Standard(s): 7.A.4
Aim: To simplify equations by applying the distributive property
Do Now:
Non- Calculator quiz on Order of Operations
Instructional Material:
Ask a student to “Please distribute the index cards ”
After the student is done ask the class what the student had done when asked to distribute the index cards. ~ Students will conclude that distributing the index cards resulted in each student getting an index card.
The distributive property is a little like passing out the index cards. Take a look at the following equation:
3 (4 + 2) = 3 x 6 = 18
Method 1:
You can first do the addition, (4 + 2), and get 6; then multiply 3 x 6 and get 18.
Order of Operations ~ PEMDAS
3 (6) =18
Method 2:
You can pass out , or distribute , the 3 over the 4 and the 2 and make up two little multiplication problems. Do the multiplication first, and then add the products. Either way you do it, you still get 18.
3 (4 + 2) = (3 x 4) + (3 x 2) = 18
When simplifying expressions with parentheses, you will be applying the Distributive Property.
That is, you will be distributing over (multiplying through) the parentheses in order to simplify a given expression.
The “eyebrow” method to illustrate the process of distributing.
Simplify 3( x + 4)
To "simplify" this, I have to get rid of the parentheses. The Distributive Property says to multiply the 3 onto everything inside the parentheses. I sometimes draw arrows to emphasize this:
Then:
3( x ) + 3(4)
→
Rewrite using the distributive property
3 x + 12
→
Simplified
Written all in one line, this would look like:
C

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The Distributive Property a (b + c) = ab +ac
(b +c) a = ba + ca
Practice:
Rewrite by using the distributive property.
1) 7(4 + 2)
7(4) + 7(2)
2) (6 – 2)5
6(5) – 2(5)
2(x + 5) = 2(x) + 2(5) = 2x + 10
(x + 5) 2 = (x) 2 + (5) 2 = 2x + 10
* Multiplication is commutative so it can be done either way
3) 2(6 + 5 + 3)
2(6) + 2(5) +2(3)
4) (4 + 2 + 3)7
4(7) + 2(7) + 3(7)
5) 2
•
3 + 2
•
8
2(3 + 8)
6) 8
•
4 - 7
•
4
(8 – 7) 4
7) 5
•
3 + 5
•
4 + 5
•
1 8) 3
•
6 –3
•
Rewrite by using the distributive property and simplify.
1) 2 (3 + 5) 2) (7 + 2) 4 2) 1/3 (15 + 27) 3) 6(2 + 3 + 5)
2(3) +2(5) 7(4) + 2(4) 1/3(15) + 1/3(27) 6(2) + 6(3) + 6(5)
28 + 8 = 36 5 + 9 = 14 12 + 18 + 35 6 + 10 =16
4) 7(2x -1)
7(2x) – 7(1)
14x -7
5) (6 – 5x) 2
6(2) – 5x(2)
12 -10x
6) 1/6(7x + 6)
1/6(7x) + 1/6 (6)
7x/6 + 1
5 + 3
5(3 + 4 +1) 3(6 – 5 + 2)
•
2
Activity: On the back of each index card is problem. The students will be asked to rewrite their problem by using the distributive property but DO NOT SIMPLIFY!
After each student re writes their problem they are to find another student in the class who’s original problem is the answer to their problem. They are to write the problem and the answer in their notebooks and one-person form each pair will write their problem and answer on the board.
**Thanks to www.purplemath.com
, www.georgiastandards.org
, & www.math.com