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Assignment # _____ REVIEW: Properties
Name _________________________
Standard: AF 1.3 Use properties of rational numbers
Pre-Algebra, Period ______
Date __________________________
A.
B.
C.
D.
E.
F.
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Additive Identity (Identity Prop. of Addition)
Multiplicative Identity (Identity Prop. of multiplication)
2+3=3+2
45=54
(1 + 3) + 5 = 1 + (3 + 5)
(3  4)  5 = 3  (4  5)
7+0=7
71=7
1 3  3
 
4 3  12
G. Inverse Property of Addition (Additive Inverse)
8 + (–8) = 0
H. Inverse Property of Multiplication (Multiplicative Inverse)
5

I. Distributive Property
1
1
5
3(3 + 4) = 3(3) + 3(4) = 9 + 12 = 21
3(4x + 5) = 3(4x) + 3(5) = 12x + 15

Using the letters above (in bold), identify each property shown.
1. 20 + 15 = 15 + 20 _______
4. 9 
2. 35 + (–35) = 0 ______
1
 1 _______
9
3.
1 5  5
______
 
4 5  20
5. (3 + 4)(5 + 6) = (5 + 6)(3 + 4) _______
8. 5x – 5y = 5(x – y) _______
6. 3 • (100 + 3) = 300 + 9 _______
7. 8 • 1 = 8 _______
9. 2(3 + 6) = 2(3) + 2(6) _______
10. –16 + 0 = –16 _______ 11.

1
 15  1 _______
15
12. (6 x 3)(5 x 2) = (5 x 2)(6 x 3) _______ 13. 4 • (5 • 6) = (4 • 5) • 6 _______

14. 14a + 14b = 14(a + b) _______
15. (x + 9) + 1 = x + (9 + 1) _______
16. 4 + 6 + 5 = 5 + 4 + 6 _______
17. 8(50 + 4) = 400 + 32 _______
18. Which expression is equivalent to 4x – 4y?
A 4xy
B 4(x – y)
C 4x – y
18. ______
D x – 4y
19. Which of the following equations illustrates the inverse property of multiplication?
A 4x1=4
B 4x0=0
D 4
C 4 x 4 = 16

19. ______
1
1
4
20. Which property is used in the following equation? (2 + 3) (5 + 4) = (5 + 4)(2 + 3)
20. ______
A associative property of addition
B commutative property of addition
C distributive property
D commutative property of multiplication
21. Which property is used in the following equation? 3(x + 8) = 3x + 24
21 ______
A distributive property
B commutative property of addition
C associative property of addition
D associative property of multiplication
22. Which equation shows the distributive property?
22. ______
A (12 + 4) + 0 = 12 + 4
B 3(4 + 6) = 12 + 18
C 4+3+6=6+4+3
D (12 + 4) + 6 = 12 + (4 + 6)
23. Which property is used in the following equation? 4 + (8 + 5) = (4 + 8) + 5
A associative property of multiplication
B commutative property of addition
C distributive property
D associative property of addition
23. ______
24. Which expression is the result of applying the distributive property to 3 x (200 + 4)?
A 600 + 12
B 3 x 204
C 600 + 4
D 3 + 212
25. Which operation will NOT CHANGE the value of any nonzero number?
A multiplying by one
B adding one
25. ______
C multiplying by zero
D dividing by zero
26. Which property is used in the following equation? 5(2 + 8) = 10 + 40
26. ______
A associative property of addition
B commutative property of addition
C associative property of multiplication
D distributive property
1 4  4
 
3 4  12
B associative property of multiplication
27. Which property provides justification for the equation?
A commutative property of multiplication
C additive identity

1
1
8
B 8x0=0
27. ______
D multiplicative identity
28. Which of the following illustrates the inverse property of multiplication?
A 8
24. _____
C 8x1=8
D 8
28. ______
8
8
8