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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 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