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Multiples

Multiples. Ch. 5 of Number Theory. Egyptian Method. Multiplication is repeated addition…wasn’t until 1650 BC that methods for multiplication began appearing.

dean-holt
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Multiples

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  1. Multiples Ch. 5 of Number Theory

  2. Egyptian Method • Multiplication is repeated addition…wasn’t until 1650 BC that methods for multiplication began appearing. • Egyptians used a method for multiplication that required the doubling of successive numbers, followed by the addition of appropriate multiples. • This method works because every whole number can be written as the sum of “doubling numbers” (or numbers of the form 2n). • Example: 142 x 28 • 1 x 142 = 142 • 2 x 142 = 284 16 + 8 + 4 = 28, • *4 x 142 = 568 so 28 x 142 = • *8 x 142 = 1136 2272 + 1136 + 568 = 3976 • *16 x 142 = 2272

  3. Examples • Using the Egyptian Multiplication Method, solve the following problems: • 34 x 154 26 x 190 • 46 x 127 54 x 111 • 22 x 91 38 x 56

  4. Some History • A book entitled IntroductioArithmetieawritten by Nicomachus of Gerasa around 100 AD provided a multiplication table up to 10 x 10. No rules of multiplication or division were included. • The Hindu-Arabic system of numbers (place value and zero included) began to be seen in Europe towards the end of the 13th century. • Luca Pacioli described some methods of multiplication in his work Summa de arithmetica, geometrica, proportioni et proportionolita(usually referred to as the Suma) in 1494. • Included in his work was the method of multiplication known as Lattice Multiplication.

  5. Line Multiplication • http://www.youtube.com/watch?v=uElp6Ptidb4 • Solve the following using the Line Multiplication: • 234 x 26 154 x 32

  6. Developmental Perspective • Students learn to multiply through a stepwise progression of multiplication methods that is similar to that of addition. • Repeated addition and skip-counting are examples of how students will initially learn multiplication. • Many methods of multiplication developed by students are supported by neither textbooks nor instruction.

  7. Prime Factoriazation • Every composite number N can be factored uniquely into prime factors. • Example: 30 / \ 15 2 / \ 3 5 So 30 = 3 x 5 x 2

  8. Material from the text, Number Theory for Elementary School Teachers By: Edward Wall • Youtube video http://www.youtube.com/watch?v=uElp6Ptidb4

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