Transcript Common Core Standard 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Student Objective:

Common Core Standard 7.EE.1
Apply properties of operations as strategies to add, subtract,
factor, and expand linear expressions with rational coefficients.
Student Objective: Use the distributive property to simplify variable expressions.
Distributive Property
a(b + c) = ab + ac
Order of Operations
6(3 + 5)
6(8)
48
Distributive Property
6(3 + 5)
6(3) + 6(5)
18 + 30
48
Use the distributive property to simplify.
1) 3(x + 7)
6) x(a + m)
ax + mx
3x + 21
2) 2(a + 4)
7) 4(3 + r)
2a + 8
12 + 4r
3) 7(8 + m)
8) 2(x + 8)
2x + 16
56 + 7m
4) 3(4 + a)
9) 7(2m + 3y + 4)
12 + 3a
5) (3 + k)5
15 + 5k
14m + 21y + 28
10) (6 + 2y + a)3
18 + 6y + 3a
Use the distributive property to simplify.
1) 4(y + 7)
6) a(c + d)
4y + 28
ac + ad
2) 3(b + 6)
7) 8(3 + r)
3b + 18
24 + 8r
3) 5(9 + m)
8) 4(x + y + 1)
45 + 5m
4x + 4y + 4
4) 5(4 + a)
9) 5(2m + 3 + t)
20 + 5a
10m + 15 + 5t
5) (7 + k)6
10) (11 + 2y)+3y
42 + 6k
11 + 5y
Geometric Model for Distributive Property
3
7
4
Two ways to find the total area.
Width by total length
4(3 + 7)
Sum of smaller rectangles
Geometric Model for Distributive Property
3
7
4 4(3)
4(7)
Two ways to find the total area.
Width by total length
4(3 + 7)
Sum of smaller rectangles
=
4(3) + 4(7)
4(10)
12 + 28
40
40
Geometric Model for Distributive Property
4
x
9
Two ways to find the total area.
Width by total length
9(4 + x)
Sum of smaller rectangles
=
9(4) + 9(x)
Geometric Model for Distributive Property
4
x
9 9(4)
9(x)
Two ways to find the total area.
Width by total length
9(4 + x)
Does Order of Operations
help to simplify here?
Sum of smaller rectangles
=
9(4) + 9(x)
36 + 9x
Factoring
Find the missing factor.
1) 15x  (5x)( 3 )
2) 12a  (2a)( 6 )
3) 2x  (x)( 2 )
4) 36a  (9a)( 4 )
5) 27x  (3x)( 9 )
Factoring
GCF - Greatest Common Factor
Find the GCF of the following mentally.
1) 15x
2) 30
3) 14m
4) 16k
12
42a
21m
40
GCF:
GCF:
3
6
GCF:
GCF:
8
7m
Factoring
One type involves the Distributive Property in
reverse.
Factor the following expression. FIND GCF first:
1) 12m  10
GCF: ___
2
2( 6m  5 )
2) 14a  7
GCF: ___
7
7( 2a  1 )
3) 15x  20y  30
GCF: ___
5
5( 3x  4y  6 )
4) 8m  12x  20
GCF: ___
4
4( 2m  3x  5 )
Factoring
One type involves the Distributive Property in
reverse.
Factor the following expression.
5) 22k  33
11( 2k  3 )
6) 15  35t
5( 3  7t )
7) 24c  12d  18
6( 4c  2d  3 )
8) 9b  6  21a
3( 3b  2  7a )
Like Terms
 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. x2 can only combine with other x2 terms.
Unlike Terms
7x
3y
Like Terms
7x
3x
2
5y
y
5y
y
10xy
2 2
a b
3
2yx
2a
3ab
4p
2
6ba
p
2
2
2
5x y
4p
7 xy
p
2
2
Simplify by combining like terms.
1) 7x + 4y + 2x + y
5) 4k + (2j) + 6k + j
9x + 5y
2) 3m + 10n + 4m + 1
7m + 10n + 1
3) 7x + 3y
7x + 3y
4) 6x + (5x) + 2x + 3
13x + 3
10k + 3j
6) 10 + 4x + 3y + 17x
21x + 3y + 10
7) 3y2  y  6y2  y
9y  2y
2
3
2
2
8) m  4t  m2  t
7
7
5 m 2 5t
7
Simplify the expression using the Distributive
Property and then combining like terms.
1) 3(a  4)  2a
3a  12  2a
5a  12
2) 5x  4(x  7)
5x  4x  28
9x  28
3) 2a  6(5  a)  a
2a  30  6a  a
9a  30
4) 3(b  4)  2(b  5)
3b  12  2b  10
5b  22
Simplify each variable expression.
5) 7(x + 4) + 2x
8) 3(b + 2) + 6b
7x + 28 + 2x
9x + 28
6) 5x + 3(x + 1)
5x + 3x + 3
8x + 3
7) a + 2(4 + a ) + 1
a + 8 + 2a + 1
3a + 9
3b + 6 + 6b
9b + 6
9) 2(3m + 1) + 4m
6m + 2 + 4m
10m + 2
10) 3(k + m) + 5(k + 2m)
3k + 3m + 5k + 10m
8k + 13m