Transcript 1-3 Integers and Absolute Value

1-3
Integers and Absolute Value
Warm Up
Problem of the Day
Lesson Presentation
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1-3 Integers and Absolute Value
Warm Up
Evaluate each expression for the given
values of the variables.
1.
2.
3.
4.
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2x – 3y for x = 17 and y = 6
16
5(x + 3) + 4y for x = 3 and y = 2 38
6.9(x – 2.7) + 7.1 for x = 5.1
23.66
5x – 4y for x = 0.3 and y = 0.2
0.7
1-3 Integers and Absolute Value
Problem of the Day
Janie’s score is 3 times the sum of 1 and
Maria’s score on the final exam. Maria
scored 12 points. Whose score is highest?
Janie
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1-3 Integers and Absolute Value
Learn to compare and order integers and to
evaluate expressions containing absolute
value.
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1-3 Integers and Absolute Value
Vocabulary
integer
opposite
additive inverse
Absolute value
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1-3 Integers and Absolute Value
Integers are the set of whole numbers and their
opposites. On a number line, opposites, or
additive inverses, are numbers that are the
same distance from 0, but on opposite sides of 0
on the number line.
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Course
1-3 Integers and Absolute Value
Remember!
Numbers on a number line increase in value as
you move from left to right.
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1-3 Integers and Absolute Value
Additional Example 1A: Sports Application
Use <, >, or = to compare the scores.
Aaron’s score is 4, and Felicity’s score is –1.
Place the scores on the number line.
•
–5
–4
–3
–1 < 4
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–2
–1
•
0
1
2
3
–1 is to the left of 4.
4
5
1-3 Integers and Absolute Value
Additional Example 1B: Sports Application
Use <, >, or = to compare the scores.
List the golf scores in order from the
lowest to the highest. The scores are –4,
2, 5, and –3.
Place the scores on the number line and read
them from left to right.
•
–5
–4
•
•
–3
–2
–1
0
1
2
•
3
4
5
In order from the lowest score to the highest
score, the scores are –4, –3, 2, and 5.
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1-3 Integers and Absolute Value
Check It Out: Additional Example 1A
Use <, >, or = to compare the scores.
France’s score is –2, and Juaqin’s score is –3.
Place the scores on the number line.
–5
–4
•
•
–3
–2
–3 < –2
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–1
0
1
2
3
4
–3 is to the left of –2.
5
1-3 Integers and Absolute Value
Check It Out: Additional Example 1B
Use <, >, or = to compare the scores.
List the golfer’s scores in order from the
lowest to the highest. The scores are –3,
1, 0, and –2.
Place the scores on the number line and read
them from left to right.
–5
–4
•
•
–3
–2
–1
•
•
0
1
2
3
4
5
In order from the lowest score to the
highest score, they are –3, –2, 0, and 1.
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1-3 Integers and Absolute Value
Additional Example 2: Ordering Integers
Write the integers 8, –5, and 4 in order from
t least to greatest.
8 > –5, 8 > 4, and –5 < 4
Compare each pair of
integers.
–5, 4, and 8.
–5 is less than both
4 and 8.
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1-3 Integers and Absolute Value
Check It Out: Additional Example 2
Write the integers 7, –12, and 13 in order
from least to greatest.
13 > –12, 13 > 7, and
–12 < 7
Compare each pair of
integers.
–12, 7, and 13.
–12 is less than both
7 and 13.
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1-3 Integers and Absolute Value
A number’s absolute value is its distance
from 0 on a number line. Absolute value is
always positive because distance is always
positive. “The absolute value of –4” is written
as –4 . Additive inverses have the same
absolute value.
4 units
–5
–4
–3
–2
–4 = 4 = 4.
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4 units
–1
0
1
2
3
4
5
Both 4 and –4 are 4 units from 0.
1-3 Integers and Absolute Value
Additional Example 3: Finding Additive Inverses
Find the additive inverse of each integer.
A. 6
–6
–6 is the same distance from 0 as 6 is on the
number line.
B. –14
14 14 is the same distance from 0 as –14 is on
the number line.
C. 0.5
–0.5 –0.5 is the same distance from 0 as 0.5 is
on the number line.
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1-3 Integers and Absolute Value
Check It Out: Additional Example 3
Find the additive inverse of each integer.
A. 12
–12 –12 is the same distance from 0 as 12 is on
the number line.
B. –1.9
1.9 1.9 is the same distance from 0 as –1.9 is
on the number line.
C. 1
–1
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–1 is the same distance from 0 as 1 is on
the number line.
1-3 Integers and Absolute Value
Additional Example 4: Evaluating Absolute-Value
Expressions
Evaluate each expression.
A. –8 + –5
–8 = 8
–8 is 8 units from 0.
–5 = 5
–5 is 5 units from 0.
8 + 5 = 13
B. 5 – 6
–1 = 1
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–1 is 1 units from 0.
1-3 Integers and Absolute Value
Check It Out: Additional Example 4
Evaluate each expression.
A. –2 + -9
–2 = 2
–2 is 2 units from 0.
–9 = 9
–9 is 9 units from 0.
2 + 9 = 11
B. 1 – 1
0 =0
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0 is 0 units from 0.
1-3 Integers and Absolute Value
Lesson Quiz
Write the integers in order from least to greatest.
1. –17, –26, 23
–26, –17, 23
2. 0, 5, –4
–4, 0, 5
Evaluate each expression.
3. The sum of 3 and the additive inverse of –8
4. – –4 + –2
11
-2
5. At the end of the course, your golf score was –2.
Your friend’s score was 7. What is the difference
between your scores? 9
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