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Date________________ Period_____
ALGEBRA 1
ASSOCIATIVE/COMMUTATIVE/DISTRIBUTIVE/IDENTITY/INVERSE Properties Worksheet
Directions:
The following expressions have been simplified. Tell which property was
used in each step. As always, SHOW ALL WORK TO RECEIVE ANY CREDIT.
ex.) 5 (2 + x) - 8x
=
(10 + 5x) - 8x
=
Distributive Property
10 + (5x – 8x)
=
Associative Property
10 + -3x
=
-3x + 10
1.)
2.)
Commutative Property
3a – 5b + 7a=
3a + 7a - 5b=
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10a – 5b
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23 + 5c + 7d – c – d - 27=
23 - 27 + 5c - c+ 7d – d =
3.)
Combining Like Terms
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-4 + 4c + 6d
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4c + 6d - 4
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3 (2 + y) - 4y=
(6 + 3y) - 4y =
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6 + (3y - 4y) =
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6 + -y
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-y + 6
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Directions:
Simplify the expression and tell which property you used for each step.
Hint: you should have about as many steps as there are lines. Use #1, 2,
and 3 as examples.
4.)
3 (4 + r) =
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5.)
7a – 2 (a + b) =
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6.)
8 – x + 4 (3x – 5)
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7.)
-11 (2x + 2) – 16x
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Directions:
Identify the properties (distributive, commutative, associative, identity
or inverse) that make the below statements true.
8.) (y + 4) – 7 = y + (4
- 7)
9.)
7x + 0 = 7x
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10.) (½) 2x = x
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12.) 32ab(1) = 32ab
11.) 5x – 7 + 7 = 5x
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13.) 4x – 5 = -5 + 4x
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