9th Grade – Math Properties
Name: ___________________
Period: ____
Use the commutative or associative property to complete the statement. Then state
which property is used.
1. -12 + 6 = 6 + _____
2. 8 + (-4) = -4 + _____
3. -6 • 3 = _____ • (-6)
4. -12 • 6 = 6 • ____
5. (4 + 7) + 8 = 4 + ( ___ + 8)
6. (-2 + 3) + 6 = -2 + (___ + 6)
7. 8 • (3 • 6) = (___ • 3) • 6
8. 6 • (4 • 2) = (6 • ___) • 2
Name the property used for each statement (commutative, associative, identity,
inverse, or distributive).
9. 12 + (-12) = 0
10. 7 + 8 = 8 + 7
11. -4 + 4 = 0
12. 10 + 9 = 9 + 10
13. (-8 + 13) + 2 = -8 + (13 + 2)
14. -2 + (10 + 5) = (-2 + 10) + 5
15. 5 x (13 x 7) = (5 x 13) x 7
16. -3 • (2 • 9) = (-3 • 2) • 9
17. 4/9(9/4) = 1
18. 3.25 + 0 = 3.25
19. (1 + 35) + 2 = 2 + (1 + 35)
20. 7(x + y) = 7x + 7y
21. – ½ = - ½ • 4/4 = - 4/8
22. 6(3x) + 6(5y) = 6(3x + 5y)
23. ¾ (4/3) = 1
24. – 9.6345 + 0 = - 9.6345
25. Awesome • 0 = 0
26. Awesome + 1 = Awesome
27. 14(p + q) = 14p + 14q
28. 1/3 = 1/3 • 7/7 = 7/21
Simplify each using the properties to make your work easier.
29. 97 + 13 + 3 + 37
33. 6x + 8 – 6x + 9
30. 106 + 8 + (-6) + (-8)
34. ½y + 5 – 5 – ½y
31. 159 + 12 + 141 + 88
35. (3/5)(-0.625)(5/3)
32. 49 + 199 + 1 + 1
36. T + (-T) + ½ (2)
37. Evaluate 10 – (5 – 3) and (10 – 5) – 3. Is subtraction associative? Explain.
38. Evaluate 150 ÷ (15 ÷ 5) and (150 ÷ 15) ÷ 5. Is division associative? Explain.
Use the distributive property to rewrite each expression. Simplify if possible.
39. 4(5 + 6)
40. 6(11 – 4)
41. 10(x + 3)
42. 5(w + 3)
43. -7(t – 5)
44. -13(x + 5)
45. – ½(24x + 32y)
46. 5z + 5w
47. 6x – 6y
48. 15(12x) + 15(5y)
49. 8(3x + 5y – 7z)
50. -2(12p – 5q + 14r)
51. 5x + 15
52. 10y – 100
53. –(-3q + 5r – 6t)
54. –(-5x – 7z)
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ID: 1
9th Grade - Combine Like Terms
Name___________________________________
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Combine Like Terms.
1) p p
2) mm
3) mm
4) nn
5) rr
6) x x
7) (b)
8) n(n)
9)  x( x)
10)  x( x)
11)  x( x)
12) (v)
13) mm(m)
14) (n)
15) (a)
16) k(k)
17)  p( p) p 
18)  x( x)
Translate each phrase into a mathematical expression. Use x as the variable. Combine like terms
when possible.
19) Five times a number, added to the sum of the
number and three.
20) Six times a number, added to the sum of the
number and six.
21) A number multiplied by - 7, subtracted from
the sum of 13 and six times the number.
22) A number multiplied by 5, subtracted from
the sum of 14 and eight times the number.
23) Six times a number added to -4, subtracted
from twice the sum of three times the number
and 4.
24) Nine times a number added to 6, subtracted
from triple the sum of 12 and 8 times the
number.
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Worksheet by Kuta Software LLC
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Answers to (ID: 1)
1)  p
2) 
3) m
4) n
5) r
6)  x
7) b
8) n  n
9)  x x 
10)  x   x
11)  x   x
12) v

13) mm
14) n
15) a
16) k
19) 5x + (x + 3); 6x + 3
20) 6x + (x + 6); 7x + 6
17)  p p 
18)  x
21) (13 + 6x) - (-7x); 13 + 13x
22) (14 + 8x) - 5x; 14 + 3x
23) 2(3x + 4) - (6x + (-4)) ; 12
24) 3(12 + 8x) - (9x + 6) ; 30 + 15x
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Worksheet by Kuta Software LLC