Properties of Real numbers

Which of the following is an example of the commutative property of addition?

• 3 + 5 = 5 + 3
• (3 + 5) + 7 = 3 + (5 + 7)
• 3 × 5 = 5 × 3
• (3 × 5) × 7 = 3 × (5 × 7)

Answer explanation

The commutative property states that changing the order of numbers does not change the sum.

What is the identity element for multiplication in real numbers?

• 0
• 1
• -1
• 10

Answer explanation

The identity element for multiplication is 1 because multiplying any number by 1 gives the same number.

The distributive property states that:

• a(b + c) = ab + ac
• a + (b + c) = (a + b) + c
• (a × b) + c = (a + b) × c
• (a + b) + c = a + (b + c)

Answer explanation

The distributive property states that a(b + c) = ab + ac.

What is the inverse of 7 under addition?

• -7
• 7
• 1/7
• 0

Answer explanation

The additive inverse of a number is the number that, when added to it, results in zero.

Which of the following is an example of the associative property of multiplication?

• (2 × 3) × 4 = 2 × (3 × 4)
• 2 × 3 = 3 × 2
• (2 + 3) + 4 = 2 + (3 + 4)
• 3 + 4 = 4 + 3

Answer explanation

The associative property states that the way numbers are grouped does not change the result.

If a × 0 = 0 for any real number a, which property does this illustrate?

• Identity property
• Zero property of multiplication
• Inverse property
• Commutative property

Answer explanation

Multiplying any number by zero always results in zero.

Which property of real numbers does this equation illustrate? 5 + (-5) = 0

• Associative property
• Additive inverse property
• Distributive property
• Multiplicative inverse property

Answer explanation

The additive inverse property states that any number plus its opposite equals zero.

If a = b, then b = a. This is an example of which property?

• Symmetric property
• Reflexive property
• Transitive property
• Commutative property

Answer explanation

The symmetric property states that if a = b, then b = a.