Properties of Real Numbers and Equality

If you multiply a number and its multiplicative inverse, what do you get?

• 0

• 1

• Not enough information

• None of these

Answer explanation

Multiplying a number by its multiplicative inverse (1 divided by the number) always results in 1. Therefore, the correct answer is 1.

3(w + 4) = 3w + 12 is an example of...

• Inverse Property

• Distributive Property

• Multiplicative Inverse

• Associative Property

Answer explanation

The equation 3(w + 4) = 3w + 12 demonstrates the Distributive Property, which states that a(b + c) = ab + ac. Here, 3 is distributed to both w and 4.

(5 + 3) + 2 = 5 + (3 + 2)

• Commutative  Addition

• Commutative Multiplication

• Associative Addition

• Associative Multiplication

Answer explanation

The equation (5 + 3) + 2 = 5 + (3 + 2) demonstrates the Associative Property of Addition, which states that the way numbers are grouped does not change their sum. Thus, the correct choice is Associative Addition.

3 + (12 + 8) = 3 + (8 + 12) 

• Associative Addition 

• Associative Multiplication 

• Commutative Addition 

• Commutative Multiplication 

Answer explanation

The equation shows that the order of addition does not affect the sum. This is an example of Commutative Addition, where a + b = b + a. Thus, 3 + (12 + 8) equals 3 + (8 + 12) due to the commutative property.

• A

• B

• C

• D

Identify the property shown.
For all real numbers, m=m.

• Symmetric

• Reflexive

• Transitive

• Substitution

Irrational numbers _______ be written as fractions. If they are written as decimals, the decimals ________ and _______ .

• Cannot; never terminate; never repeat

• Cannot; terminate; never repeat

• Can; terminate; repeat

• Can; never terminate; repeat

Which is true about irrational numbers?

• Irrational numbers are terminating decimals.

• Irrational numbers are non-repeating, non-terminating decimals.

• Irrational numbers are fractions.

• Irrational numbers are repeating decimals.

Identify the property you would use to solve this equation:
4x = 72

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Answer explanation

To solve the equation 4x = 72, you would use the Division Property of Equality. This property states that if you divide both sides of the equation by the same non-zero number (in this case, 4), the equality holds.

Identify the property you would use to solve this equation:
y – 7 = 28

• Additive Property of Equality

• Subtraction Property of Equality

• Multiplicative Property of Equality

• Division Property of Equality

Answer explanation

To solve y – 7 = 28, you need to isolate y. You can do this by adding 7 to both sides of the equation. This demonstrates the Additive Property of Equality, which states that you can add the same value to both sides of an equation.