Objective - To use the distributive property to simplify numerical and variable expressions.
Distributive Propertya(b c) a b a c
a(b c) a b a c or
3(4 5) 3(9) 27Order of Operations
Distributive Property
3(4) 3(5)12 15
27It 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)
5540 15
55same
6(10 3) 6(10) 6(3) 6(7)42
60 1842
same
8(11 5) 8(11) 8(5) 8(6)48
88 4048same
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
Use the distributive property to write anequivalent variable expression. Then 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 11mm(6 11)
17m
8 x
7 3x
4 5
Use the distributive property to help simplify thefollowing 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 thefollowing 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
