Add and Subtract Integers

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Name Date Period
EOC Practice
1.
2.
Based on the diagram, what is the total number of
students who did not participate in soccer or
basketball?
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Integers???
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Name Date Period Topic To find sums,
differences, products, and quotients of real
numbers Essential Question How do the rules of
integers relate to the properties of real numbers
and the definitions of operations?

• Vocabulary
• Integers , -2, -1, 0, 1, 2,
  
• Whole Numbers 0, 1, 2,
• Natural Numbers 1, 2, 3,

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Adding Subtracting Integers
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Addition Rule

• 1) When the signs are the same,
• ADD and keep the sign.
• (-2) (-4) -6
• 2) When the signs are different,
• SUBTRACT and use the sign of the larger number.
• (-2) 4 2
• 2 (-4) -2

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Examples Use the number line if necessary.
1) (-4) 8

• 4
• 2) (-1) (-3)
• -4
• 3) 5 (-7)
• -2

7
-1 3 ?

1. -4
2. -2
3. 2
4. 4

8
-6 (-3) ?

1. -9
2. -3
3. 3
4. 9

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When subtracting, change the subtraction to
adding the opposite (keep-change-change) and then
follow your addition rule.

• Example 1 - 4 - (-7)
• - 4 (7)
• Diff. Signs --gt Subtract and use larger sign.
• 3
• Example 2 - 3 - 7
• - 3 (-7)
• Same Signs --gt Add and keep the sign.
• -10

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Okay, heres one with a variable! Example 3 11b
- (-2b)

• 11b (2b)
• Same Signs --gt Add and keep the
  sign.
• 13b

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Which is equivalent to-12 (-3)?

1. 12 3
2. -12 3
3. -12 - 3
4. 12 - 3

12
7 (-2) ?

1. -9
2. -5
3. 5
4. 9

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Simplify

• 8 7
• 5 (-3)
• 15 2
• -6 4
• -9 3
• -2 (-1)
• -10 (-12)
• 17 (-13)

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1) If the problem is addition, follow your
addition rule.2) If the problem is subtraction,
change subtraction to adding the opposite
(keep-change-change) and then follow the
addition rule.
Review
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Same rule Applies to absolute value
Absolute Value
of a number is the distance from zero. Distance
can NEVER be negative! The symbol is a, where a
is any number.
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Examples
?7?
7
10
?10?
100
?-100?
?5 - 8?
?-3? 3
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7 -2 ?

1. -9
2. -5
3. 5
4. 9

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-4 (-3) ?

1. -1
2. 1
3. 7
4. Purple

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Independent Practice

• ?6 - 2?
• ?8 - 15?
• ?7 (-8)?
• ?-82? 3
• ?16?- (-4)
• ?9 (-5)?

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Multiplying Dividing Integers
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Multiplying and Dividing Integers

• If Then
• (3) x (-7) (-21) (-21) (3) (-7)
• (-5) x (-4) (20) (20) (-5) (-4)
• (-3) x (8) (-24) (-24) (-3) (8)
• (5) x (6) (30) (30) (5)
  (6)
• Are the rules the same?

Yes!
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Multiplying and Dividing Integers

• RULES
• 1) When multiplying or dividing integers with
  the same signs, the answer will be positive.
• 2) When multiplying or dividing integers with
  different signs, the answer will be negative.

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Multiplying Dividing Rule
Just in case you didnt get it!
Positive times Positive
Positive (
) Negative times Negative
Positive ( - -
) Positive times Negative
Negative ( -
-) Negative times Positive
Negative ( - -)
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Practice
3 -4 -7 -2 8 3 -9 2 30 -2 -24
-6 -4 2 14 7
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1. A deep-sea diver must move up or down in the
water in short steps in order to avoid getting a
physical condition called the bends. Suppose a
diver moves up to the surface in five steps of 11
feet. Represent her total movements as a product
of integers, and find the product.
Multiply
What does This mean?
(11 feet)
(5 steps)
(55 feet)
5 11 55
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2. At noon the temperature is 8C. If the
temperature decreases 4C per hour, what is the
temperature at 6 pm?
How much does the temperature decrease
each hour?
How long Is it from Noon to 6 pm?
6 hours
- 4 degrees
(6 hours)(- 4 degrees per hour)
Add this to the original temp.
- 24 degrees
8 (- 24) - 16C