Patterns, Functions and Algebra
SOL 8.15c
8.15c
1
1.
a
A
B
C
D
multiplicative identity
multiplicative property of zero
commutative property of multiplication
multiplicative inverse
8.15c
2.

a
 1 illustrates which property of real numbers?
Which property of real numbers justifies the following statement?
4 – 2ab = 4 – 2ba
A
B
C
D
8.15c
distributive property
commutative property of multiplication
associative property of multiplication
symmetric property
3.
4(x  2)  4x  8 . Which property of the real numbers is used here?
A
B
C
D
distributive property
associative property
commutative property
closure property
8.15c
4.
What is the first step in solving the following equation?
2x – 3 = 5
A
B
C
D
adding 3 to both sides
dividing both sides by 2
subtracting 5 from both sides
multiplying both sides by x
Copyright © 1999-2011, S.S. Flanagan & D.E. Mott
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Do not reproduce without permission. 7-1-11
Patterns, Functions and Algebra
SOL 8.15c
8.15c
5.
Which property is illustrated in the following?
n (m + c) = nm + nc
A
B
C
D
associative property for multiplication
commutative property for addition
distributive property of multiplication over addition
reflexive property of addition
8.15c
6.
In solving the equation,
given.
Step
1:
1
x  24
3
1
x  24, the following steps and reasons are
3
Reason
given
1 
2: 3  x   3 24
3 
multiplicative property of equations
 1
3:  3   x  3 24
 3
associative property of multiplication
4: 1x  72
multiplication
5: x  72
???
What property justifies step 5?
A
B
C
D
Reflexive Property
Additive Identity
Multiplicative Inverse
Multiplicative Identity
Copyright © 1999-2011, S.S. Flanagan & D.E. Mott
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Do not reproduce without permission. 7-1-11
Patterns, Functions and Algebra
SOL 8.15c
8.15c
7.
Consider the procedure used below to solve the given equation.
Given:
Step 1:
Step 2:
Step 3:
3(x – 2) = 18
3x – 6 = 18
3x = 24
x=8
Which of the following properties is a justification for Step 1?
A
B
C
D
Associative property of addition
Commutative property of addition
Distributive property
Transitive property of equality
Use this sequence to answer the next question.
3(x + 4) + x = (3x + 3  4) + x
(3  4 + 3x) + x
12 + (3x + x)
12 + 4x
8.15c
Step
Step
Step
Step
1
2
3
4
8.
How do you justify Step 1?
A
B
C
D
associative property of multiplication
commutative property of multiplication
distributive property of multiplication
additive identity
Copyright © 1999-2011, S.S. Flanagan & D.E. Mott
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Do not reproduce without permission. 7-1-11
Patterns, Functions and Algebra
SOL 8.15c
8.15c
9.
To simplify
I.
II.
1
1  4 x  , step I through step IV below were completed:
4
1
1  4 x  = 1 1  1  4x 
4
4
4
=
1
1 
1    4  x
4
4 
III.
=
1
1  1 x
4
IV.
=
1
x
4
Which properties were used for steps I and II?
A
the distributive and associative properties of multiplication
B
the distributive property of multiplication and the property of reciprocals
C
the identity and the distributive properties of multiplication
D
the identity property of multiplication
8.15c
10. Which of the equations below represents Step 2 of the solution process?
Step
Step
Step
Step
Step
A
B
C
D
1: 3(2x + 1) + 6 = 45
2: ???
3: 6x + 3 = 45
4: 6x = 42
5: x = 7
6x  3 + 6 = 45
3(2x + 7) = 45
6x + 1 + 6 = 45
3(2x + 6) + 1 = 45
Copyright © 1999-2011, S.S. Flanagan & D.E. Mott
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Do not reproduce without permission. 7-1-11