Distributive Property

Definition of Distributive Property

• Distributive property states that the product of a number  and a sum is equal to the sum of the individual products of addends and the number.

That is: a(b + c) = ab + ac

                             

Examples of Distributive Property

• 5(3 + 1) = 5 × 3 + 5 × 1

Consider LHS: 5(3 + 1) = 5(4) = 20

Consider RHS: 5 × 3 + 5 × 1 = 15 + 5 = 20

LHS = RHS

                                                    

More about Distributive Property

• The property is true for any number of addends.

That is: a(b + c + d + . . . .) = ab + ac + ad + . . . . .

• Also:

a(b - c) = ab - ac  and

a (b - c - d - . . . )  = ab - ac - ad - . . .

                                          

Solved Example on Distributive Property

Evaluate x(y + 2), for x = 2 and y = 5 using distributive property.

Choices:

A. 14

B. 12

C. 20

D. 9

Correct Answer: A

Solution:

Step 1: x(y + 2) = xy + 2x, using distributive property

Step 2: Substitute the values of x and y in the expression.

Step 3: = 2 × 5 + 2 × 2 = 10 + 4 = 14.

                                                          

Related Terms for Distributive Property

• Sum
• Product
• Addend

                                            

Additional Links for Distributive Property

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