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 N atural 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 N egative Numbers {..., -3, -2, -1}
    • All these numbers are called The Whole Numbers 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
    • 1 st . First, solve the parenthesis
    • 2 nd . After that, solve the multiplication and division operations.
    • 3 rd . 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