Concept explainers
Work all of the problems in this self-test without using a calculator. Then check your work by consulting the answers in the back of the book. Where weaknesses show up, use the reference that follows each answer to find the section in the test that provides the necessary review.
1. Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property:
(A) Commutative (·): x(y + z) = ?
(B) Associative (+): 2 + (x + y) = ?
(C) Distributive: (2 + 3)x = ?
(A)
To find: The equivalent expression of
Answer to Problem 1E
The expression
Explanation of Solution
Given:
The expression is
Property used:
Commutative property:
“The order of factors does not affect the result of expression”.
That is, if x commutes with y under the operation
Illustration:
The factors of the given expression
Apply the commutative property by changing the order of factors to obtain the required equivalent expression.
That is,
Therefore, the expression
(B)
To find: The equivalent expression of
Answer to Problem 1E
The expression
Explanation of Solution
Given:
The expression is
Property used:
Associative property:
The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.
That is, the property of associative under “
Illustration:
Apply the associative property by changing the group of terms to obtain the required equivalent expression.
That is,
Therefore, the expression of
(C)
To find: The equivalent expression of
Answer to Problem 1E
The expression
Explanation of Solution
Given:
The expression is
Property used:
Distributive property:
The property of left distributive under multiplication over addition state that
Illustration:
Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.
That is,
Hence, the expression of
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