Answer/Discussion to 1a

 xy

Using the commutative property of multiplication (where changing the order of a product does not change the value of it), we get

(return to problem 1a)

Answer/Discussion to 1b

.1 + 3x

Using the commutative property of addition (where changing the order of a sum does not change the value of it), we get

(return to problem 1b)

Answer/Discussion to 2a

(a + b) + 1.5

Using the associative property of addition (where changing the grouping of a sum does not change the value of it), we get 

(return to problem 2a)

Answer/Discussion to 2b

5(xy)

Using the associative property of multiplication (where changing the grouping of a product does not change the value of it), we get 

Answer/Discussion to 3a

-2(x - 5)

Answer/Discussion to 3b

 7(5a + 4b + 3c)

Answer/Discussion to 4a

 -7

The opposite of -7 is 7, since -7 + 7 = 0.

The reciprocal of -7 is -1/7, since -7(-1/7) = 1.

(return to problem 4a)

Answer/Discussion to 4b

3/5

The opposite of 3/5 is -3/5, since 3/5 + (-3/5) = 0.

The reciprocal of 3/5 is 5/3, since (3/5)(5/3) = 1.

(return to problem 4b)