*xy*

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

*xy = yx*

.1 + 3*x*

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

**.1 + 3 x = 3x + .1**

(*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

**( a + b) +
1.5 = a + (b +
1.5)**

5(*xy*)

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

**5( xy) = (5x)y**

-2(*x *- 5)

7(5*a *+ 4*b* + 3c)

-7

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

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

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.

Last revised on July 24, 2011 by Kim Seward.

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