Transcript Subtracting Integers 1.6

LESSON
1.5 Adding Integers
Scuba Diver. A scuba diver
studying marine life is 4
feet below sea level. From
that depth, the diver
descends 72 feet to the
ocean floor and then rises
61 feet. The diver rests
there to avoid
decompression illness.
Where is the diver relative
to sea level?
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EXAMPLE 1
Find the sum –5 + (–3) using a number line.
SOLUTION
Start at 0. Move 5 units to the left.
Then move 3 more units to the left.
ANSWER The final position is –8, so –5 + (–3) = –8.
Adding Integers - Rules
1. Same sign: Add the absolute values
and use the common sign.
2. Different Signs: Subtract the lesser
absolute value from the greater
absolute value and use the sign of
the number with greater absolute
value.
3. Opposites: The sum of a number
and its opposite is 0.
8 + 12 = 20
-6 + (-4) = -10
5 + (-8) = -3
-11 + 13 = 2
7 + (-7) = 0
GUIDED PRACTICE
for Examples 1 and 2
Use a number line (if needed) to find the sum.
1.
–9 + (–5)
ANSWER
2.
3.
–14
–7 + 4
ANSWER
ANSWER
4.
–3
6 + (–13)
–7
12 + (–9)
ANSWER
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LESSON
1.5 Adding Integers
A scuba diver studying
marine life is 4 feet below
sea level. From that depth,
the diver descends 72 feet
to the ocean floor and then
rises 61 feet. The diver
rests there to avoid
decompression illness.
Where is the diver relative
to sea level?
Solution?
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To answer the question about the position of
the scuba diver, you can find the sum
-4 + (-72) + 61.
Solution:
-4 + (-72) + 61 = -76 + 61 (add -4 and -72.)
= -15
(add -76 and 61)
ANSWER: The diver is -15, so the diver is
15 feet below sea level.
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LESSON
1.6 Subtracting Integers
Earth Science Kick-’em-Jenny is an underwater
volcano in the Caribbean Sea.
Eruptions have caused the volcano to grow. In 1962, the summit elevation of
Kick-’em-Jenny was –235 meters. In 2002, the summit elevation was –182
meters. By how many meters did the elevation of the volcano change? You
will use integer subtraction to answer this question.
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LESSON
1.6 Subtracting Integers
As you can see from the number lines below, the expression 5 – 4 and
5 + (–4) have the same value, 1.
5–4
–1
0
1
2
3
5 + (–4)
4
5
6
–1
0
1
2
3
4
5
6
These equivalent expressions suggest the following rule for subtracting integers.
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LESSON
1.6 Subtracting Integers
Subtracting Integers
Words
To subtract an integer, add its opposite.
Numbers
3 – 7 = 3 + (–7) = –4
Algebra
a – b = a + (–b)
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LESSON
1.6 Subtracting Integers
EXAMPLE
1
Subtracting Integers
4 – 10 = 4 + (–10)
= –6
To subtract 10, add its opposite, –10.
Add 4 and –10.
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LESSON
1.6 Subtracting Integers
EXAMPLE
1
Subtracting Integers
4 – 10 = 4 + (–10)
= –6
7 – (–5) = 7 + 5
= 12
To subtract 10, add its opposite, –10.
Add 4 and –10.
To subtract –5, add its opposite, 5.
Add 7 and 5.
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LESSON
1.6 Subtracting Integers
EXAMPLE
1
Subtracting Integers
4 – 10 = 4 + (–10)
= –6
7 – (–5) = 7 + 5
= 12
–2 – (–9) = –2 + 9
=7
To subtract 10, add its opposite, –10.
Add 4 and –10.
To subtract –5, add its opposite, 5.
Add 7 and 5.
To subtract –9, add its opposite, 9.
Add –2 and 9.
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LESSON
1.6 Subtracting Integers
EXAMPLE
2
Evaluating Variable Expressions
Evaluate the expression when x = –9.
x – (–40)
SOLUTION
x – (–40) = –9 – (–40)
Substitute –9 for x.
= –9 + 40
To subtract –40, add 40.
= 31
Add –9 and 40.
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LESSON
1.6 Subtracting Integers
EXAMPLE
2
Evaluating Variable Expressions
Evaluate the expression when x = –9.
7–x
SOLUTION
7 – x = 7 – (–9)
Substitute –9 for x.
=7+9
To subtract –9, add 9.
= 16
Add 7 and 9.
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LESSON
1.6 Subtracting Integers
Evaluating Change You can use subtraction to find the change in a
variable quantity such as elevation or temperature. Subtract the original
value of the quantity from the value after the change.
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LESSON
1.6 Subtracting Integers
EXAMPLE
3
Evaluating Change
By how many meters did the elevation of the volcano Kick-’em-Jenny
change if the elevation in 1962 was –235 meters and –182 meters in
2002? To answer this question, you can subtract the elevation in 1962
from the elevation in 2002. Write a verbal model.
Change in
elevation
ANSWER
=
Elevation in
2002
–
Elevation in
1962
= –182 – (–235)
Substitute values.
= –182 + 235
To subtract –235, add 235.
= 53
Add –182 and 235.
The difference is 53, so the summit elevation of Kick-’emJenny increased by 53 meters from 1962 to 2002.
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