Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 8: Properties of Real Numbers
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
xy = yx
(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
.1 + 3x = 3x + .1
(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
(a + b) +
1.5 = a + (b +
1.5)
(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
5(xy) = (5x)y
(return to problem
2b) 
Answer/Discussion
to 3a
2(x  5) 

*Distribute 2 to EVERY term
*Multiply

Answer/Discussion
to 3b
7(5a + 4b + 3c) 

*Distribute 7 to EVERY term
*Multiply

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) 
Last revised on July 24, 2011 by Kim Seward.
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