Distributive property is a fundamental concept in mathematics that is used to simplify and manipulate algebraic expressions.

The correct option for the distributive property is:

B) a×( b÷c)

Explanation:

The distributive property states that when you multiply a number (a) by the sum or difference of two other numbers (b and c), you can distribute the multiplication to each term inside the parentheses. In other words, you can multiply the first number (a) by each term inside the parentheses separately and then combine the results.

For example, let's say we have the expression a × (b + c). Using the distributive property, we can simplify this expression as:

a × (b + c) = a × b + a × c

This means that we can multiply a by both b and c separately and then add the results. The distributive property allows us to break down complex expressions into simpler ones, making it easier to manipulate and solve equations.

Option A) a× b =c = b× a

This option does not represent the distributive property. It simply shows that multiplication is commutative, meaning the order of multiplication does not affect the result. The distributive property, on the other hand, involves distributing the multiplication over addition or subtraction.

Option C) none of these

This option is incorrect because the distributive property is a valid mathematical concept, and it is represented by option B.

Option D) all of above

This option is incorrect because the distributive property is only represented by option B. The other options do not demonstrate the distributive property.

In conclusion, the distributive property is represented by option B, which states that a multiplied by the quotient of b divided by c is equal to the product of a and b divided by the product of a and c. This property allows us to simplify and manipulate algebraic expressions by distributing the multiplication over addition or subtraction.