Question

42(4 + 2) = (42 \times 4) + (42 + 2) is an example of
A) Closure property
B) Commutative property
C) Associative property
D) Distributive property

Answer 1

Hint: In this question we need to state which property among the options is used in the numerical expression \[42(4 + 2) = (42 \times 4) + (42 + 2)\] .First, we write the definitions of all four properties mentioned above and then check which property is used in the numerical expression, \[42(4 + 2) = (42 \times 4) + (42 + 2)\].

Complete step-by-step answer:
Closure property of addition: Closure property applies for addition and multiplication of real numbers. The sum of any two real numbers will yield a real number.

Example: \[12{\text{ + }}0 = 12,{\text{ }}9 + 7 = 16.\]

Commutative property of addition: The sum of numbers remain unchanged irrespective of where they are placed. For example: \[4{\text{ + }}2 = 2 + 4{\text{ = 6}}\].

Associative property of addition: The sum of more than two numbers remains unchanged irrespective of the manner of arrangement of numbers. For example, \[\left( {2 + 3} \right) + 4 = 2 + \left( {3 + 4} \right)\;\].

Distributive property: Let x, y, z be three unique numbers then the following equation must be obeyed $x \times (y + z) = x \times y + x \times z$ which is known as distributive property.

So from the definitions of the above properties, the numerical expression \[42(4 + 2) = (42 \times 4) + (42 + 2)\] is an example of distributive property.

So, the correct answer is “Option D”.

Note: Just as these properties are with respect to addition they also have with respect to multiplication.

Closure property of multiplication: The product of any two real numbers yields a real number.

Commutative property of multiplication. : The product of numbers remains unchanged irrespective of where they are placed.

For example: \[4{\text{ }} \times 2 = 2 \times 4{\text{ = 8}}\]

Associative property of multiplication: The associative property says that the manner in which numbers are grouped in a multiplication does not change the product.