Introduction to Integers

1
Introduction to Integers

• The Pluses and Minuses of Life

2
Integers Defined

• Integers are the set of whole numbers and their
  opposites
• Integers are positive and negative numbers
• The number line goes on forever in both
  directions and is indicated by arrows
• Whole numbers greater than zero are called
  positive integers and these numbers are to the
  right of zero on the number line

opposite integers
-6 -5 -4 -3 -2 -1 0 1 2
3 4 5 6
negative integers
positive integers
3
Integers Defined

• Whole numbers less than zero are called negative
  integers and these numbers are to the left of
  zero on the number line.
• The integer zero is neither positive nor negative
• The sign of an integer is either positive () or
  negative (-), except zero, which has no sign.
• Opposite Integers when two numbers are the same
  distance away from zero, on opposite sides of the
  number line, one will have a positive sign, the
  other a negative sign.

4
Write an integer to represent each situation

• 15degrees above zero
• 15

• a loss of 11 dollars
• -11

• a gain of 8 points
• 8

• 3 steps backward
• -3

-10 -9 -8 -7 -6 -5 -4 -3 -2
-1 0 1 2 3 4 5 6 7 8
9 10
5
Name the opposite of each integer.

• -11

11
27
-27
14
-14
-4
4
-10 -9 -8 -7 -6 -5 -4 -3 -2
-1 0 1 2 3 4 5 6 7 8
9 10
6
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 or losing yards in a football game

-10 -9 -8 -7 -6 -5 -4 -3 -2
-1 0 1 2 3 4 5 6 7 8
9 10
Note A positive integer does not have to have a
sign. For example, 3 and 3 are the same.
7
The Problem

• The highest elevation in Northern Lookout is Snow
  Peak, which is 15 237 feet above sea level. The
  lowest elevation is Tree Valley, which is 368
  feet below sea level. What is the distance from
  the top of Snow Peak to the bottom of Tree
  Valley?

8
Solution

• We can represent each elevation as an integer
•  

Elevation Integer
15 237 feet above sea level 15 237
Sea level 0
368 feet below sea level -368
The distance from the top of Snow Peak to the
bottom of Tree Valley is the same as the distance
from 15 237 to -368 on the number line. We add
the distance from 15 237 to 0, and the distance
from 0 to -368, for a total of 15 605 feet.
9
Points to Remember

• Integers are the set of whole numbers and their
  opposites
• Whole numbers larger than zero are called
  positive integers whole numbers less than zero
  are called negative integers
• The integer zero is neither positive nor
  negative.
• Two integers are opposites if they are the same
  distance away from zero, but on opposite sides of
  the number line.
• Positive integers may be written with or without
  a sign.