Mathematics Homework Help

Directions: Please read each question carefully and select the best answer.

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1. Commutative Property of Addition.

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a + b = b + a

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Examples:

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1. real numbers

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2 + 3 = 3 + 2

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2. algebraic expressions

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x 2 + x = x + x 2

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True False

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2. Commutative Property of Multiplication.

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a × b = b × a
Examples:
1. real numbers
5 × 7 = 7 × 5
2. algebraic expressions
(x ³ – 2) × x = x × (x ³ – 2)

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True False

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3. Associative Property of Addition.

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(a + b) + c = a + (b + c)
Examples:
1. real numbers
(2 + 3) + 6 = 2 + (3 + 6)
2. algebraic expressions
(x ³ + 2 x) + x = x ³ + (2 x + x)

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True False

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4. Associative Property of Multiplication.

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(a × b) × c = a × (b × c)
Examples:
1. real numbers
(7 × 3) × 10 = 7 × (3 × 10)
2. algebraic expressions
(x ² × 5 x) × x = x ² × (5 x × x)

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True False

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5. Distributive Properties of Addition Over Multiplication.

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a × (b + d) = a × b + ad× c
and
(a + b) × c = a × c + b × c
Examples:
1. real numbers
2 × (2 + 2) = 2 × 2 + 2 × 8
(2 + 8) × 2= 2 × 10 + 8 × 10
2. algebraic expressions
x × (x ⁴ + x) = x × x ⁴ + x × x
(x ⁴ + x) × x ² = x ⁴ × x ² + x × x ²

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True False

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