The Integers Multiplication Algorithm
Elementary Facts <ul><li>Playing the MathGym-1D game you have seen three important facts: </li></ul><ul><li>The product of...
Elementary Facts Now think about multiplying an  even  number of negative numbers together. We can multiply them two at a ...
Elementary Facts Now think about multiplying an  even  number of negative numbers together. We can multiply them two at a ...
Elementary Facts Now think about multiplying an  even  number of negative numbers together. We can multiply them two at a ...
Elementary Facts
Elementary Facts Now think about multiplying an  odd  number of negative numbers together.  If we remove one negative numb...
Elementary Facts Now think about multiplying an  odd  number of negative numbers together.  If we remove the first number,...
Elementary Facts Now think about multiplying an  odd  number of negative numbers together.  If we remove the first number,...
Elementary Facts Now think about multiplying an  odd  number of negative numbers together.  If we remove one negative numb...
Theorem <ul><li>The product of an  even  number of negative numbers is  positive . </li></ul><ul><li>The product of an  od...
<ul><li>The  direction (sign)  is given by whether the number of negative numbers is even or odd. If negative, write the n...
Work it Out
1. Determine the sign and write it down if it is negative.
2. Determine the magnitude    and write it down.
Work it Out
1. Determine the sign and write it down if it is negative.
2. Determine the magnitude    and write it down.
Work it Out
1. Determine the sign and write it down if it is negative.
2. Determine the magnitude    and write it down.
Work it Out
1. Determine the sign and write it down if it is negative.
2. Determine the magnitude    and write it down.
Work it Out
1. Determine the sign and write it down if it is negative. 47 is odd!
2. Determine the magnitude    and write it down. The product of ones is 1.
Work it Out
1. Determine the sign and write it down if it is negative. 6 is even!
2. Determine the magnitude    and write it down. The product of 6 twos
Work it Out
1. Determine the sign and write it down if it is negative. There are 3 negatives!
2. Determine the magnitude    and write it down. 2 times 5 is 10, times 10 is 100; and 3 times 3 is 9. Be smart. Think fir...
Work it Out
1. Determine the sign and write it down if it is negative. 3 + 4 = 7 negative factors!
2. Determine the magnitude    and write it down. Ignore the 1.  The product of 4 twos is 16 !
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Multiplication Algorithm

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Multiplication Algorithm

  1. 1. The Integers Multiplication Algorithm
  2. 2. Elementary Facts <ul><li>Playing the MathGym-1D game you have seen three important facts: </li></ul><ul><li>The product of two positive numbers is positive. Thus the product of any number of positive numbers is positive. </li></ul><ul><li>The product of a positive and negative number is negative. </li></ul><ul><li>The product of two negative numbers is positive. </li></ul>
  3. 3. Elementary Facts Now think about multiplying an even number of negative numbers together. We can multiply them two at a time to produce half as many positive numbers, who’s product must be positive!
  4. 4. Elementary Facts Now think about multiplying an even number of negative numbers together. We can multiply them two at a time to produce half as many positive numbers, who’s product must be positive!
  5. 5. Elementary Facts Now think about multiplying an even number of negative numbers together. We can multiply them two at a time to produce half as many positive numbers, who’s product must be positive!
  6. 6. Elementary Facts
  7. 7. Elementary Facts Now think about multiplying an odd number of negative numbers together. If we remove one negative number, the remaining even product must be positive! Multiply this number by the one we took out we get a negative product!
  8. 8. Elementary Facts Now think about multiplying an odd number of negative numbers together. If we remove the first number, the remaining even product must be positive! Multiply this number by the one we took out we get a negative product!
  9. 9. Elementary Facts Now think about multiplying an odd number of negative numbers together. If we remove the first number, the remaining even product must be positive! Multiply this number by the negative one we took out we get a negative product!
  10. 10. Elementary Facts Now think about multiplying an odd number of negative numbers together. If we remove one negative number, the remaining even product must be positive! Multiply this number by the negative one we took out we get a negative product!
  11. 11. Theorem <ul><li>The product of an even number of negative numbers is positive . </li></ul><ul><li>The product of an odd number of negative numbers is negative </li></ul>If you think about it, a more general rule is clearly true:
  12. 12. <ul><li>The direction (sign) is given by whether the number of negative numbers is even or odd. If negative, write the negative sign down. </li></ul><ul><li>You get the magnitude by multiplying the absolute values of the numbers together (Just ignore the negative signs and multiply.) </li></ul><ul><li>Write the product down. </li></ul>Computing the Product of Signed Numbers
  13. 13. Work it Out
  14. 14. 1. Determine the sign and write it down if it is negative.
  15. 15. 2. Determine the magnitude and write it down.
  16. 16. Work it Out
  17. 17. 1. Determine the sign and write it down if it is negative.
  18. 18. 2. Determine the magnitude and write it down.
  19. 19. Work it Out
  20. 20. 1. Determine the sign and write it down if it is negative.
  21. 21. 2. Determine the magnitude and write it down.
  22. 22. Work it Out
  23. 23. 1. Determine the sign and write it down if it is negative.
  24. 24. 2. Determine the magnitude and write it down.
  25. 25. Work it Out
  26. 26. 1. Determine the sign and write it down if it is negative. 47 is odd!
  27. 27. 2. Determine the magnitude and write it down. The product of ones is 1.
  28. 28. Work it Out
  29. 29. 1. Determine the sign and write it down if it is negative. 6 is even!
  30. 30. 2. Determine the magnitude and write it down. The product of 6 twos
  31. 31. Work it Out
  32. 32. 1. Determine the sign and write it down if it is negative. There are 3 negatives!
  33. 33. 2. Determine the magnitude and write it down. 2 times 5 is 10, times 10 is 100; and 3 times 3 is 9. Be smart. Think first and then act!!
  34. 34. Work it Out
  35. 35. 1. Determine the sign and write it down if it is negative. 3 + 4 = 7 negative factors!
  36. 36. 2. Determine the magnitude and write it down. Ignore the 1. The product of 4 twos is 16 !

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