Transcript The-Distributive-Property

The Distributive Property
6.EE.A.2b, 6.EE.A.3, and 6.EE.A.4
Bellwork
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Simplify
-7a(-8t)
-6j(3)(5k)
-2xy if x = -8 and y = 5
Objective
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Students will use the distributive
property to re-write numerical and
algebraic equations.
The Distributive Property
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The distributive property states:
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To multiply a number by a sum, multiply
each number inside the parentheses by the
number outside the parentheses
The distributive property can be used
with multiplication and addition or
multiplication and subtraction
Let’s see what it looks like…
Example 1
5(3 + 2)
15 + 10 = 25
Proof: 5(3+2) = 5(5) = 25
Algebraic Expressions
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The distributive property can be used to
re-write algebraic expressions.
Use the same process…multiply what’s
on the outside of the parenthesis by
each term within the parenthesis
Let’s see what that looks like…
Example 2
3(x + 1)
3x + 3
Note: In this instance 3x and 3 are not like terms.
Therefore, you cannot combine them…so the expression
is simplified to just 3x + 3
Distributive Property
There are 2 ways that you can see the distributive
property
 With the multiplier on the left of the parenthesis
 With the multiplier on the right of the parenthesis
Example
5(2 + 3)
OR
(b + 3)5
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In either event you multiply what’s on the
out side of the parenthesis with EACH term
inside the parenthesis
Comments
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The distributive property is a key
algebraic concept…make no mistake
about it…you are REQUIRED to be
able to recognize and work with the
distributive property if you are to pass
Algebra.
Common Errors
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The most common error that students
make when working the distributive
property is that they only multiply what
on the outside of the parenthesis with
the first term within the parenthesis
The other common error is that
students get the signs wrong…I do not
give partial credit for incorrect signs!
Example - Common Error
3(x - 1)
3x - 1
THIS IS INCORRECT!
Your turn
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2.
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Use the distributive property to rewrite
the expression
8(5 + 7)
(b + 9)6
(6 – z)5
3(x+2)+9
2 -3(x+7)
Another Example
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Write two expressions that are
equivalent to 4(2x + 7y).
Summary
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summarize the key concepts covered in
today’s lesson
Today we discussed
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The distributive property
How will you recognize it?
How does it work?
Homework
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Worksheet:
Reminder
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This assignment is due tomorrow
Make sure you write the problem
Draw the arrows like we did in the
examples
Display your answer below the problem