2.2 add real numbers day 1-2
TRANSCRIPT
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