Transcript Introduction to Integers

Introduction to Integers
The Pluses and Minuses of Life
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
negative integers
0 +1 +2 +3 +4
+5 +6
positive integers
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.
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
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
Name 4 real life situations in which
integers can be used.
•
•
•
•
-10 -9
Spending and earning money
Rising and falling temperatures
Stock market gains and losses
Gaining or losing yards in a football
game
-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.
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?
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.
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.