Interesting Integers

1
Interesting Integers!
2
What You Will Learn

• -What is the connection between negative numbers
  and the real world?
• -What rules exist for adding and subtracting
  integers?
• -How can I prove to myself that the rules are
  true?

Are you ready??
3
Definition

• Positive number a number greater than zero.

0
1
2
3
4
5
6
4
Definition

• Negative number a number less than zero.

0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
5
Definition

• Opposite Numbers numbers that are the same
  distance from zero in the opposite direction

0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
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Opposites-Try It

• What is the opposite of
• 4
• -4
• -20
• 20
• 1
• -1
• -2
• 2
• 58
• -58

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Definition

• Integers Integers are all the whole numbers and
  all of their opposites on the negative number
  line including zero.

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Definition

• Absolute Value The size of a number with or
  without the negative sign.

The absolute value of 9 or of 9 is 9.
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Say It!

• I-3I 3
• I3I 3

• Read as the absolute value of negative 3
• Read as the absolute value of 3

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Say It!

• I4I 4
• I1,000I 1,000
• I-8I 8
• I-.05I .05
• I-1/2I ½
• I-yI y

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Where do we use Negative Integers??
12
Negative Numbers Are Used to Measure Temperature
13
Negative Numbers Are Used to Measure Under Sea
Level
30
20
10
0
-10
-20
-30
-40
-50
14
Negative Numbers Are Used to Show Debt
Lets say your parents bought a car but had to
get a loan from the bank for 5,000. When
counting all their money they add in -5,000 to
show they still owe the bank.
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Hint

• If you dont see a negative or positive sign in
  front of a number it is positive.

9

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Comparing Integers
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7

• Use the number line to compare each pair of
  integers
• Remember Numbers on a number line increase in
  value as you move from bottom to top

-3
-5
gt
17
Comparing Integers Try It!
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
-2
lt
-6
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Comparing Integers Try It!
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
1
lt
-1
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Comparing Integers Try It!
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
-7
gt
0
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Addition of Integers
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One Way to Add Integers Is With a Number Line
When the number is positive, count up. When the
number is negative, count down.
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7

-
22
Add Integers With a Number Line-Try It!
-2
3 -5
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
23
Add Integers With a Number Line-Try It!
7
3 4
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
24
Add Integers With a Number Line-Try It!
-7
-3 -4
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
25
Add Integers With a Number Line-Try It!
2
6 -4
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
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Add Integers With a Number Line-Try It!
-4
3 -7
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
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Add Integers With a Number Line-Try It!
4
-3 7
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
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Add Integers With a Number Line-Try It!
-5
-7 2
7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
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Add Integers With a Number Line-Try It!
-5
-7 2
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Integer Addition Rules

• Rule 1 If the signs are the same, pretend the
  signs arent there. Add the numbers and then put
  the sign of the addends in front of your answer.

9 5 14
-9 -5 -14
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Solve the Problems

• -3 -5
• 4 7
• (3) (4)
• -6 -7
• 5 9
• -9 -9

-8
11
7
-13
14
-18
32
Solve the problems on Part A of your worksheet
now. Click to the next slide when done.
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Check Your Answers
1. 8 13 21 2. 22 -11 -33 3. 55 17
72 4. 14 -35 -49
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Integer Addition Rules

• Rule 2 If the signs are different pretend the
  signs arent there. Subtract the smaller from the
  larger one. Put the sign of the one that over
  powers in front of your answer.

-9 5
Larger abs. value
Answer - 4
9 - 5 4
35
Solve These Problems
-2

• 3 -5
• -4 7
• (3) (-4)
• -6 7
• 5 -9
• -9 9

5 3 2
3
7 4 3
-1
4 3 1
1
7 6 1
-4
9 5 4
0
9 9 0
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Solve the problems on Part B of your worksheet
now. Click to the next slide when done.
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Check Your Answers
1. 12 22 10 2. 20 5 15 3. 14 (-7)
7 4. 70 15 -55
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Subtracting Integers

• Rule 1- When you see a subtraction sign
• Change it to addition
• Change the sign of the second number to its
  opposite.
• When Subtracting.Add the Opposite

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Integer Subtraction Rule
Subtracting a negative number is the same as
adding a positive. Change the signs and add.
2 (-7) is the same as 2 (7) 2 7 9!
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Hint

• NEVER change the sign of the first number in the
  equation!

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Here are some more examples.
12 (-8) 12 (8) 12 8 20
-3 (-11) -3 (11) -3 11 8
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Here are some more examples Add the opposite
-10 (3) -10 ( -3) -13
-2 (9) -2 ( -9) -11
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Solve the problems on Part C of your worksheet
now. Click to the next slide when done.
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Check Your Answers
1. 8 (-12) 8 12 20 2. 22 (-30)
22 30 52 3. 17 (-3) -17 3 -14 4.
52 5 -52 (-5) -57
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Prove that Subtraction Works
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How do we know that Subtracting a negative
number is the same as adding a positive is true?
We can use the same method we use to check our
answers when we subtract.
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Suppose you subtract a b and it equals c a
b c 5 2 3 To check if your answer is
correct, add b and c a b c 5 2 3
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Here are some examples a b c a b c 9
5 4 9 5 4 a b c a b c 20 3
17 20 3 17
49
If the method for checking subtraction works, it
should also work for subtracting negative
numbers.
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If a b c, and. 2 (-5) is the same as 2
(5), which equals 7, Then lets check with the
negative numbers to see if its true
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a b c a b c 2 (-5) 7 2 -5
7 It works! a b c a b c -11 (-3)
-8 -11 -3 -8 YES!
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Solve the problems on Part D of your worksheet
now. Click to the next slide when done.
53
Check Your Answers
1. Solve 3 10 7 Check 3 10 (-7)
2. Solve 17 ( 12) 29
Check 17 -12 29
Continued on next slide
54
Check Your Answers
1. Solve 20 ( 5) 25
Check 20 -5 25
1. Solve -7 ( 2) -5
Check -7 -2 -5
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You have learned lots of things About adding and
subtracting Integers. Lets review!
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Discuss with a partner ways that you know that
that is problem is solved correctly.
6 (-9) 15
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Arent integers interesting?