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TRANSCRIPT
Bell Work
1) 5a + 7a 2) 6.1y - 3.2y 3) 4x2y + x2y���
4) 3m2n + 10mn2 + 7m2n - 4mn2
Objective - To use the distributive property to simplify numerical and variable expressions.
Distributive Property a(b c) a b a c+ = • + •
a(b c) a b a c− = • − •or
3(4 5)+ 3(9)= 27=Order of Operations
Distributive Property
3(4) 3(5)+12 15+27
It works!
Why use the distributive property? 3(x 2)+ 3(x) 3(2)= + 3x 6= +
Simplify using the distributive property. 1)
2)
3)
4)
5)
6)
5(x 3)+5 3•
5x 15+
6(y 7)+6 7•
6y 42+
3(m 8)−3 8•
3m 24−
4(3 y)−4 3 4 y• − •12 4y−
10(x 7)+10 x 10 7• + •10x 70+
4(k 2)−4 k 4 2• − •4k 8−
5 x• +
6 y• +
3 m• −
Use the distributive property to write an equivalent expression. Then simplify both to show they have the same value.
1)
2)
3)
5(8 3)+ 5(8) 5(3)= +5(11)55
40 15+55same
6(10 3)− 6(10) 6(3)= −6(7)42
60 18−42same
8(11 5)− 8(11) 8(5)= −8(6)48
88 40−48same
Simplify using the distributive property. 1)
2)
3)
4)
5)
6)
4(x 7)−4 7•
4x 28−
y(y 3)+y 3•
2y 3y+
x(2x 9)−x 9•
22x 9x−
7(8 x)−7 8 7 x• − •56 7x−
x(a b c)+ +x a x b x c• + • + •ax bx cx+ +
4(3 m k)− −4 3 4 m 4 k• − • − •
12 4m 4k− −
4 x• −
y y• +
x 2x• −
Geometric Model for Distributive Property
Two ways to find the area of the rectangle.
4
5 2
As a whole As two parts
A w l= •
( )4 5 2• +
Geometric Model for Distributive Property
Two ways to find the area of the rectangle.
4
5 2
As a whole As two parts
A w l= •
( )4 5 2• + 4 5• + 4 2•
4 5• 4 2•
same
( )4 5 2 4 5 4 2• + = • + •
Find the area of the rectangle in terms of x, y and z in two different ways.
x
y z
As a whole As two parts
A w l= •
( )x y z• +
Find the area of the rectangle in terms of x, y and z in two different ways.
x
y z
As a whole As two parts
A w l= •
( )x y z• + x y• + x z•
x y• x z•
same
Bell Work Use the distributive property to simplify. 1)
2)
3)
4)
5)
6)
8(x 4)−8 4•
8x 32−
7(3x 2)+7 2•
21x 14+
4(5 3x)−4 3x•
20 12x−
y(5) y(8)+y(5 8)+13y
a 3 a 4• + •a(3 4)+7a
6m 11m+m(6 11)+17m
8 x• −
7 3x• +
4 5• −
Use the distributive property to help simplify the following without a calculator. 1) 2) 5(9.96)
5(10) 5(0.04)−
5(10 0.04)−
50 0.20−
49.80
7(8.2)
7(8) 7(0.2)+
7(8 0.2)+
56 1.4+
57.4
Use the distributive property to help simplify the following without a calculator. 3) 4) 8($11.30)
8($11) 8($0.30)+
8($11 $0.30)+
$88 $2.40+
$90.40
7 5.95×
7(6) 7(0.05)−
7(6 0.05)−
42 0.35−
41.65