The document contains information about rational numbers including integers, fractions, and decimals. It provides examples of adding and subtracting rational numbers on a number line. Key points include: - Rational numbers include integers, fractions, and decimals. - Zero is a whole number but not a positive integer. - Examples are given of comparing rational numbers and performing addition and subtraction on a number line. - Properties of addition like commutativity and inverses are illustrated.

1. Pg. 67 (#1-3,10,11,13,16,20,23-25,42-44) Rational number -2 Zero is in the set of whole numbers, but not in the positive integer set. 8 > -12 -1 > -5 13. -2 > -20 -12 -8 -4 0 4 8 12 -6 -5 -4 -3 -2 -1 0

2. 1-3,10,11,13,16,20,23-25,42-44 0.25 rational -0.5 rational 0.2 rational -2 integer & rational 20. -2.7 rational ½ rational 0.3 rational -7 rat. & integer -7, -2.7, 0.3, 1/2 -2, -0.5, 0.2, 0.25

3. 1-3,10,11,13,16,20,23-25,42-44 -6, 6 3, 3 18, 18 42. 0.75 1 0

4. l

5. Add Real Numbers Section 2.2 P. 74 -79

6. Properties of Addition Commutative Property: - the orderin which two numbers are added does NOT change the sum. 4 + -8 = -8 + 4 Associative Property: The way you group three numbers when adding does NOT change the sum. (-5 + 8) + 9 = -5 + ( 8 + 9 )

7. Properties of Addition Identity Property: The sum of a number and zero is always the number. -9 + 0 = -9 x + 0 = x Inverse Property: The sum of a number and its opposite is 0. a + (- a ) = 0 -4 + 4 = 0

8. ANSWER The final position is3. So, –3+6 = 3. EXAMPLE 1 Add two integers using a number line Use a number line to find the sum. a.– 3 + 6

9. ANSWER The final position is–9. So, –4+ (–5) =–9. EXAMPLE 1 Add two integers using a number line b.– 4 + (– 5)

10. Units to the left. – 2 Move Start at 7 End at 5 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 ANSWER The final position is3. So, 7+(– 2) = 5. for Example 1 GUIDED PRACTICE Use a number line to find the sum. 1. 7 +(– 2)

11. Units to the left. – 11 Move End at -3 Start at 8 -11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 ANSWER The final position is– 3. So, 8 +(– 11) = – 3. for Example 1 GUIDED PRACTICE Use a number line to find the sum. 2. 8 +(– 11)

12. Units to the right. Move 4 End at - 4 Units to the right. – 2 Move Start at - 8 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 ANSWER The final position is– 4. So, – 8 +4 = – 4. for Example 1 GUIDED PRACTICE Use a number line to find the sum. 3.– 8 + (4)

13. Units to the left. – 4 Move Units to the right. – 2 Move Start at – 1 End at –5 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 ANSWER The final position is– 5. So, – 1 + (– 4) = – 5. for Example 1 GUIDED PRACTICE Use a number line to find the sum. 3.–1 + (– 4)

14. EXAMPLE 2 Add real numbers Find the sum. a.– 5.3 + (– 4.9) Rule of same signs = – (5.3 + 4.9) Take absolute values. = – 10.2 Add. b. 19.3 + (–12.2) Rule of different signs =19.3 –12.2 Take absolute values. =7.1 Subtract.

15. Identify properties of addition EXAMPLE 3 Property illustrated Statement Associative property of addition a.(x + 9) + 2 = x + (9 + 2) b.8.3 + (– 8.3) = 0 Inverse property of addition c. – y + 0.7 = 0.7 + (– y) Commutative property of addition

16. Solve a multi-step problem EXAMPLE 4 BUSINESS The table shows the annual profits of two piano manufacturers. Which manufacturer had the greater total profit for the three years?

17. Solve a multi-step problem EXAMPLE 4 SOLUTION STEP1 Calculate the total profit for each manufacturer. Manufacturer A: Total profit = – 5.8 + 8.7 + 6.8 = – 5.8 + (8.7 + 6.8) = – 5.8 + 15.5 = 9.7

18. ANSWER Manufacturer A had the greater total profit. Solve a multi-step problem EXAMPLE 4 Manufacturer B: = – 6.5 + 7.9 + 8.2 Total profit = – 6.5 + (7.9 + 8.2) = – 6.5 + 16.1 = 9.6 STEP2 Compare the total profits: 9.7 > 9.6.

20. for Examples 2, 3 and 4 GUIDED PRACTICE Find the sum. 7. – 13.1 + 8.7 Rule of different signs = – 13.1 + 8.7 Take absolute values. = – 4.4 Subtract. Identify the property being illustrated. Inverse property of addition 8.7 + (– 7) = 0 9.– 12 + 0 = – 12 Identity property of addition 10. 4+ 8 = 8 + 4 Commutative property of addition

21. Assignment: P. 77 (#1-31) No Calculator Copy the problem in some form on your paper!!

23. 2 pts 2 pts 33 pts possible

24. Day two of 2.2 Review rules What is the best way to do these problems? Why? -3 2/3 + (5 ¼ + - 6 1/3) (-3.5 + 0.08) + 0.92 (-3.9 + 7) + (-4 + 3.9)

25. Fill in the blank and name the property-15 + ____ = -15 (-4 + 5) + 10 = -4 + ( ___ + 10) 27 + _____ = 0 -1/2 + 7 = ____ + -1/2

26. Evaluate when x = -3 x + 5 + (-7) = ______ (-x) + 5.3 + -7.6 + ______

27. Evaluate when x = -5 -3 + (-x) + 10.2

28. 77-78 (#32-41, 48, 49, 53-57, 64) No Calculators – put work on your paper! I = PRT review question!

29. P 77-78 32-41, 48,49, 53-57, 64

30. P 77-78 32-41, 48,49, 53-57, 64 48. 49. 7 degrees 55 ft a) 1.5 diopters b) -3.75 diopters c) part ‘b’ C a) your friend b) No, if you score 2 double eagles, you will have the same score I = PRT $36 22 points today 33 yesterday 55 total