Download number line

Integers & The
Number Line
Number Lines
-10
-5
0
5
• 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.
10
Number Lines
-10
-5
0
5
Number lines can be used to represent:
A. Whole numbers – the set {0, 1, 2, 3, …}
B. Positive numbers – any number that is greater than zero
C. Negative numbers – any number that is less than zero
D. 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.
10
Graphing on Number Lines
-5
-10
0
5
A number can be graphed on a number line by placing a
point at the appropriate position on the number line.
Example
a)
{4}
(blue point)
b)
{integers between –10 and –5}
(purple)
10
Graphing on Number Lines
-10
-5
0
5
• Name the set of numbers that is graphed.
{-8, -4, 1, 5, 8}
{-8, -4, 1, 5, 8}
10
Moving on Number Lines
-10
-5
0
5
• 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
10
You Try It!
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
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
Problems 1 & 2
-10
-5
2  7
-10
-5
9  4
0
5
10
5
10
7  2
0
4  9
Problems 3 & 4
-5
-10
0
5
10
5
10
Show 3 + 7 using the number line.
Start at 3 and move 7 places to the right.
3 + 7 = 10
-10
-5
0
Show -1 +(-7) using a number line.
Start at -1 and move 7 places to the left.
-1 + (-7) = -8
Problems 5 & 6
-5
-10
0
5
10
5
10
Show –9 + 5 using the number line.
Start at –9 and move 5 places to the right.
–9 + 5 = –4
-5
-10
0
Show -6 + 6 using a number line.
Start at -6 and move 6 places to the left.
-6 + 6 = 0