Transcript Intro to Integers

Chapter Two
Integers
Section 2.1
Introduction to Integers
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
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-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
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Some signed numbers are integers. Integers
consist of the numbers labeled on the number
line below.
The integers are
{ …, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, …}
zero
negative numbers
-6 -5 -4 -3 -2 -1
positive numbers
0
1
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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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-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
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.
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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 5 6
-2 is 2 because -2 is 2 units from 0.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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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.
0 0
zero
-6  6
a positive number
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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
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5 is the opposite of -5
and
-5 is the opposite of 5.
The opposite of 4
-
(4) =
The opposite of -4
-
is -4 is written as
-4
is 4 is written as
(-4) =
4
- (-4) = 4
If a is a number, then - (-a) = a.
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Helpful Hint
Remember that 0 is neither positive
nor negative. Therefore, the opposite
of 0 is 0.
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