Question 1

Which of the following statements correctly illustrates the distributive property of real numbers?

Accepted Answer

$$3(x + 8) = 3x + 3 	imes 8$$

Question 2

What is the reciprocal of $$-2$$?

Accepted Answer

$$-\dfrac{1}{2}$$

Question 3

Which property is demonstrated by the equation $$a + b = b + a$$?

Accepted Answer

Commutative Property

Question 4

A chemist mixes $$x$$ grams of substance A with $$y$$ grams of substance B, then adds $$z$$ grams of substance C. Which property allows her to group the additions in any order without changing the total mass?

Accepted Answer

Associative Property

Question 5

What is the opposite of $$\dfrac{3}{4}$$?

Accepted Answer

$$-\dfrac{3}{4}$$

Question 6

Which property is used in the equation $$2 + (-2) = 0$$?

Accepted Answer

Additive Inverse Property

Question 7

A patient is prescribed a medication that requires the dose to be multiplied by $$1 to $$maintain the same amount. Which property justifies this calculation?

Accepted Answer

Multiplicative Identity Property

Question 8

Which of the following is the reciprocal of $$\dfrac{5}{7}$$?

Accepted Answer

$$\dfrac{7}{5}$$

Question 9

Which property is illustrated by the equation $$0 + 8 = 8$$?

Accepted Answer

Additive Identity Property

Question 10

A company distributes $$x$$ units of a product to $$y$$ stores, then multiplies the total by $$z to $$account for packaging. Which property allows the calculation $$x(yz) = (xy)z$$?

Accepted Answer

Associative Property of Multiplication

Question 11

Which of the following is the correct application of the distributive property to $$x(x - 2)$$?

Accepted Answer

$$x^2 - 2x$

Question 12

If $$a = 5$$, what is the multiplicative inverse of $$a$$?

Accepted Answer

$$\dfrac{1}{5}$$

Question 13

Which property is used in the equation $$\dfrac{2}{3} 	imes \dfrac{3}{2} = 1$$?

Accepted Answer

Multiplicative Inverse Property

Question 14

A recipe calls for $$a$$ cups of flour and $$b$$ cups of sugar. If you switch the order of addition, which property ensures the total amount remains the same?

Accepted Answer

Commutative Property of Addition

Question 15

Which of the following is the opposite of $$7$$?

Accepted Answer

$$-7$$

Question 16

Which property is illustrated by $$1 	imes (-3) = -3$$?

Accepted Answer

Multiplicative Identity Property

Question 17

If $$a = -4$$, what is the opposite and reciprocal of $$a$$?

Accepted Answer

Opposite: $$4$$, Reciprocal: $$-\dfrac{1}{4}$$

Question 18

Which property allows you to write $$a(b + c) = ab + ac$$?

Accepted Answer

Distributive Property

Question 19

A scientist doubles the amount of a chemical, then adds $$0$$ grams. Which property ensures the total amount remains unchanged after adding zero?

Accepted Answer

Additive Identity Property

Question 20

Which of the following is a correct application of the associative property of addition?

Accepted Answer

$$(3 + x) + 2 = 3 + (x + 2)$$

Properties of Real Numbers: Opposites, Reciprocals, and Fundamental Properties

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