Practice with Properties of Real Numbers Topic Index | Algebra Index | Regents Exam Prep Center

Test your skills on the following problems:

 1. x + 9 = 9 + x  is an example of which property? Choose: associative property of addition additive identity commutative property of addition additive inverse Explanation You are interchanging 2 elements. Therefore, it is the commutative property of addition.

 2. 2( x + 3 ) = 2x + 6   is an example of which property? Choose: associative property of multiplication distributive property commutative property of multiplication multiplicative inverse property Explanation You are taking the elements of addition inside the parenthesis and multiplying each by the element in front of the parenthesis. Therefore, it is the distributive property.

 3. x + ( y + 3 ) = x + ( 3 + y ) is an example of which property? Choose: associative property of addition distributive property additive identity commutative property of addition Explanation You are interchanging only the 2 elements inside the parenthesis.  Therefore, it is the commutative property of addition.

 4. ( 5 y ) • ( 1 ) = 5 y is an example of which property? Choose: multiplicative identity property multiplicative inverse property commutative property of multiplication associative property of multiplication Explanation An expression times the number one brings you back to the epression. This is the multiplicative identity property.

 5. ( x y ) z = x ( y z ) is an example of which property? Choose: commutative property of multiplication associative property of multiplication distributive property multiplicative inverse property Explanation Since you are regrouping the elements, it is the associative property of multiplication.

 6. ( x + 5 ) ( 7 + x ) =  ( x + 5 )•( 7 )+( x + 5 )•( x ) is an example of which property? (**tough problem!!**) Choose: associative property of addition commutative property of multiplication associative property of multiplication distributive property Explanation You are taking the first expression times each component of the second expression. This is an example of the distributive property.

 7. (y + 2) + (-y + -2) = 0 is an example of which property? Choose: multiplicative identity property additive identity property multiplicative inverse property additive inverse property Explanation An expression plus its negation give the identity element (0).  This is an example of the additive inverse property.

 8. is an example of which property? Choose: multiplicative identity property multiplicative inverse property commutative property of multiplication associative property of multiplication Explanation An expression times its reciprocal gives the multiplicative identity (1) as the answer. This is an example of the multiplicative inverse property.

 9. Determine which equation illustrates the commutative property. Choose: a + 0 = a a + (b + c ) = (a + b) + c a + b = b + a a(b + c) = ab + ac Explanation The communtative property "commutes" the order of the values. They physically move, such as a + b becoming b + a.

 10 Which property is illustrated by the equation                        ax +  ay = a(x + y) Choose: associative commutative distributive identity

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