1. 1.1 Positive and Negative Numbers 1.2 Addition with Negative Numbers 1.3 Subtraction with Negative Numbers

2. 1.1- Definition  Positive number – a number greater than zero. 0 12 3 4 5 6

3. Definition  Negative number – a number less than zero. 0 1 2 3 456 -2-3-4 -5 -6

4. Definition  Opposite Numbers – numbers that are the same distance from zero in the opposite direction 0 1 2 3 456 -2-3-4 -5 -6

5. Definition  Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero. 7 opposite -7

6. Definition  Absolute Value – The size of a number with or without the negative sign. The absolute value of 9 or of –9 is 9.

7. Negative Numbers Are Used to Measure Temperature

8. Negative Numbers Are Used to Measure Under Sea Level 0 10 20 30 -10 -20 -30 -40 -50

9. Negative Numbers Are Used to Show Debt Let’s say you bought a car but had to get a loan from the bank for $5,000. When counting all your money you would add in -$5,000 to show you still owe the bank $5,000.

10. Hint  If you don’t see a negative or positive sign in front of a number it is positive. 9 +

11. Pg 93 #28, 30, 32, 34 28) -4 -40 Place either between each of the following pairs of numbers so that the statement is true. 30) |8| -2 33) |-2| |-7| 34) |-3| |-1| < > > >

12. Pg 93 #40, 46, 50, 64, 68  Find each of the following absolute values. 40) |-9| 46) |-350| 50) |457|  Simplify each of the following. 64) -(-5) 68) -|-5| 9 350 457 5 -5

13. 1.2 -Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 -9 + (-5) = -14

14.  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.  Rule #2 – If the signs are different pretend the signs aren’t there.  Subtract the smaller from the larger one  put the sign of the one with the larger absolute value in front of your answer.

15. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there.  Subtract the smaller from the larger one  put the sign of the one with the larger absolute value in front of your answer. -14+ 7 = 14 - 7 = 7 Larger abs. value Answer = - 7

16. One Way to Add Integers Is With a Number Line When the number is positive, count to the right. When the number is negative, count to the left. +- 0 1 2 3 456 -2-3-4 -5 -6

17. One Way to Add Integers Is With a Number Line + - +3 + (-5) = -2 0 1 2 3 456 -2-3-4 -5 -6

18. One Way to Add Integers Is With a Number Line + - +6 + (-4) = +2 0 1 2 3 456 -2-3-4 -5 -6

19. + - +3 + (-7) = -4 0 1 2 3 456 -2-3-4 -5 -6 One Way to Add Integers Is With a Number Line

20. - + -3 + 7 = 4 0 1 2 3 456 -2-3-4 -5 -6

21. Solve the Problems  Pg 101-102  33, 44, 58, 68, 72

22. Pg 101-102 33, 44, 58, 68, 72, 79 33) -375 + 409 44) -27 + (-56) + (-89) 58) (-11 + 5) + (-3 + 2) 72) What number do you add to -5 to get -8? Rule #2: 409 – 375 = 34 Rule #1: 27 + 56 + 89 =172= -172 Rule #2: (11 – 5) = 6 = -6 Rule #2: (3 - 2) = 1 = -1 Order of operations: Rule #1: -6 + (-1) = -7 n + (-5) = -8 n = -3 -3 + (-5) = -8

23. 1.3 Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9!

24. 1.3 Integer Subtraction Rule If a and b represent any two numbers, then it is always true that a – b = a + (-b) (Change the signs and add) 2 – 7 is the same as 2 + (-7) Rule #2: 7 – 2 = 5 = -5

25. Table in Example 3

26. Here are some more examples. 12 – (-8) 12 + (+8) 12 + 8 = 20 -67 – (-17) -67 + (+17) -67 + 17 = -50

27. Solve the Problems  Pg 109-110 24, 27, 41, 44, 46, 61, 62

28. Pg 109-110 #24, 27, 41, 44, 46 24) -86 – 31 27) -35 – (-14) 41) -900 + 400 – (-100) 44) Subtract 8 from -2. 45) Find the difference of -5 and -1. (-86) + (-31) = -117 (-35) + 14 = -21 -900 + 400 + 100 = -900 + 500 = -400 -2 – 8 = -2 + (-8) = -10 -5 – (-1) = -5 + 1 = -4

29. Pg 110 #61, 62 61) On Monday, the temperature reached a high of 28 degrees above 0. That night it dropped to 16 degrees below 0. What is the difference between the high and the low temperature for Monday? 61) A gambler loses $35 playing poker one night and then loses another $25 the next night. Express the situation with numbers. How much did the gambler lose? 28 – (-16) = 28 + 16 = 44 deg. -35 – 25 = -35 + (-25) = -60