Integers 11-1

1
Integers 11-1

• I can identify positive and negative integers
• SPI 6.2.8

2
Positive numbers are greater than 0. They may be
written with a positive sign (), but they are
usually written without it.
Negative numbers are less than 0. They are always
written with a negative sign ().
3
Additional Example 1 Identifying Positive and
Negative Numbers in the Real World Name a
positive or negative number to represent each
situation. A. a jet climbing to an altitude of
20,000 feet B. taking 15 out of the bank
Positive numbers can represent climbing or rising.
20,000
Negative numbers can represent taking out or
withdrawing.
15
4
Check It Out Example 1 Name a positive or
negative number to represent each situation. A.
300 feet below sea level B. a hiker hiking to
an altitude of 4,000 feet
Negative numbers can represent values below or
less than a certain value.
300
Positive numbers can represent climbing or rising.
4,000
5
Representing Integers 11-2

• SPI 6.1.3
• I CAN use pictorial, concrete, and symbolic
  representation for integers.

6
You can graph positive and negative numbers on a
number line.
On a number line, opposites are the same distance
from 0 but on different sides of 0.
Integers are the set of all whole numbers and
their opposites.
Opposites
Positive Integers
Negative Integers
0 is neither negative nor positive.
7
The absolute value of an integer is its distance
from 0 on a number line. The symbol for absolute
value is .
3 3 3 3
lt--3 units--gt lt--3 units--gt

• Absolute values are never negative.
• Opposite integers have the same absolute value.
• 0 0

8
Additional Example 3A Finding Absolute Value Use
a number line to find the absolute value of each
integer. A. 2
2 is 2 units from 0, so 2 2
2
9
Additional Example 3B Finding Absolute Value Use
a number line to find the absolute value of each
integer. B. 8
8 is 8 units from 0, so 8 8
8
10
Mt. McKinley
The total distance is 20,602 feet.
11
Additional Example 1 Comparing Integers

Use the number line to compare each pair
of integers. Write lt or gt. A. 2 2 B.
3 5 C. 1 4
2 is to the left of 2 on the number line.
2 lt 2
3 gt 5
3 is to the right of 5 on the number line.
1 is to the right of 4 on the number line.
1 gt 4
12
Additional Example 2 Ordering Integers Order
the integers in each set from least to
greatest. A. 2, 3, 1 B. 4, 3, 5, 2
Graph the integers on the same number line.
Then read the numbers from left to right 2, 1,
3.
Graph the integers on the same number line.
Then read the numbers from left to right 5, 3,
2, 4.
13
Additional Example 3 Problem Solving
Application
In a golf match, Craig scored 2, Cameron scored
3, and Rob scored 1. Who won the golf match?

• The answer will be the player with the lowest
  score. List the important information
• Craig scored 2.
• Cameron scored 3.
• Rob scored 1.

14
Check It Out Example 3 Continued
You can draw a diagram to order the scores from
least to greatest.
Draw a number line and graph each players score
on it.



Tristas score, 3, is farthest to the left, so
it is the lowest score. Trista won the golf match.
15
Check It Out Example 3 Continued
Look Back
Negative integers are always less than positive
integers, so Melissa cannot be the winner. Since
Tristas score of 3 is less than Alyssas score
of 1, Trista won.
16
Name 4 real life situations in which integers can
be used.

• Spending and earning money.
• Rising and falling temperatures.
• Stock market gains and losses.
• Gaining and losing yards in a football game.