Algebraic Properties and Order Relations of Real Numbers

Match the Property to Its Equation

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Property

Additive identity

Multiplicative identity

Distributive

Associative (addition)

Commutative (addition)

Equation

a · 1 = a

a + b = b + a

(a + b) + c = a + (b + c)

a · (b + c) = a·b + a·c

a + 0 = a

Match each algebraic property of real numbers with the equation that expresses it.

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Explanation

The Additive Identity

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What is the additive identity of the real numbers?

0

-1

1

Undefined

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Explanation

The Multiplicative Inverse

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What is the multiplicative inverse of a nonzero real number \(a\)?

1/a

-a

0

a

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Explanation

Does Zero Have a Multiplicative Inverse?

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True or False: The real number 0 has a multiplicative inverse.

True

False

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Applying the Order Properties

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Given \(a < b\), select every statement below that is always true.

If c < 0, then a·c < b·c

If c > 0, then a·c < b·c

a + c < b + c for any real c

If c < 0, then a·c > b·c

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Explanation

The Law of Trichotomy

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The Law of Trichotomy states that for any two real numbers a and b, exactly one of which statements is true?

a > b and a < b simultaneously

a = 0 or b = 0

a + b = 0

a = b, a < b, or b < a

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Explanation

Reciprocals of Positive Numbers

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If \(0 < a < b\), which of the following is true?

Cannot be determined

1/a < 1/b

1/a > 1/b

1/a = 1/b

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Complete the Property Name

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Missing

If \(a < b\) and \(b < c\), then \(a < c\). This is known as the ______ property.

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Adding Two Inequalities

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Given \(a < b\) and \(c < d\), which property lets us conclude \(a + c < b + d\)?

Trichotomy

Transitive property

Addition of inequalities

Distributive property

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Match the Property to Its Equation

Property

Equation

Correct Answer

Explanation

The Additive Identity

Correct Answer

Explanation

The Multiplicative Inverse

Correct Answer

Explanation

Does Zero Have a Multiplicative Inverse?

Correct Answer

Explanation

Applying the Order Properties

Correct Answer

Explanation

The Law of Trichotomy

Correct Answer

Explanation

Reciprocals of Positive Numbers

Correct Answer

Explanation

Complete the Property Name

Correct Answer

Explanation

Adding Two Inequalities

Correct Answer

Explanation

Quran Recitation

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