Transcript mgpia3e_ppt_01_01

Chapter 2
Integers and
Introduction to
Solving Equations
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
2.1
Introduction to
Integers
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Positive and Negative Numbers
Numbers greater than 0 are called positive numbers. Numbers
less than 0 are called negative numbers.
zero
negative numbers
-6 -5 -4 -3 -2 -1
positive numbers
0
1
2
3
4
5
6
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Integers
Some signed numbers are integers.
The integers are
{ …, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, …}
negative numbers
–6 –5 –4 –3 –2 –1
zero
0
positive numbers
1
2
3
4
5
6
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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Negative and Positive Numbers
–3 indicates “negative three.”
3 and +3 both indicate “positive three.”
The number 0 is neither positive nor negative.
zero
negative numbers
–6 –5 –4 –3 –2 –1
positive numbers
0
1
2
3
4
5
6
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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Comparing Integers
We compare integers just as we compare whole
numbers. For any two numbers graphed on a number
line, the number to the right is the greater number and
the number to the left is the smaller number.
<
means
“is less than”
>
means
“is greater than”
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Graphs of Integers
The graph of –5 is to the left of –3, so –5 is less than –3,
written as –5 < –3 .
We can also write –3 > –5.
Since –3 is to the right of –5, –3 is greater than –5.
–6 –5 –4 –3 –2 –1 0
1
2
3
4
5
6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Absolute Value
The absolute value of a number is the number’s distance
from 0 on the number line. The symbol for absolute
value is | |.
2 is 2 because 2 is 2 units from 0.
–6 –5 –4 –3 –2 –1 0 1 2 3 4
2 is 2 because –2 is 2 units from 0.
5
6
–6 –5 –4 –3 –2 –1
5
6
0
1
2
3
4
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Helpful Hint
Since the absolute value of a number is that number’s
distance from 0, the absolute value of a number is
always 0 or positive. It is never negative.
6 =6
0 =0
zero
a positive number
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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Opposite Numbers
Two numbers that are the same distance from 0 on the
number line but are on the opposite sides of 0 are called
opposites.
5 units
–6 –5 –4 –3 –2 –1
5 units
0
1
2
3
4
5
6
5 and –5 are opposites.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Opposite Numbers
5 is the opposite of –5 and –5 is the opposite of 5.
The opposite of 4 is –4 is written as
–(4) = –4
The opposite of –4
is 4 is written as
–(–4) =
4
–(–4) = 4
If a is a number, then –(–a) = a.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Helpful Hint
Remember that 0 is neither positive nor
negative. Therefore, the opposite of 0 is 0.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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