Pg. 67 (#1-3,10,11,13,16,20,23-

25,42-44)1. Rational number

2. -2

3. Zero is in the set of whole numbers, but

not in the positive integer set.

10.8 > -12

11. -1 > -5

13. -2 > -20-6 -5 -4 -3 -2 -1 0

-12 -8 -4 0 4 8 12

1-3,10,11,13,16,20,23-25,42-44

16. 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

1-3,10,11,13,16,20,23-25,42-44

23. -6, 6

24. 3, 3

25. 18, 18

42. 0.75

43.1

44. 0

l

Add Real Numbers

Section 2.2

P. 74 -79

Properties of Addition

• Commutative Property: - the order in

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 )

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

EXAMPLE 1 Add two integers using a number line

Use a number line to find the sum.

a. – 3 + 6

ANSWER

The final position is 3. So, – 3 + 6 = 3.

EXAMPLE 1

b. – 4 + (– 5)

ANSWER

The final position is – 9. So, – 4 + (– 5) = – 9.

Add two integers using a number line

GUIDED PRACTICE for Example 1

Use a number line to find the sum.

1. 7 +(– 2)

ANSWER

The final position is 3. So, 7 +(– 2) = 5.

Move Units to the left.– 2

End at 5 Start at 7

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

GUIDED PRACTICE for Example 1

Use a number line to find the sum.

3. – 8 + (4)

ANSWER

The final position is – 4. So, – 8 +4 = – 4.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Start at - 8 End at - 4

Move Units to the right.4

GUIDED PRACTICE for Example 1

Use a number line to find the sum.

3. –1 + (– 4)

ANSWER

The final position is – 5. So, – 1 + (– 4) = – 5.

– 7 – 6 – 5 – 4 – 3 – 2 – 1 0

Start at – 1End at – 5

Move Units to the left.– 4

EXAMPLE 2 Add real numbers

Find the sum.

Rule of same signs

Take absolute values.= – (5.3 + 4.9)

= – 10.2 Add.

a. – 5.3 + (– 4.9)

Rule of different signs

Take absolute values. = 19.3 – 12.2

= 7.1 Subtract.

b. 19.3 + (–12.2)

EXAMPLE 3 Identify properties of addition

Statement Property illustrated

a. (x + 9) + 2 = x + (9 + 2) Associative property of

addition

b. 8.3 + (– 8.3) = 0 Inverse property of addition

c. – y + 0.7 = 0.7 + (– y) Commutative property of

addition

3 11 5

4 2

36 12

8

GUIDED PRACTICE for Examples 2, 3 and 4

Find the sum.

Take absolute values.= – 13.1 + 8.7

= – 4.4

7. – 13.1 + 8.7 Rule of different signs

Identify the property being illustrated.

8. 7 + (– 7) = 0 Inverse property of addition

9. – 12 + 0 = – 12 Identity property of addition

10. 4 + 8 = 8 + 4 Commutative property of addition

Subtract.

• Assignment: P. 77 (#1-31)

No Calculator

Copy the problem in

some form on your paper!!

33 pts

possible

2 pts

2 pts

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)

Fill in the blank and name the property

-15 + ____ = -15

(-4 + 5) + 10 = -4 + ( ___ + 10)

27 + _____ = 0

-1/2 + 7 = ____ + -1/2

Evaluate when x = -3

x + 5 + (-7) = ______

(-x) + 5.3 + -7.6 + ______

Evaluate when x = -5

-3 + (-x) + 10.2

P. 77-78 (#32-41, 48, 49, 53-57, 64)

No Calculators – put work on your paper!

I = PRT review question!

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

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

48.

49.

53. 7 degrees

54. 55 ft

55. a) 1.5 diopters

b) -3.75 diopters

c) part ‘b’

56.C

4 0 4

18 ( 18) 0

57.a) your friend

b) No, if you

score 2 double

eagles, you will

have the same

score

64.I = PRT $36

22 points today

33 yesterday

55 total