Transcript Ch 1-3 Integers and Absolute Value

1-3
Integers and Absolute Value
Evaluating
Algebraic Expressions
California
Standards
NS2.5 Understand the meaning of
the absolute value of a number;
interpret the absolute value as the
distance of the number from zero on a
number line; and determine the
absolute value of real numbers.
Also covered: NS1.1
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Integers and Absolute Value
Evaluating Algebraic Expressions
Integers are the set of whole numbers and their
opposites. Opposites are numbers that are the
same distance from 0 on a number line, but on
opposite sides of 0.
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Integers and Absolute Value
Evaluating Algebraic Expressions
Remember!
Numbers on a number line increase in value as
you move from left to right.
Integers and Absolute Value
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Additional Example 1A: Sports Application
Evaluating
Algebraic
Expressions
Aaron’s
score is 4,
and Felicity’s
score is –1.
Use <, >, or = to compare the scores.
Place the scores on the number line.
–5
–4
–3
–1 < 4
–2
–1
0
1
2
3
4
5
–1 is to the left of 4.
Felicity's score is less than Aaron's score.
Integers and Absolute Value
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Additional Example 1B: Sports Application
List
the golf scores
in order from
the
Evaluating
Algebraic
Expressions
lowest to the highest. The scores are –4,
2, 5, and –3.
Use <, >, or = to compare the scores.
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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Integers and Absolute Value
Check It Out! Example 1A
Evaluating
Expressions
Francie’s
score is Algebraic
–2, and Joaquin's
score is –3.
Use <, >, or = to compare the scores.
Place the scores on the number line.
–5
–4
–3
–3 < –2
–2
–1
0
1
2
3
4
5
–3 is to the left of –2.
Joaquin's score is less than Francie's score.
Integers and Absolute Value
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Check It Out! Example 1B
Evaluating
Algebraic
Expressions
List
the golfer’s scores
in order
from the
lowest to the highest. The scores are –3,
1, 0, and –2.
Use <, >, or = to compare the scores.
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 –3, –2, 0, and 1.
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Integers and Absolute Value
Additional Example 2: Ordering Integers
Write
the integers
8, –5, and Expressions
4 in order
Evaluating
Algebraic
from least to greatest.
Graph the integers on a number line. Then
read them from left to right.
–5
–4
–3 –2
–1
0
1
2
3
4
5
6
7
The integers in order from least to greatest are
–5, 4, and 8.
8
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Integers and Absolute Value
Check It Out! Example 2
Write
the integers
–4, –5, and
4 in order
Evaluating
Algebraic
Expressions
from least to greatest.
Graph the integers on a number line. Then
read them from left to right.
–5
–4
–3 –2
–1
0
1
2
3
4
5
6
7
The integers in order from least to greatest are
–5, –4, and 4.
8
Integers and Absolute Value
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A number’s absolute value is its distance
from 0 on a number line. Absolute value is
Evaluating
Algebraic
always
positive because
distanceExpressions
is always
positive. “The absolute value of –4” is written
as |–4|. Opposites have the same absolute
value.
4 units
–5
–4
|–4| = 4
–3
–2
4 units
–1
0
1
2
3
4
5
|4| = 4
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Integers and Absolute Value
Additional Example 3: Simplifying Absolute-Value
Expressions
Simplify
each expression.
Evaluating
Algebraic Expressions
A. |–3|
3 units
–5
–4
–3
–2
–1
0
1
2
3
4
5
–3 is 3 units from 0, so |–3| = 3.
B. |17 – 6|
|17 – 6| = |11|
= 11
Subtract first: 17 – 6 = 11.
Then find the absolute value:
11 is 11 units from 0.
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Integers and Absolute Value
Additional Example 3: Simplifying Absolute-Value
Expressions
Evaluating
Algebraic
Simplify
each expression.
C. |–8| + |–5|
|–8| + |–5| = 8 + 5
= 13
Expressions
Find the absolute values
first: –8 is 8 units from 0.
–5 is 5 units from 0. Then
add.
D. |5 + 1| + |8 – 6|
|5 + 1| + |8 – 6| = |6| + |2| 5 + 1 = 6, 8 – 6 = 2.
=6+2
=8
6 is 6 units from 0, 2
is 2 units from 0.
Add.
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Integers and Absolute Value
Check It Out! Example 3
Simplify each expression.
Evaluating Algebraic Expressions
A. |–5|
5 units
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5 is 5 units from 0, so |–5| = 5.
B. |12 – 4|
|12 – 4| = |8|
=8
Subtract first: 12 – 4 = 8.
Then find the absolute value:
8 is 8 units from 0.
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Integers and Absolute Value
Check It Out! Example 3
Simplify each expression.
Evaluating Algebraic Expressions
C. |–2| + |–9|
|–2| + |–9| = 2 + 9
= 11
Find the absolute values
first: –2 is 2 units from 0.
–9 is 9 units from 0. Then
add.
D. |3 + 1| + |9 – 2|
|3 + 1| + |9 – 2| = |4| + |7| 3 + 1 = 4, 9 – 2 = 7.
=4+7
= 11
4 is 4 units from 0, 7
is 7 units from 0.
Add.