Integers

1
Integers and the Number Line
2
Number Lines
A number line is a line with marks on it that
are placed at equal distances apart. One mark
on the number line is usually labeled zero and
then each successive mark to the left or to the
right of the zero represents a particular unit
such as 1 or ½.
On the number line above, each small mark
represents ½ unit and the larger marks represent
1 unit.
3
Number Lines

• Number lines can be used to represent
• Whole numbers The set 0, 1, 2, 3, .
• Positive numbers any number that is greater
  than zero.
• Negative numbers any number that is less than
  zero.
• Integers The set of numbers represented as
• , -3, -2, -1, 0, 1, 2, 3,

The arrows at the ends of the number line show
that the number line continues in both directions
without ending.
4
Graphing Numbers
A number can be graphed on a number line by
placing a point at the appropriate position on
the number line.

• Example
• 4 (blue point)

• integers between 10 and 5 (purple)

5
Graphing Numbers
Name the set of numbers that is graphed.
-8, -4, 1, 5, 8
6
Moving On A Number Line
Movement to the right on the number line is in
the positive direction (increasing). Movement to
the left on the number line is in the negative
direction (decreasing).
Make the following moves on the number line.
Start at 5 and move left 7.
-2
Where did you stop?
How can we represent this mathematically?
5 (-7) -2
7
You Try It
Graph the set of numbers on a number line. Write
two inequalities comparing the two numbers.
1. -2, 7 2. -9, -4 3. 3, 8
Find each sum using a number line.

• 3 7 5. -1 (-7)
• -4 12 7. -9 5
• 8. -6 6

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Problems 1-3
9
Problem 4
3 7
Start at 3 and move 7 places to the right.
3 7 10
10
Problem 5
-1 (-7)
Start at -1 and move 7 places to the left.
-1 (-7) -8
11
Problem 6
-4 12
Start at -4 and move 12 places to the right.
-4 12 8
12
Problem 7
-9 5
Start at -9 and move 5 places to the right.
-9 5 -4
13
Problem 8
-6 6
Start at -6 and move 6 places to the right.
-6 6 0