Download Properties of Algebra

Properties of Algebra
Name: _________________________________________ Date: _____________________
Directions: Give examples of the following Properties using real numbers.
1. Associative Property of Addition
6. Reflexive Property
2. Identity Property of Addition
7. Transitive Property
3. Distributive Property
8. Associative Property of Multiplication
4. Identity Property of Multiplication
9. Zero Product Property
5. Commutative Property of Addition
10. Commutative Property of Multiplication
Directions: Name the property shown. Associative Property, Commutative Property, Identity
Property, Distributive Property, Reflexive Property, Transitive Property or Zero Product Property.
11. 4 + 0 = 4
19. 8j + 32k = 32k + 8j
12. (6 + 3) + 1 = 6 + (3 + 1)
20. (6 + 3) + 1 = 6 + (3 + 1)
13. 7 · 51 = 51 · 7
21. 46(0) = 0
14. 17(w + 3) = 17w + 51
22. 1 · 5 = 5
15. (8 · 2) · 5 = 8 · (2 · 5)
23. 199 = 199
16. 0 + 12 = 12
24. 7(a + b) = 7a + 7b
17. (2x + 3y) + 8z = 2x + (3y + 8z)
25. 93(0) = 0
18. 5 · 456 = 456 · 5
26. 230 + 0 = 230
27. 7 = 7
28. 5x + 4 = 27 – y
27 – y = 4m + 2, therefore
5x + 4 = 4m + 2
Directions: Justify each step of solving the following equation by writing which algebraic
property is being used. The first justification is done for you.
-8x + 2x2 + 10x – 62 =22
2x2 – 8x + 10x – 62 = 22
__commutative property_____________________
2(x2 – 4x + 5x – 31) = 22
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2(x2 + x – 31) = 22
combining like-terms
x2 + x – 31 = 11
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x2 + x – 31 – 11 = 0
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x2 + x – 42 = 0
combining like-terms
(x + 7)(x – 6) = 0
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x + 7 = 0 or x – 6 = 0
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x = -7 or x = 6
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