Powerpoint Sept 20

```1-2
Preview
Warm Up
California Standards
Lesson Presentation
1-2
Warm Up
Simplify.
1. |–3|
3
2. –|4|
–4
Write an improper fraction to represent each
mixed number.
6
2
14
55
3. 4 3
4. 7 7
3
7
Write a mixed number to represent each
improper fraction.
5.
12
5
2
2
5
6.
24
9
2
2
3
1-2
California
Standards
2.0 Students understand and use such
operations as taking the opposite, finding the
reciprocal, taking a root, and raising to a fractional
power. They understand and use the rules of
exponents.
1-2
Vocabulary
real numbers
absolute value
opposites
1-2
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.
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.
1-2
Numbers on a Number Line
Add or subtract using a number line.
–4 + (–7)
+ (–7)
Start at 0. Move left to –4.
To add –7, move left 7 units.
11 10 9 8 7 6 5 4 3
–4 + (–7) = –11
–4
2 1 0
1-2
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 -2 -1 0 1 2 3 4 5 6 7 8 9
3 – (–6) = 9
1-2
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 -2 -1 0 1 2 3 4 5 6 7 8 9
–3 + 7 = 4
1-2
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
1-2
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 4 3 2 1 0 1 2
–5 – (–6.5) = 1.5
1-2
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
-6 -5 - 4 -3 -2 -1 0 1 2 3 4 5 6
|–5| = 5
|5| = 5
1-2
1-2
A.
Different signs: subtract the
absolute values.
Use the sign of the number with
the greater absolute value.
B. –6 + (–2)
(6 + 2 = 8)
–8
Same signs: add the absolute values.
Both numbers are negative, so the
sum is negative.
1-2
Check It Out! Example 2
a. –5 + (–7)
(5 + 7 = 12)
–12
values.
Both numbers are negative, so
the sum is negative.
b. –13.5 + (–22.3)
(13.5 + 22.3 = 35.8)
values.
Both numbers are negative, so
–35.8
the sum is negative.
1-2
Check It Out! Example 2c
c. 52 + (–68)
(68 – 52 = 16)
–16
Different signs: subtract the
absolute values.
Use the sign of the number with
the greater absolute value.
1-2
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.
1-2
1-2
To subtract signed numbers, you can use additive
inverses. Subtracting a number is the same as
adding the opposite of the number.
1-2
Subtracting Real Numbers
1-2
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.
(6.7 + 4.1 = 10.8)
–10.8
values.
Both numbers are negative, so
the sum is negative.
1-2
Additional Example 3B: Subtracting Real Numbers
Subtract.
5 – (–4)
5 − (–4) = 5 + 4
(5 + 4 = 9)
9
Both numbers are positive, so
the sum is positive.
1-2
Additional Example 3C: Subtracting Real Numbers
Subtract.
To subtract
Rewrite
of 10.
with a denominator
values .
–5.3
.
Both numbers are negative,
so the sum is negative.
1-2
On many scientific and graphing calculators,
there is one button to express the opposite of a
number and a different button to express
subtraction.
1-2
Check It Out! Example 3a
Subtract.
13 – 21
13 – 21 = 13 + (–21)
(21 – 13 = 8)
Different signs: subtract
absolute values.
–8
Use the sign of the number
with the greater absolute
value.
1-2
Check It Out! Example 3b
Subtract.
To subtract –3 1 , add 3 1 .
2
2
values.
4
Both numbers are positive,
so the sum is positive.
1-2
Check It Out! Example 3c
Subtract.
–14 – (–12)
–14 – (–12) = –14 + 12
(14 – 12 = 2)
–2
Different signs: subtract
absolute values.
Use the sign of the number
with the greater absolute
value.
1-2
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
elevation at
minus
of iceberg
top of iceberg
–
75
–247
75 – (–247)
75 – (–247) = 75 + 247
= 322
absolute values.
1-2
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.
1-2
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
minus
elevation of the
Titanic
550
–
–12,468
550 – (–12,468)
550 – (–12,468) = 550 + 12,468
= 13,018
To subtract –12,468,
absolute values.
1-2
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.
1-2
Lesson Quiz
Add or subtract using a number line.
1. –2 + 9
7
3. –23 + 42
19
2. –5 – (–3) –2
4. 4.5 – (–3.7) 8.2
5.
6. The temperature at 6:00 A.M. was –23°F.
At 3:00 P.M., it was 18°F. Find the difference
in the temperatures. 41°F
```

– Cards

– Cards

– Cards

– Cards

– Cards