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THE WHOLE NUMBERS

THE WHOLE NUMBERS. Z +3 -5 -9 . . . From the hot-air balloon, the radar falls down into the water. What is the distance from the hot-air balloon to the radar? What is the distance from the helicopter to the subamarine?.

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THE WHOLE NUMBERS

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  1. THE WHOLE NUMBERS Z +3 -5 -9 . . .

  2. From the hot-air balloon, the radar falls down into the water. What is the distance from the hot-air balloon to the radar? • What is the distance from the helicopter to the subamarine?

  3. How many floors are there between the shop (0) and the parking (-2)? • And how many floors are there between the restaurant (1) and the gymnasium (-1)?

  4. What’s the avg. temperature in the Sahara Desert? • What’s the avg. temperature in Alaska?

  5. 1.- The Whole Numbers Set. • As you can see, the Natural Numbers N = {0, 1, 2, ...} are not enough to express many life situations (places under the sea, flats under ground, temperatures below zero,...) • We need more numbers. • We must add new numbers to the set of the Natural Numbers, the Negative Numbers{..., -3, -2, -1} • All these numbers are called The WholeNumbers Z = {..., -3, -2, -1, 0, 1, 2, ...}

  6. The sign of a whole number If the whole number is a natural number, we can writte it with the sign + before it. Ex: +5, +7 The sign is positive If the whole number is not a natural number, we must writte it with the sign – before it: Ex: -5, -9 The sign is negative

  7. The absolute value of a whole number. The absolute value of a whole number is the same number but always positive. Ex: I -7 I = 7 I 4 I = 4 • The opposite number of a whole number. The opposite number of a whole number is the same number but with the opposite sign. Ex: The opposite of 5 = -5 The opposite of -3 = 3

  8. 2.- Addition and Subtraction • 1 case: Both numbers have the same sign We add the absolute values and we put the sign. Ex: 5 + 2 = 7 -2 -10 = -10 • 2 case: The numbers have different signs We subtract the absolute values and we put the sign of the greatest. Ex: -2 + 7 = 5 4 - 9 = -5

  9. 3.- Multiplication and Division The sign rule: (+) * (+) = (+) (+) : (+) = (+) (+) * ( - ) = ( -) (+) : ( - ) = ( -) (-) * (+) = (+) (-) : (+) = (+) (-) * (-) = (+) (-) : (-) = (+)

  10. Example: (+5) * ( - 4) = - 20 (-5) * ( - 4) = + 20 (+9) * ( + 7) = + 63 (-9 ) * ( + 7) = - 63

  11. Example: (-20) : ( - 4) = + 5 (-20) : ( + 4) = - 5 ( +63 ) : ( + 7) = + 63 ( +63 ) : ( - 7) = - 63

  12. 4.- Operations hierarchy 1st. First, solve the parenthesis 2nd. After that, solve the multiplication and division operations. 3rd. Finally, solve the addition and the subtraction operations.

  13. Example: 15 – 3 * [ 7 – ( -6 ) : (+3)] = 15 - 3 * [ 7 - (-2)] = 15 – 3 * [ +9] = 15 – 27 = -12

  14. 5.- Activities • 1. Use whole numbers, positive or negative, to express each situation: • A helicopter flies at 100 m ................. • A diver swims 15 m underwater........... • A submarine navigates 50 m underwater.................................................... • An airplane flies 10.000 m above the sea.. • Mt. Everest rises 8.845 m above sea level.

  15. 6.- On the internet • http://bilingualproject.wikispaces.com/Resources • http://www.youtube.com/watch?v=0wteb5T2PmM • http://www.mathgoodies.com/lessons/toc_vol3.html

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