Transcript Example 3

1-5 Properties of Numbers
Aim: How can we identify the
properties of operations and use them to
solve problems?
Warm up
1. True or False? (Explain): 8.5 + 15 = 15 + 8.5
2. Evaluate: 12 + (-12) + 12 =
3. True or False? (Explain): 7 x (-4) = (-4) x 7
4. Evaluate: 11 x (-4) x (-2) =
5. True or False? (Explain): 3(2+5) = 3⋅2+3⋅5
6. Evaluate: 2(3.5 + 4) =
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Commutative Property of
Addition and Multiplication
The order in which items are added or
multiplied do not effect the answer.
Example:
7 + 12.9 = 12.9 + 7
Example:
4 x 2.5 = 2.5 x 4
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Associative Property of
Addition and Multiplication
The order in which the same grouped
items are added or multiplied do not
effect the answer.
Example:
(5+7) + 9 = 9 + (5+7)
Example:
(3+2) x 4 = 4 x (3+2)
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Distributive Property
The ability to distribute the factor
outside the set of parentheses to each
item inside, and then add the results.
Example:
(8)(2 + 4) = (16) + (32) = 48
Example:
(-5)(7 + 3) = (-35) + (-15) = (-50)
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Using Mental Math
Example 1:
Simplify : 16 + 37 + 4 =
Example 2:
Simplify: 5 ⋅(-2) ⋅8 =
Example 3:
Simplify: (-2.5) ⋅ (-4) ⋅(-10) =
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Think, Turn and Talk
(Part One)
How can the following expressions be rewritten then
evaluated?
•13(2 + a) =
•(5 - b)(-3) =
1.4 ⋅ 4 + 4 ⋅ 3 =
Think, Turn and Talk
(Part Two)
•
At Six Flags Great Adventures a roller coaster plunges down
a vertical drop of 73.4 feet. At the beginning of the drop,
the coaster was located at 95.5 feet above the ground.
1.Write an integer that represents this change in height.
2.Write an expression that represents the change in height
for the roller coaster during the drop.
3.How high is the roller coaster when it reaches the bottom of
the drop?
Think, Turn and Talk
(Part Three)
At a candy store, a child bought 4 pounds
of chocolate at $3.76 per pound, 3
milkshakes at $1.25 each and 5 buckets
of popcorn at $2.29 each.
What is the total cost for all items
purchased?
(Hint: Think of how many variables you will need for your equation.)
Exit Ticket
Error Analysis
A student claims that: 7 ⋅ 5 + 4 = 7 ⋅ 4 + 5, by
the use of the Commutative Property of
Addition.
• What is the error?
• How can the original equation be rewritten
correctly?
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