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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?
 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)?
What’s
the avg. temperature
in the Sahara Desert?
What’s
the avg. temperature
in Alaska?
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 Whole
Numbers Z = {..., -3, -2, -1, 0, 1, 2, ...}
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
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
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
3.- Multiplication and Division
The sign rule:
(+) * (+) = (+)
(+) * ( - ) = ( -)
(-) * (+) = (+)
(-) * (-) = (+)
(+) : (+) = (+)
(+) : ( - ) = ( -)
(-) : (+) = (+)
(-) : (-) = (+)
Example:
(+5) * ( - 4) = - 20
(-5) * ( - 4) = + 20
(+9) * ( + 7) = + 63
(-9 ) * ( + 7) = - 63
Example:
(-20) : ( - 4) = + 5
(-20) : ( + 4) = - 5
( +63 ) : ( + 7) = + 63
( +63 ) : ( - 7) = - 63
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.
Example:
15 – 3 * [ 7 – ( -6 ) : (+3)] =
15 - 3 * [ 7 - (-2)] =
15 – 3 * [ +9] =
15 – 27 =
-12
5.- Activities

a)
b)
c)
d)
e)
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.
6.- On the internet
http://bilingualproject.wikispaces.com/Res
ources
http://www.youtube.com/watch?v=0wteb5
T2PmM
http://www.mathgoodies.com/lessons/toc_
vol3.html