a new album were "beginning to flourish" as she worked with producer Fernando Garibay, while the accompanying tour for Born This Way was materializing.^[101][102] Gaga's manager, Vincent Herbert, revealed that Gaga will is working on her upcoming album during the tour, stating that the material is "insane, great records."^[103] The Born This Way Ball Tour began on April 27, 2012, at the Olympic Stadium in Seoul, South Korea.^[104] The tour was met with protests from several religious groups who denounced the tour as satanic and against religious values, resulting in protests mainly from the Islamic Defenders Front, causing a cancellation in the Indonesian city of Jakarta, where Gaga was denied a license to perform. The concert however was still in question as concert promoters were optimistic that the performance will in fact go on. However, due to threats of violence from Muslim hardliners, Gaga decided to cancel the concert although 52,000 tickets have sold out in just a few days.^{[105][106][107]} On May 20, 2012, Gaga guest-starred on the 23rd season finale of The Simpsons entitled "Lisa Goes Gaga".^[108]