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THE WHOLE NUMBERSTHE WHOLE NUMBERS
Z+3 -5 -9 . . .
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?
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)?
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?
What’s the avg. temperature in the Sahara Desert?
What’s the avg. temperature in Alaska?
1.- The Whole Numbers Set.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, ...}
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 numberIf the whole number is a natural number, we can writte it with the sign + before it. Ex: +5, +7The sign is positive
If the whole number is not a natural number, we must writte it with the sign – before it: Ex: -5, -9The sign is negative
The sign of a whole numberIf the whole number is a natural number, we can writte it with the sign + before it. Ex: +5, +7The sign is positive
If the whole number is not a natural number, we must writte it with the sign – before it: Ex: -5, -9The 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
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 Subtraction2.- 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
1 case: Both numbers have the same signWe 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 Division3.- Multiplication and Division
The sign rule:
(+) * (+) = (+) (+) : (+) = (+)(+) * ( - ) = ( -) (+) : ( - ) = ( -)(-) * (+) = (+) (-) : (+) = (+)(-) * (-) = (+) (-) : (-) = (+)
The sign rule:
(+) * (+) = (+) (+) : (+) = (+)(+) * ( - ) = ( -) (+) : ( - ) = ( -)(-) * (+) = (+) (-) : (+) = (+)(-) * (-) = (+) (-) : (-) = (+)
Example:
(+5) * ( - 4) = - 20(-5) * ( - 4) = + 20
(+9) * ( + 7) = + 63(-9 ) * ( + 7) = - 63
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
Example:
(-20) : ( - 4) = + 5(-20) : ( + 4) = - 5( +63 ) : ( + 7) = + 63( +63 ) : ( - 7) = - 63
4.- Operations hierarchy4.- 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.
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
Example:
15 – 3 * [ 7 – ( -6 ) : (+3)] =
15 - 3 * [ 7 - (-2)] =
15 – 3 * [ +9] =
15 – 27 =
-12
5.- Activities5.- Activities 1. Use whole numbers, positive or negative,
to express each situation:a) A helicopter flies at 100 m .................b) A diver swims 15 m underwater...........c) A submarine navigates 50 m
underwater....................................................d) An airplane flies 10.000 m above the sea..e) Mt. Everest rises 8.845 m above sea level.
1. Use whole numbers, positive or negative, to express each situation:
a) A helicopter flies at 100 m .................b) A diver swims 15 m underwater...........c) A submarine navigates 50 m
underwater....................................................d) An airplane flies 10.000 m above the sea..e) Mt. Everest rises 8.845 m above sea level.
6.- On the internet6.- On the internet http://bilingualproject.wikispaces.com/Res
ources
http://www.youtube.com/watch?v=0wteb5T2PmM
http://www.mathgoodies.com/lessons/toc_vol3.html
http://bilingualproject.wikispaces.com/Resources
http://www.youtube.com/watch?v=0wteb5T2PmM
http://www.mathgoodies.com/lessons/toc_vol3.html
