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explain distributive property

Distributive Property:

 

Distributive property for multiplication over addition

a × (b + c) = a × b + a × c

a × (b + c) means that first of all we need to add b and c, then this result is multiplied with a.

Multiply a with b and a with c. The sum of the products, a × b + a × c is same as the a × (b + c).

Consider a, b, c equals to 2, 4 and 6 respectively.

Now, a × (b + c) = 2 × (4 + 6) = 2 × 10 = 20

and a × b + a × c = 2 × 4 + 2 × 6 = 8 + 12 = 20

Hence, a × (b + c) = a × b + a × c
Distributive property for multiplication over subtraction
a × (b – c) = a × b – a × c

a × (b – c) means that first of all we need to subtract c from b, then this result is multiplied with a.

Multiply a with b and a with c. The difference of the products, a × b – a × c is same as the a × (b – c).

You can also verify this property by considering any numerical value of a, b and c.

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View Full Answer

The distributive property is the ability of one operation to "distribute" over another operation contained inside a set of parenthesis. Most commonly, this refers to the property of multiplication distributing over addition or subtraction, such that x(a+b) = xa + xb.

When we say that multiplication distributes over addition, it means we can distribute the factor outside the set of parenthesis to each item inside, and then add the results. For example, 4(3+7) is equivalent to 4*3 + 4*7 because the multiplication by four was distributed across the addition inside the parenthesis.

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