Transcript 1-2 - Plain Local Schools

Addingand
andSubtracting
SubtractingReal Numbers
Adding
1-2
1-2 Real Numbers
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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
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2
2
5
6. 24
9
2
2
3
1-2 Adding and Subtracting Real Numbers
Objectives
Add real numbers.
Subtract real numbers.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Vocabulary
absolute value
opposites
additive inverse
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
All the numbers 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.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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)
11 10 9 8 7 6 5 4 3
–4+ (–7) = –11
Holt Algebra 1
–4
2 1 0
1-2 Adding and Subtracting Real Numbers
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 -2 -1 0 1 2 3 4 5 6 7 8 9
3 – (–6) = 9
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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.
–3
–7
11 10 9 8 7 6 5 4 3 2 1 0
–3 – 7 = –10
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 1c
Add or subtract using a number line.
–5 – (–6.5)
Start at 0. Move left to –5.
To subtract negative 6.5 move
right 6.5 units.
–5
– (–6.5)
8 7 6 5 4 3 2 1 0 1 2
–5 – (–6.5) = 1.5
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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
Holt Algebra 1
|5| = 5
1-2 Adding and Subtracting Real Numbers
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Example 2A: Adding Real Numbers
Add.
When the signs of numbers are
different, find the difference of the
absolute values:
Use the sign of the number with
the greater absolute value.
The sum is negative.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Example 2B: Adding Real Numbers
Add.
y + (–2) for y = –6
y + (–2) = (–6) + (–2)
(–6) + (–2)
–8
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First substitute –6 for y.
When the signs are the same,
find the sum of the absolute
values: 6 + 2 = 8.
Both numbers are negative,
so the sum is negative.
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 2a
Add.
–5 + (–7)
–5 + (–7) = 5 + 7
5 + 7 = 12
–12
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When the signs are the same,
find the sum of the absolute
values.
Both numbers are negative, so
the sum is negative.
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 2b
Add.
–13.5 + (–22.3)
–13.5 + (–22.3)
13.5 + 22.3
–35.8
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When the signs are the same,
find the sum of the absolute
values.
Both numbers are negative so,
the sum is negative.
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 2c
Add.
x + (–68) for x = 52
First substitute 52 for x.
x + (–68) = 52 + (–68)
When the signs of the
numbers are different, find the
difference of the absolute
values.
68 – 52
–16
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Use the sign of the number
with the greater absolute
value.
The sum is negative.
1-2 Adding and Subtracting Real Numbers
Two numbers are opposites if their
sum is 0. A number and its opposite
are on opposite sides of zero on a
number line, but are the same
distance from zero. They have the
same absolute value.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
A number and its opposite are additive inverses.
To subtract signed numbers, you can use additive
inverses.
Subtracting 6 is the same
as adding the inverse of 6.
Additive inverses
11 – 6 = 5
11 + (–6) = 5
Subtracting a number is the same as adding the
opposite of the number.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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.
When the signs of the numbers
are the same, find the sum of the
absolute values: 6.7 + 4.1 = 10.8.
= –10.8
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Both numbers are negative, so
the sum is negative.
1-2 Adding and Subtracting Real Numbers
Example 3B: Subtracting Real Numbers
Subtract.
5 – (–4)
5 − (–4) = 5 + 4
9
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To subtract –4 add 4.
Find the sum of the absolute
values.
1-2 Adding and Subtracting Real Numbers
Example 3C: Subtracting Real Numbers
Subtract.
First substitute
To subtract
Rewrite
of 10.
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for z.
, add
.
with a denominator
1-2 Adding and Subtracting Real Numbers
Example 3C Continued
When the signs of the numbers are
the same, find the sum of the
absolute values:
.
Write the answer in the simplest form.
Both numbers are negative, so the
sum is negative.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 3a
Subtract.
13 – 21
13 – 21 = 13 + (–21)
To subtract 21 add –21.
When the signs of the
numbers are different, find
the difference of the absolute
values: 21 – 13 = 8.
–8
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Use the sign of the number
with the greater absolute
value.
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 3b
Subtract.
4
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To subtract –3 1 add 3 1 .
2
2
When the signs of the
numbers are the same, find
the sum of the absolute
values: 3 1 + 1 = 4.
2
2
Both numbers are positive
so, the sum is positive.
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 3c
Subtract.
x – (–12) for x = –14
x – (–12) = –14 – (–12)
–14 + (12)
First substitute –14 for x.
To subtract –12, add 12.
When the signs of the
numbers are different, find
the difference of the absolute
values: 14 – 12 = 2.
–2
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Use the sign of the number
with the greater absolute
value.
1-2 Adding and Subtracting Real Numbers
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
top of iceberg
75
Minus
–
elevation at bottom
of iceberg
–247
75 – (–247)
75 – (–247) = 75 + 247
To subtract –247, add 247.
Find the sum of the
= 322
absolute values.
The height of the iceberg is 322 feet.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Check It Out! Example 4
What if…? The tallest known iceberg in the North
Atlantic rose 550 feet above the oceans 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
550
Minus
–
elevation of the
Titanic –12,468
550 – (–12,468)
To subtract –12,468,
550 – (–12,468) = 550 + 12,468 add 12,468.
Find the sum of the
= 13,018
absolute values.
Distance from the iceberg to the Titanic is 13,018 feet.
Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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 6:00 A.M. was –23°F.
At 3:00 P.M. it was 18°F. Find the difference
in the temperatures. 41°F
Holt Algebra 1