THE WHOLE NUMBERS

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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?.

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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?
• 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 WholeNumbers 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

• 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
• 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/Resources