student objective: use the distributive property to simplify variable expressions. distributive...
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Student Objective: Use the distributive property to simplify variable expressions.
Distributive Propertya(b + c) = ab + ac
Order of Operations Distributive Property
6(3 + 5) 6(3 + 5)6(8)
48
6(3) + 6(5)
18 + 30
48
Common Core Standard 7.EE.1 Apply properties of operations as strategies to add, subtract,
factor, and expand linear expressions with rational coefficients.
Use the distributive property to simplify.
1) 3(x + 7)
2) 2(a + 4)
3) 7(8 + m)
4) 3(4 + a)
5) (3 + k)5
6) x(a + m)
7) 4(3 + r)
8) 2(x + 8)
9) 7(2m + 3y + 4)
10) (6 + 2y + a)3
3x
2a
56
12
15
ax + mx
12 + 4r
2x + 16
14m + 21y + 28
18 + 6y + 3a
+ 21
+ 8
+ 7m
+ 3a
+ 5k
Use the distributive property to simplify.
1) 4(y + 7)
2) 3(b + 6)
3) 5(9 + m)
4) 5(4 + a)
5) (7 + k)6
6) a(c + d)
7) 8(3 + r)
8) 4(x + y + 1)
9) 5(2m + 3 + t)
10) (11 + 2y)+3y
4y + 28
3b + 18
45 + 5m
20 + 5a
42 + 6k
ac + ad
24 + 8r
4x + 4y + 4
10m + 15 + 5t
11 + 5y
Geometric Model for Distributive Property3 7
4
Two ways to find the total area.
Width by total length Sum of smaller rectangles
4(3 + 7)
Geometric Model for Distributive Property3 7
4
Two ways to find the total area.
Width by total length Sum of smaller rectangles
4(3 + 7) 4(3) + 4(7)
4(3) 4(7)
=4(10) 12 + 28
40 40
Geometric Model for Distributive Property4 x
9
Two ways to find the total area.
Width by total length Sum of smaller rectangles
9(4 + x) 9(4) + 9(x)=
Geometric Model for Distributive Property4 x
9
Two ways to find the total area.
Width by total length Sum of smaller rectangles
9(4 + x) 9(4) + 9(x)=
9(4) 9(x)
Does Order of Operations help to simplify here?
36 + 9x
Find the missing factor.
1)
2)
3)
15x (5x)( )
4)
5)
12a (2a)( )
2x (x)( )
36a (9a)( )
27x (3x)( )
3
6
2
4
9
Factoring
GCF - Greatest Common Factor
3
6
7 m
Factoring
Find the GCF of the following mentally.
1)
2)
3)
15x 12
30 42a
14m 21m
4) 16k 40 8
GCF:
GCF:
GCF:
GCF:
7( )
Factoring
Factor the following expression. FIND GCF first:
1)
2)
3)
4)
12m 10
14a 7
15x 20y 30
8m 12x 20
2( )6m 5
2a 1
5( )3x 4y 6
4( )2m 3x 5
One type involves the Distributive Property in reverse.
GCF: ___ GCF: ___
GCF: ___GCF: ___
2
7
5
4
5( )
Factor the following expression.
5)
6)
7)
8)
22k 33
15 35t
24c 12d 18
9b 6 21a
11( )2k 3
3 7t
6( )4c 2d 3
3( )3b 2 7a
Factoring
One type involves the Distributive Property in reverse.
Variable terms that differ only in their coefficients. Variables must be same letters and powers (exponents).Ex) x can only combine with other x terms. x can only combine with other x terms.
Like Terms Unlike Terms
7x 3x
5y y
10xy 2yx
7x 3y
5y 2y
2a 3ab
2
32a b 26ba 25x y 7 2xy
4 2p 2p 4p 2p
Like Terms
22
Simplify by combining like terms.1) 7x + 4y + 2x + y
2) 3m + 10n + 4m + 1
3) 7x + 3y
4) 6x + (5x) + 2x + 3
5) 4k + (2j) + 6k + j
6) 10 + 4x + 3y + 17x
7)
8)
9x
7m
7x + 3y
13x
10k
21x
+ 5y
+ 10n + 1
+ 3
+ 3j
+ 3y + 102 23y y 6y y
29y 2y2 23 2m 4t m t
7 7 25 m
7 5t
Simplify the expression using the Distributive Property and then combining like terms.
1)
2)
3)
4)
3(a 4) 2a
5x 4(x 7)
2a 6(5 a) a
3(b 4) 2(b 5)
3a 12 2a
5a 12
4x 285x 9x 28
30 6a2a a9a 30
3b 12 2b 10 5b 22
Simplify each variable expression.5) 7(x + 4) + 2x
6) 5x + 3(x + 1)
7) a + 2(4 + a ) + 1
7x + 28 + 2x
9x + 28
5x + 3x + 3
8x + 3
a + 8 + 2a + 1
3a + 9
8) 3(b + 2) + 6b
9) 2(3m + 1) + 4m
10) 3(k + m) + 5(k + 2m)
3b + 6 + 6b
9b + 6
6m + 2 + 4m
10m + 2
3k + 3m
8k + 13m
+ 5k + 10m