Beginning Algebra Tutorial 8

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 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

(return to problem 1a)
 

 
 

.1 + 3x

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

.1 + 3x = 3x + .1

(return to problem 1b)
 

 

(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)

(return to problem 2a)
 

 

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

(return to problem 2b)
 

 

-2(x - 5)
 

 
 

 

 7(5a + 4b + 3c)
 

 
 

 

 -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)
 

 

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)
 

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Last revised on July 24, 2011 by Kim Seward.
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