Properties of Numbers

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

• 4 x 5 = 5 x 4

• 12 x 0 = 0

• 6 x (3 x 2) = ( 6 x 3) x 2

• 1 x 8 = 8

Answer explanation

The Identity property of multiplication states that any number multiplied by 1 remains unchanged. In this case, 1 x 8 = 8 shows that multiplying 8 by 1 does not change its value, making it the correct example.

Which of the following illustrations shows Distributive Property of Multiplication?

• 12 x 5 = 5 x 12

• 8 x ( 4 x 2 ) = (8 x 4) x 2

• 1 x 13 = 13

• 4 x ( 6 + 2) = (4 x 6) +( 4 x 2)

Answer explanation

The Distributive Property states that a(b + c) = ab + ac. The correct choice, 4 x (6 + 2) = (4 x 6) + (4 x 2), demonstrates this property by distributing 4 across the sum of 6 and 2.

Using the Distributive Property of Multiplication, how will you rewrite this number; 12 x (4 + 3) ?

• (12 x 4) + (12 x 3)

• 12 x 4 x 12 x 3

• (12 x 4) + 3

• 4 + 3 x 12

Answer explanation

Using the Distributive Property, 12 x (4 + 3) can be rewritten as (12 x 4) + (12 x 3). This shows that you multiply 12 by each term inside the parentheses, making the correct choice (12 x 4) + (12 x 3).

For any numbers a, b, and c, if a = b and b = c, then a = c.

• Transitive Property         

• Symmetric Property

• Reflexive Property

• Substitution Property

Answer explanation

The statement a = b and b = c implies that a and c are equal. This is an example of the Transitive Property, which states that if a = b and b = c, then a = c. Thus, the correct answer is the Transitive Property.

For any numbers a and b, if a = b, then b = a.

• Transitive Property         

• Reflexive Property 

• Symmetric Property   

• Substitution Property

Answer explanation

The statement 'if a = b, then b = a' illustrates the Symmetric Property, which states that if one quantity equals another, then the reverse is also true. This is distinct from the other properties listed.

Name the property described:
∠B≅∠B

• Reflexive

• Symmetric

• Transitive

• Addition

Answer explanation

The property ∠B≅∠B illustrates the Reflexive Property, which states that any geometric figure is congruent to itself. This is a fundamental property in geometry.

Name the property described:
If MN = OP and OP = QR, then MN = QR

• Reflexive

• Symmetric

• Transitive

• Addition

Answer explanation

The property described is Transitive. It states that if MN = OP and OP = QR, then it follows that MN = QR. This is a fundamental property of equality in mathematics.

Name the property:
9 + 0 = 9

• Identity Property of Multiplication

• Associative Property of Addition

• Identity Property of Addition

• Additive Inverse Property

Answer explanation

The equation 9 + 0 = 9 demonstrates the Identity Property of Addition, which states that adding zero to any number does not change its value. Thus, the correct choice is the Identity Property of Addition.

Name the property: 
1 ^_x 12 =12

• Identity Property of Multiplication

• Commutative Property of Multiplication

• Multiplication Property of One

• Distributive Property

Answer explanation

The equation 1 x 12 = 12 demonstrates the Identity Property of Multiplication, which states that any number multiplied by 1 remains unchanged. Thus, the correct choice is the Identity Property of Multiplication.

Which example shows Multiplicative Inverse Property? (a)  

• a + 1 = 1

• a x 1 = 1

• a x a = 1

Answer explanation

The Multiplicative Inverse Property states that a number multiplied by its reciprocal equals 1. The correct choice, \(a \cdot \frac{1}{a} = 1\), illustrates this property, while the other options do not.