Powerpoint Sept 20

1
Preview
Warm Up
California Standards
Lesson Presentation
2
Warm Up Simplify. 1.
4
4
2.
3
3
Write an improper fraction to represent
each mixed number.
6
2
3.
4
4.
7
3
7
Write a mixed number to represent each improper
fraction.
12
24
5.
6.
5
9
3

4
Vocabulary
real numbers absolute value opposites additive
inverse
5
The set of all numbers that can be represented on
a number line are called real numbers. You can
use a number line to model addition and
subtraction of real numbers. Addition To model
addition of a positive number, move right. To
model addition of a negative number, move
left. Subtraction To model subtraction of a
positive number, move left. To model subtraction
of a negative number, move right.
6
Additional Example 1A Adding and Subtracting
Numbers on a Number Line
Add or subtract using a number line.
4 (7)
Start at 0. Move left to 4.
To add 7, move left 7 units.
(7)
4
4 (7) 11
7
Additional Example 1B Adding and Subtracting
Numbers on a Number Line
Add or subtract using a number line.
3 (6)
Start at 0. Move right to 3.
To subtract 6, move right 6 units.
(6)
3
3 (6) 9
8
Check It Out! Example 1a
Add or subtract using a number line.
3 7
Start at 0. Move left to 3.
To add 7, move right 7 units.
7
3
3 7 4
9
Check It Out! Example 1b
Add or subtract using a number line.
3 7
Start at 0. Move left to 3.
To subtract 7, move left 7 units.
7
3
11
10
9
8
7
6
5
4
3
2
1
0
3 7 10
10
Check It Out! Example 1c
Add or subtract using a number line.
Start at 0. Move left to 5.
5 (6.5)
To subtract 6.5, move right 6.5 units.
(6.5)
5
8
7
6
5
2
1
0
1
2
4
3
5 (6.5) 1.5
11
The absolute value of a number is the distance
from zero on a number line. The absolute value of
5 is written as 5.
5 units
5 units
-
-
-
-
-
2
1
0
1
5
6
6
5
4
3
-
2
3
4
5 5
5 5
12
(No Transcript)
13
Additional Example 2 Adding Real Numbers
Add.
A.
Different signs subtract the absolute values.
Use the sign of the number with the greater
absolute value.
B.
6 (2)
(6 2 8)
Same signs add the absolute values.
8
Both numbers are negative, so the sum is negative.
14
Check It Out! Example 2
Add.
5 (7)
a.
Same signs add the absolute values.
(5 7 12)
12
Both numbers are negative, so the sum is negative.
13.5 (22.3)
b.
Same signs add the absolute values.
(13.5 22.3 35.8)
Both numbers are negative, so the sum is negative.
35.8
15
Check It Out! Example 2c
Add.
c. 52 (68)
(68 52 16)
Different signs subtract the absolute values.
Use the sign of the number with the greater
absolute value.
16
16
Two numbers are opposites if their sum is 0. A
number and its opposite are additive inverses and
are the same distance from zero. They have the
same absolute value.
17
(No Transcript)
18
To subtract signed numbers, you can use additive
inverses. Subtracting a number is the same as
adding the opposite of the number.
19
Subtracting Real Numbers
20
Additional Example 3A Subtracting Real Numbers
Subtract.
6.7 4.1
6.7 4.1 6.7 (4.1)
To subtract 4.1, add 4.1.
Same signs add absolute values.
(6.7 4.1 10.8)
Both numbers are negative, so the sum is negative.
10.8
21
Additional Example 3B Subtracting Real Numbers
Subtract.
5 (4)
5 - (4) 5 4
To subtract 4, add 4.
Same signs add absolute values.
(5 4 9)
9
Both numbers are positive, so the sum is positive.
22
Additional Example 3C Subtracting Real Numbers
Subtract.
Same signs add absolute values .
Both numbers are negative, so the sum is negative.
5.3
23
(No Transcript)
24
Check It Out! Example 3a
Subtract.
13 21
13 21
To subtract 21, add 21.
13 (21)
Different signs subtract absolute values.
(21 13 8)
Use the sign of the number with the greater
absolute value.
8
25
Check It Out! Example 3b
Subtract.
Same signs add absolute values.
Both numbers are positive, so the sum is positive.
4
26
Check It Out! Example 3c
Subtract.
14 (12)
14 (12) 14 12
To subtract 12, add 12.
(14 12 2)
Different signs subtract absolute values.
Use the sign of the number with the greater
absolute value.
2
27
Additional Example 4 Oceanography Application
An iceberg extends 75 feet above the sea. The
bottom of the iceberg is at an elevation of 247
feet. What is the height of the iceberg?
Find the difference in the elevations of the top
of the iceberg and the bottom of the iceberg.
elevation at bottom of iceberg
elevation at top of iceberg
minus

247
75
75 (247)
75 (247) 75 247
To subtract 247, add 247.
Same signs add the absolute values.
322
28
Additional Example 4 Continued
An iceberg extends 75 feet above the sea. The
bottom of the iceberg is at an elevation of 247
feet. What is the height of the iceberg?
The height of the iceberg is 322 feet.
29
Check It Out! Example 4
What if? The tallest known iceberg in the North
Atlantic rose 550 feet above the ocean's surface.
How many feet would it be from the top of the
tallest iceberg to the wreckage of the Titanic,
which is at an elevation of 12,468 feet?
elevation at top of iceberg
elevation of the Titanic
minus

550
12,468
550 (12,468)
To subtract 12,468, add 12,468.
550 (12,468) 550 12,468
13,018
Same signs add the absolute values.
30
Check It Out! Example 4 Continued
What if? The tallest known iceberg in the North
Atlantic rose 550 feet above the ocean's surface.
How many feet would it be from the top of the
tallest iceberg to the wreckage of the Titanic,
which is at an elevation of 12,468 feet?
Distance from the top of the iceberg to the
Titanic is 13,018 feet.
31
Lesson Quiz
Add or subtract using a number line.
2. 5 (3)
2
1. 2 9
7
Add or subtract.
3. 23 42
19
4. 4.5 (3.7)
8.2
5.
6. The temperature at 600 A.M. was 23F. At
300 P.M., it was 18F. Find the difference in
the temperatures.
41F