Thursday, November 30, 2017

long division

Let's see how it is done with:
long division 425 / 25
  • the number to be divided into is called the dividend
  • The number which divides the other number is called the divisor
And here we go:
divide step 14 ÷ 25 = 0 remainder 4The first digit of the dividend(4) is divided by the divisor.
divide step 2 The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 325 × 0 = 0The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
divide step 44 − 0 = 4Now we subtract the bottom number from the top number.
divide step 5 Bring down the next digit of the dividend.
divide step 642 ÷ 25 = 1 remainder 17Divide this number by the divisor.
divide step 7 The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 825 × 1 = 25The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
divide step 942 − 25 = 17Now we subtract the bottom number from the top number.
divide step 10 Bring down the next digit of the dividend.
divide step 11175 ÷ 25 = 7 remainder 0Divide this number by the divisor.
divide step 12 The whole number result is placed at the top. Any remainders are ignored at this point.
divide step 1325 × 7 = 175The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
divide step 14175 − 175 = 0Now we subtract the bottom number from the top number.
  There are no more digits to bring down. The answer must be 17

Wednesday, November 29, 2017

mathematicians

mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
Mathematician
Euclid.jpg
Euclid (holding calipers), Greek mathematician, known as the "Father of Geometry"
Occupation
Academic
Description
CompetenciesMathematics, analytical skillsand critical thinking skills
Education required
Doctoral degree, occasionally master's degree
Fields of
employment
universities,
private corporations,
financial industry,
government
Related jobs
statisticianactuary
Mathematics is concerned with numbersdataquantitystructurespacemodels, and change.

History

In 1938 in the United States, mathematicians were desired as teachers, calculating machine operators, mechanical engineers, accounting auditor bookkeepers, and actuary statisticians
One of the earliest known mathematicians was Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed.[1] He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem.
The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number".[2] It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins.
The first woman mathematician recorded by history was Hypatia of Alexandria (AD 350 - 415). She succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles).[3]
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs,[4] and it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on opticsmaths and astronomy of Ibn al-Haytham.
The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer).
As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag[ing] productive thinking.”[5] In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to “take account of fundamental laws of science in all their thinking.” Thus, seminars and laboratories started to evolve.[6]
British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and autonomythe changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt. The Universities of Oxfordand Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than even German universities, which were subject to state authority.[7] Overall, science (including mathematics) became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminarsor laboratories and began to produce doctoral theses with more scientific content.[8]According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge.[9] The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France.[10] In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research, teaching and study.”[11]

Tuesday, November 28, 2017

number puzzles

  1. Kenken
    In Kenken, you need to place the counting numbers in the squares just like in Sudoku, but additionally, you are given boxes with clues with math operations. The numbers you place in each box have to make the "clue" number using the given operation.
    So, Kenken is an excellent game to practice the four operations and logical thinking. Lower elementary children can use addition/subtraction and others can use multiplication/division or all four operations.
    Play Kenken online here. You can choose the size of the game, operations, and the difficulty level.
  2. Numbers in a triangle


    Put the numbers from 1 to 9 in the circles so that the sum of the numbers on each side of a triangle is the same.

    At CoolMath4Kids you can view a hint and the solution.
  3. Kakuro
    Kakuro puzzles are "cross-sum" puzzles—like mathematical crossword puzzles. Each "word" must add up to the number provided in the clue above it or to the left.
    Download 5x5 Kakuro puzzles at KrazyDad. Other sizes exist also.
  4. Same number - or twice as many

    Here is a puzzle that seems simple, but is a good critical thinking challenge for lower elementary school kids. You can easily reword it for example to have two flocks of birds in two trees. 
    Farmer Brown and Farmer Green were ruminating one day on the fence between their farms. Farmer Brown says, "You know I was just thinking. If you gave me one of your cows, then we would have the same number of cows." Farmer Green replies, "If you gave me one of your cows, then I would have twice as many as you!"

    How many cows does Farmer Brown have and how many cows does Farmer Green have?
  5. More than two animals

    This puzzle is from Grace Church School's collection of Abacus problems 2013-2014 for grades 3-8. The site does not supply the answers, but students are encouraged to submit their answers and they will receive a reply. 
    I have more than two animals at home. All of them are dogs, except for two. All of them are cats, except for two. All of them are hamsters, except for two. What kinds of animals and how many of each animal do I have?
  6. Brick's weight

    This is well-known problem that sounds so simple, yet it fools many people!
    A brick weighs one kilogram plus half of the brick. What is the weight of one brick?
  7. Average Miles per Hour
    A car is going up a hill. The hill is one mile long. The driver goes up the hill at an average speed of 30 miles per hour. When the driver reaches the top of the hill, he starts down the other side. The downhill side is also one mile long. How fast must the driver go down the hill in order to average 60 miles per hour?
  8. Legs in the bus
    1. There are 7 girls on a bus.
    2. Each girl has 7 backpacks.
    3. In each backpack, there are 7 big cats.
    4. For every big cat there are 7 little cats.

    How many legs are on the bus, not counting the driver?
  9. How can these be equal?

    Here's a short but puzzling puzzle that someone sent for the contest:
    In which meaning 1070 = 1110 ?
  10. Coconut trader
    An intelligent trader travels from 1 place to another carrying 3 sacks having 30 coconuts each.No sack can hold more than 30 coconuts. On the way he passes through 30 checkpoints and on each checkpoint he has to give 1 coconut for each sack he is carrying. How many coconuts are left in the end?
  11. Milkman's Containers
    A milkman has an 8-liter container full of milk, and also two empty containers that measure 5 liters and 3 liters. He needs to deliver 4 liters of milk to a customer.

    The milkman has no other spare containers and no way to mark any containers. He does not want to pour milk away. How will he measure the 4 liters of milk?
  12. Farmer and his ducks
    A farmer was asked how many ducks he had. "Well," he said, "they ran down the path just now and I saw one duck in front of two ducks, a duck behind two ducks, and a duck between two ducks." How many ducks were there?
  13. Number puzzles with many operations
    Enter each of the numbers from 1 to 9 in the squares, each one only once. The order of operations doesn't apply! These puzzles are available in four different levels of difficulty. 

algebra puzzles

Algebra Puzzles
ABCD × E = DCBA (Replace letters with digits and have the sum be true. A,B,C,D and... Try Puzzle >>
Solve this: ALFA + BETA + GAMA = DELTA Replace letters with digits and have the sum... Try Puzzle >>
Each letter represents a digit 0 to 9: ABC + DEF = GHIJ Try Puzzle >>
Solve the following (each letter is a digit): ABCDEF × 3 = BCDEFA Try Puzzle >>
Solve the following (each letter represents a particular digit): ABCD × D = DCBA Try Puzzle >>
Solve the following (each letter is a different digit): ABC × DEF = 123456, if A =... Try Puzzle >>
Solve the following (each letter is a digit): CAT = (C + A + T) × C × A ×... Try Puzzle >>
Solve the following (each letter is a digit): COW × COW = DEDCOW Try Puzzle