Introduction to Integers - Copyright free ppt.

1. Introduction to
Integers

2. Integers Defined…
• An integer (pronounced IN-tuh-jer)
o is a whole number
o Is not a fraction.
o Is a number that can be positive, negative, or zero.
opposite integers
-6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6
negative integers positive integers

3. Four 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 metres in an NRL 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.

4. Multiplying Integers

5. Dividing Integers

6. Adding and Subtracting
with Integers
Using a number line you add by moving to the right.
e.g. -2+3 = 1 (As shown on the diagram below).

7. Subtracting Integers
Similarly, when you are subtracting integers, you are
Moving the arrow to the left.
No matter where you start on the number
line, you always move to the left.
E.g. (-5) – 2 = -7

8. Adding and Subtracting
Integers
Some different, slightly more difficult examples
•3+(-7) becomes 3 – 7 = -4
•-5 + (-2) becomes -5 – 2 = -7
•5-(-3) becomes 5 + 3 = 8
•-6-(-3) becomes -6 + 3 = -3

9. •
The Problem:
The highest elevation in Northern Lookout is
Snow Peak, which is 15 237 metres above
sea level. The lowest elevation is Tree
Valley, which is 368 metres below sea level.
What is the distance from the top of Snow
Peak to the bottom of Tree Valley?

10. Solution
We can represent each elevation as an integer:
Elevation Integer
15 237 metres above +15 237
sea level
Sea level 0
368 metres below -368
sea level
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 metres.

11. • 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.