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# The Whole Numbers

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### The Whole Numbers

1. 1. THE WHOLE NUMBERS Z +3 -5 -9 . . .
2. 2. <ul><li>From the hot-air balloon, the radar falls down into the water. What is the distance from the hot-air balloon to the radar? </li></ul><ul><li>What is the distance from the helicopter to the subamarine? </li></ul>
3. 3. <ul><li>How many floors are there between the shop (0) and the parking (-2) ? </li></ul><ul><li>And how many floors are there between the restaurant (1) and the gymnasium (-1) ? </li></ul>
4. 4. <ul><li>What’s the avg. temperature in the Sahara Desert? </li></ul><ul><li>What’s the avg. temperature in Alaska? </li></ul>
5. 5. 1.- The Whole Numbers Set . <ul><li>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,...) </li></ul><ul><li>We need more numbers. </li></ul><ul><li>We must add new numbers to the set of the Natural Numbers, the N egative Numbers {..., -3, -2, -1} </li></ul><ul><li>All these numbers are called The Whole Numbers Z = {..., -3, -2, -1, 0, 1, 2, ...} </li></ul>
6. 6. <ul><li>The sign of a whole number </li></ul><ul><li>If the whole number is a natural number, we can writte it with the sign + before it. Ex: +5, +7 </li></ul><ul><li>The sign is positive </li></ul><ul><li>If the whole number is not a natural number, we must writte it with the sign – before it: </li></ul><ul><li>Ex: -5, -9 </li></ul><ul><li>The sign is negative </li></ul>
7. 7. <ul><li>The absolute value of a whole number. </li></ul><ul><li>The absolute value of a whole number is the same number but always positive. </li></ul><ul><li>Ex: I -7 I = 7 </li></ul><ul><li>I 4 I = 4 </li></ul><ul><li>The opposite number of a whole number. </li></ul><ul><li>The opposite number of a whole number is the same number but with the opposite sign. </li></ul><ul><li>Ex: The opposite of 5 = -5 </li></ul><ul><li>The opposite of -3 = 3 </li></ul>
8. 8. 2.- Addition and Subtraction <ul><li>1 case : Both numbers have the same sign </li></ul><ul><li>We add the absolute values and we put the sign. Ex: 5 + 2 = 7 </li></ul><ul><li>-2 -10 = -10 </li></ul><ul><li>2 case : The numbers have different signs </li></ul><ul><li> We subtract the absolute values and we put the sign of the greatest. Ex: -2 + 7 = 5 </li></ul><ul><li> 4 - 9 = -5 </li></ul>
9. 9. 3.- Multiplication and Division <ul><li>The sign rule: </li></ul><ul><li>(+) * (+) = (+) (+) : (+) = (+) </li></ul><ul><li>(+) * ( - ) = ( -) (+) : ( - ) = ( -) </li></ul><ul><li>(-) * (+) = (+) (-) : (+) = (+) </li></ul><ul><li>(-) * (-) = (+) (-) : (-) = (+) </li></ul>
10. 10. <ul><li>Example: </li></ul><ul><li> (+5) * ( - 4) = - 20 </li></ul><ul><li>(-5) * ( - 4) = + 20 </li></ul><ul><li>(+9) * ( + 7) = + 63 </li></ul><ul><li>(-9 ) * ( + 7) = - 63 </li></ul>
11. 11. <ul><li>Example: </li></ul><ul><li>(-20) : ( - 4) = + 5 </li></ul><ul><li>(-20) : ( + 4) = - 5 </li></ul><ul><li>( +63 ) : ( + 7) = + 63 </li></ul><ul><li>( +63 ) : ( - 7) = - 63 </li></ul>
12. 12. 4.- Operations hierarchy <ul><li>1 st . First, solve the parenthesis </li></ul><ul><li>2 nd . After that, solve the multiplication and division operations. </li></ul><ul><li>3 rd . Finally, solve the addition and the subtraction operations. </li></ul>
13. 13. <ul><li>Example: </li></ul><ul><li>15 – 3 * [ 7 – ( -6 ) : (+3)] = </li></ul><ul><li>15 - 3 * [ 7 - (-2)] = </li></ul><ul><li>15 – 3 * [ +9] = </li></ul><ul><li>15 – 27 = </li></ul><ul><li>-12 </li></ul>
14. 14. 5.- Activities <ul><li>1. Use whole numbers, positive or negative, to express each situation: </li></ul><ul><li>A helicopter flies at 100 m ................. </li></ul><ul><li>A diver swims 15 m underwater........... </li></ul><ul><li>A submarine navigates 50 m underwater.................................................... </li></ul><ul><li>An airplane flies 10.000 m above the sea.. </li></ul><ul><li>Mt. Everest rises 8.845 m above sea level. </li></ul>
15. 15. 6.- On the internet <ul><li>http://bilingualproject.wikispaces.com/Resources </li></ul><ul><li>http://www.youtube.com/watch?v=0wteb5T2PmM </li></ul><ul><li>http://www.mathgoodies.com/lessons/toc_vol3.html </li></ul>