What everyone needs and wants to know.

1
INTEGERS

• What everyone needs and wants to know.
• What they are?
• How do you work with them?
• Why do they exist?
• By Mrs. Tonya Woods

2
What are integers?

• 0 -1
• 20 -20
• 7 -7
• 100 -100

3
Definition

• The whole numbers and their opposites
• -5 -4 -3 -2 -1 0 1 2 3 4 5
  
• Negatives Zero Positives

4
Okay, now what are opposites?

• Opposites are two integers the same distance
  from zero on a number line, but in opposite
  directions.
• . . . -4 -3 -2 -1 0 1 2 3 4 . .
  .
• 4 is the opposite of -4
• -4 is the opposite of 4

5
Do you know what absolute values are?

• Opposite integers are the same distance from zero
  on the number line. This means they have the
  same absolute value.
• The absolute value of an integer is its distance
  from zero on the number line.
• . . . -4 -3 -2 -1 0 1 2 3 4 . . .
• -4 4 4 4

6
Now lets do some work!!(click the mouse to go
on)

• A B C
• -6 0 1
  6
• A
• B
• C
• the opposite of 5 is _____
• the opposite of -7 is ____
• -15 8

7
Answers to previous problems(click the mouse to
go on)

• A -6
• B -2
• C 2
• The opposite of 5 is 5
• The opposite of 7 is 7
• -15 15
• 8 8

8
How do we work with integers?

• We can add, subtract, multiply and divide
  integers.
• But first we have to learn a few basic rules for
  each operation above.

9
Adding integers

• To add two integers with the same sign () (-
  -), add the absolute values of the integers. The
  sum will have the same sign as the addends.
• To add two integers with different signs (-)
  find the differences of the absolute values of
  the addends. The sum has the sign of the integer
  with the greater absolute value.

10
Lets see this with pictures.Same Sign Integers

• represents positive numbers
• represents negative numbers
• 4 3 7
• -4 -3 -7

11
Different Signs

• positive (one positive cancels one
  negative)
• negative
• 4 -3 1
• -4 3 -1

12
Lets try it with the number line.

• To solve -43
• -4 -3 -2 -1 0 1 2 3 4
• Begin at 0 and move 4 units to the left to
  negative 4.
• Begin at -4 and move 3 units to the right to
  negative 1.

13
Now it is your turn to try.(click the mouse to
go on)

• Use pictures to represent -83
• Use pictures to represent 6 (-2)
• Use a number line to represent each of the above
  problems.

14
Now check your answers(your pictures may be
different)(click the mouse to go on)

• positive negative
• (check your number lines with your teacher)

15
Subtracting Integers

• To subtract an integer, add its opposite.
• -8 - 2 add the opposite of 2
• -8 (-2)
• now choose a method of adding integers and find
  the solution

16
Want to see a picture?

• positive
• negative
• -6 - 2
• -6 (-2)
  -8

17
Lets try another

• positive
• negative
• -5 - (-3 )
• -5 3 2

18
Multiplying integers

• To multiply two integers, find the product of the
  absolute values of the integers. Then use these
  rules.
• The product of two integers with the same sign is
  positive
• () () (-)(-)
• The product of two integers with different signs
  is negative
• ()(-) - (-)() -

19
Try a few. . .(Click on the mouse to go on)

• Tell if the product is positive or negative
• -3(8)(-24) 8(-83)
• Find the answer.
• (3)(3) (-7)(24)
• (6)(-9) (-27)(-11)
  

20
Now Check your answers(Click on the mouse to go
on)

• Positive
• Negative
• (3)(3) 9
• (6)(-9) -54

• (-7)(24) -168
• (-27)(-11) 297

21
Why do integers exist ?

• Integers are used to show the distance and
  direction something is from the beginning point

22
In math integers are used to show the distance
and direction a number is from zero on the number
line.

• -5 -4 -3 -2 -1 0 1 2 3 4 5
• The number 2 is 2 units to the right of zero.
• The number -2 is 2 units to the left of zero.

23
In weather, integers are used to show the
temperature above and below freezing

• At 600am the temperature was 63ºF, at noon
  the temperature had risen 25º. What was the
  temperature in Fahrenheit at noon?

24
In science, integers are used to show the
distance an object is above or below sea level.

• If a plane is at 25,524 feet above sea level
  then crashes into the sea and settles at 12,500
  feet below sea level, how far did the airplane
  fall?

25
In banking, integers are used to show the amount
of money a person has above or below 0.

• Ryan has 132.48 in has account. He writes
  three checks, 32.87, 81.00, and 3.42. How
  much money does he have in his account now?

26
In the stock market, integers are used to show
how much a stock has risen or fallen form the
previous reading.

• You buy stock in McDonalds at 23½. The next
  day it falls 3¾. What is the closing value at
  the end of the day?

27
Integers are even used in football to show gain
or loss of yards on a play.

• Chad Pennington was snapped the ball on his own
  15 yard line. He passes the ball for a gain of 7
  yards. At what yard line will the ball be placed
  for the next play?

28
And last but not least integers are used to show
golf scores above and below par.

• Tiger Woods played a course with a par of 72.
  He finished the 18 holes with a score of 7 under.
  What was his actual score at the end of the day?

29
INTEGERS

• What are they?
• How do you work with them?
• Why do they exist?
• Now that you have seen the answers to the above
  questions, I hope that you have a better
  understanding.
• Now lets begin working with integers