Download 6.7 Notes

Name_________________________________Mailbox #______ Math 1 2 3 4
LESSON 6.7: The Distributive Property
Warm-up:
1) Your teacher has given you 12 Algebra tiles. Arrange your tiles in two rows with six chips in each
row. Fill in the following blanks:
__________  __________ = ____________
number of
number of
total number of tiles
rows
tiles in
each row
2) Now draw picture of your model, enter the expression and the total number of chips, in the table
below.
PICTURE OF MODEL
EXPRESSION
TOTAL NUMBER OF CHIPS
1)
2)
3)
4)
3) Keeping the chips in two rows, put some space between the first four chips in each row and the
last two chips in each row. Fill I the blanks below to represent your model from this step.
__________ (__________ + ___________) = ____________
number of
number of
number of
total number of tiles
rows
tiles in
tiles in
first group
second group
of first row
of first row
4) Now complete the second row of the table above using the information from #3.
5) Using only the tiles in the first group, write an expression to represent this group and record it in
the third row of your table.
__________  __________
number of
number of
rows
tiles in
each row
6) Using only the tiles in the second group, write an expression to represent this group and record it
in the fourth row of your table.
__________  __________
number of
number of
rows
tiles in
each row
7) How does the sum of the expressions in rows 3 and 4 of your table compare to the total number
of chips in row 2?
8) Use the totals in rows 2-4 of your table to fill in the blanks and write an equation.
____________ = __________ + __________
9) Replace the totals in the equation you just wrote with the expressions that represent them.
____________ = __________ + __________
10) Explain how to simplify the left side of the equation in number 9 to get the right side.
Vocabulary
Equivalent expressions:
The Distributive Property
Algebra For all numbers a, b, and c,
a (b + c) =______ +______
Numbers 8 (10 + 4) =_______ + ______
a (b – c)=______ – ______
and
and
3(4 – 2) =______ - _______
EXAMPLE 1: Writing Equivalent Expressions
Use the distributive property to write an equivalent expression. Check your answer by
evaluating the expressions on each side of the equal sign.
a) 8(2 + 9) =
b) –6 (2 + 7) =
c) 3(75 – 25) =
Now YOU Try It ! Use the distributive property to write an equivalent expression. Check
your answer by evaluating the expressions on each side of the equal sign.
1)
5(6 + 9) =
2) –4(7 + 5) =
3) 9(15 – 8) =
EXAMPLE 2: Reverse the distributive property.
a) 4(3) + 4(6) =
b) 10(7) + 10(2) =
c) 8(4) – 8(2) =
Now YOU Try It! Reverse the distributive property. Check your answer by evaluating the
expressions on each side of the equal sign.
4)
4(6) + 4(9) =
5) –4(7) + (-4)(5) =
6) 3(8) – 3(2) =
EXAMPLE 3: Using the Distributive Property
The distributive property can be used to make mental math easier!
a) 4(52) =
b) 8(43) =
Now YOU Try It! Use the distributive property to multiply.
7) 3(78) =
8) 4(18) =
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