PLEASE HAVE OUT: u 1. PENCIL and PAPER (Possibly Eraser and Calculator) u 2. Yesterday’s HOMEWORK.  PLEASE BE QUIET after the bell rings !

Yesterday’s Homework Assignment -- Wednesday (10/7) u Pgs : 10, 12, 14, 18, 22. u 10. Associative Property of Mltplctn u 12. Associative Property of Addition  14. Sample: 14  2 = 7, but 2  14 = 1 / 7 u u 22. $600

Clear-Off-Desk except for: u PENCIL and PAPER! Possibly Eraser and Calculator Focus on Lesson!

1.8 “The Distributive Property”  Goal 1 - You will simplify expressions by applying the distributive property and justify the process used.

In In Algebra Arithmetic Words Distributive Property a(b a(b + c) c) c) c) = ab ab +ac a(b a(b - c) c) c) c) = ab ab -ac 4(3 4(3 + 8) = 4(3) + 4(8) -8) = 4(3) -4(8) You You multiply the outside factor by the first inside term and then by the second inside term.

u The Distributive Property is NOT very important in arithmetic. It just interesting to know.  The Distributive Property is very important in Algebra. u It is vital to know! Distributive Property

 Distribute mean to spread over an area.  Notice how the Distributive Property spreads a value over two or more terms. Distributive Property

Example 1 – Using the Distributive Property  A.  A. Use the distributive property to write an equivalent numerical expression for the expression: 8(3 + 5). ä Solution ä 8(3 8(3 + 5) 5) = 8(3) 8(3) + 8(5)8(5)8(5)8(5)

Example 1 – Using the Distributive Property  B.  B. Show that the two expressions in part A have the same value. 8(3 8(3 + 5) 5) = 8(3) 8(3) + 8(5)8(5)8(5)8(5) ä Solution ä 8(3 ä 8(3 + 5) 5) = 8(8) 8(8) = 64 ä 8(3) ä 8(3) + 8(5)= 8(5)= = 64 ä The ä The expressions have the same value so they are equivalent.

Equivalent Variable Expressions  Equivalent  Equivalent variable expressions expressions always have the same values when numbers are substituted for the variables. ä You ä You can use the distributive property to write equivalent variable expressions.

Example 2 – Using the Distributive Property ä Write ä Write an equivalent expression. Then simplify.  A.  A. 2( x 2( x + 2)  Solution  2( x  2( x + 2) = 2( x ) 2( x ) + 2(2) Distribute the the 2  = 2x 2x 2x 2x + 4 Simplify

Write an equivalent expression. Then simplify.  B.  B. x(x x(x x(x x(x + 7)  Solution x(x x(x x(x x(x + 7) = x ( x ) x ( x ) + x (7) x (7) Distribute the the x = x2 x2 x2 x2 + 7x 7x 7x 7x Simplify

Write an equivalent expression. Then simplify.  C.  C. 2(3 x 2(3 x - 5)  Solution  2(3 x  2(3 x - 5) = 2(3 x ) 2(3 x ) - 2(5) Distribute the the 2 = 6x 6x 6x 6x - 10 Simplify

Write an equivalent expression. Then simplify.  D.  D. 5x 5x 5x 5x + 9x9x9x9x  Solution 5x 5x 5x 5x + 9x 9x 9x 9x = (5 + 9) x 9) x Reverse Distribution = 14 x 14 x Simplify

The Distributive Property ä The ä The distributive property also applies to sums with more than two variables.  a(b  a(b + c + d) d) d) d) = ab ab +ac +ad

Example 3 – Using the Distributive Property  Write  Write an equivalent expression. Then simplify. 8( )  Solution  8(2  8( ) = 8(2) + 8(3) + 8(4) Distribute the the 8 = Multiply = Add

1.8 “The Distributive Property” ä Are there any questions about The Distributive Property?

1.8 “The Distributive Property”  Goal 2 - You will use the distributive property to solve life-like problems. ä Use two methods to solve Example 4.

Example 4 Applying the Distributive Property You are carpeting a bedroom and a closet. One square yard of carpet costs $20. What will the total cost be? Use two methods. 6 yd 3 yd 2 yd

Example 4 Applying the Distributive Property Solution Find the total area of the room and closet. 6 yd 3 yd 2 yd

Solution – Method A Think of the region as one large rectangle. A = lw = 6(3 +2) = 6(5) = 30 yd 2 6 yd 3 yd 2 yd

Solution – Method B Think of the region as two smaller rectangles. A = 6(3) + 6(2) = = 30 yd 2 6 yd 3 yd 2 yd

Solution Multiply the cost for a square yard of carpeting by the number of square yards needed. 20 x 30 = 600 Answer: It will cost $600 to carpet the bedroom and the closet. 6 yd 3 yd 2 yd

1.8 “The Distributive Property” ä Are there any questions about Applying the Distributive Property? ä Classwork ä 1.8 Pgs : 1-20 and ä SHOW STEPS!

Make sure you have the proper heading and format. ä 930 Danny Dana  10 / 7 ä Math 7 - Dequer and Pg.40-41: 1-20 and Please work Quietly and On-Your- Own for 15 min. SHOW STEPS ! You may now get help from and give help to near neighbors, etc.

u 1. 3(2 + 7) = 3(2) + 3(7) = = 27 3(2 + 7) = 3(9) = 27 u 2. 11(10 + 5) = 11(10) + 11(5) = = (10 + 5) = 11(15) = 165  3. 17( ) = 17(8.5) - 17(1.5) = = ( ) = 17(7) = “Guided Practice” Pgs : 1-20 and 44-45

 4. 9(8 - 7) = 9(8) - 9(7) = = 9 9(8 - 7) = 9(1) = 9  5. Incorrect ; 2(3 + 5) = 2(3) + 2(5)  6. Correct  7. Incorrect ; 6(4 x ) + 6(1) = 24 x + 6  8. Incorrect ; 2(3 a + 6) = = 6 a “Guided Practice” Pgs : 1-20 and 44-45

 9. 4( x + 9) = 4( x ) + 4(9) = 4 x + 36  10. 3(5 x + 1) = 3(5 x ) + 3(1) = 15 x + 3  11. 8(4 - q ) = 8(4) - 8( q ) = q  12. 2( x - 25) = 2( x ) - 2(25) = 2 x - 50  a + 8 a = (32 + 8) a = 40 a  14. y (7) + y (9) = y (7 + 9) = 16 y 1.8 “Guided Practice” Pgs : 1-20 and 44-45

 15. a ( b c ) = ab + 4 a + ac  16. r ( s + t ) = rs + rt  17. 8(10) + 8(20) = 240 8( ) = 240   44. D 45. H 1.8 “Guided Practice” Pgs : 1-20 and 44-45

Make-Up Tests  Math 7 Make-Up Quizzes are still available TODAY, Thursday, (10/7/04), at 3:05 p.m. here in Room 29. ä If it is a retest bring the original Blue Scantron Form and colored quiz (if possible) with you.

Class/Homework Assignment -- Thursday (10/7) u 1. Pgs : 22, 24, 28, 32, 36, and 38. u Prove you’ve done the problems by SHOWING STEPS ! u Yes, you may continue your homework on the classwork paper.