Integers

1
Integers 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 on Number Lines

• 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 on Number Lines

• Name the set of numbers that is graphed.
• -8, -4, 1, 5, 8

-8, -4, 1, 5, 8
6
Moving on Number Lines

• Movement to the right on the number line is in
  the positive direction (increasing). Do this to
  add a positive .
• Movement to the left on the number line is in the
  negative direction (decreasing). Do this to add
  a negative .
• Make the following moves on the number line.
  Start at 5 and move left 7 integers.
• Where did you stop?

-2
How can we represent this mathematically?
5 (-7) -2
7
You Try It!

• 2) Find each sum using a number line. Place the
  1st on a line, then move to the right or
  left.
• a) 3 7
• b) -1 (-7)
• c) -4 12
• d) -9 5
• e) -6 6

• 1) Graph these pairs of numbers on a number
  line. Write two inequalities comparing the two
  numbers.
• a) -2, 7
• b) -9, -4
• c) 3, 8

8
Problems 1 2
9
Problems 3 4
Show 3 7 using the number line. Start at 3 and
move 7 places to the right. 3 7 10
Show -1 (-7) using a number line. Start at -1
and move 7 places to the left. -1 (-7) -8
10
Problems 5 6
Show 9 5 using the number line. Start at 9
and move 5 places to the right. 9 5 4
Show -6 6 using a number line. Start at -6 and
move 6 places to the left. -6 6 0