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 the 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

Using the distributive property, evaluate x(y + 2), for x = 2 and y = 5.
Choices:
A. 14
B. 12
C. 20
D. 9
Correct Answer: A
Solution:
Step 1: x(y + 2) = xy + 2x, using the 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