Distributive Property Definition

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Distributive property definition helps to understand the property and show you how to implement in mathematics. Distributive property is the most frequently used property in mathematics. Distributive property let you multiply a number to a sum by multiplying each addend separately and then add the products. We need to use a lot in algebra. This property states that multiplying a number by a group of number added together is same as when we multiply them separately.

The following examples illustrates the use of distributive property

Problem 1:  3 *(5 + 2) use distributive property to calculate.

Solution: 3 *(5 + 2),

=> 3 can be distributed across 5 and 2 in to 3 times 5 and 3 times 2

=> So, 3 *(5 + 2) = 3 * 5 + 3 * 2 = 15 + 6 = 21.

Problem 2: Show whether the statement using distributive property or not.

Solution: 5(4 + 1) = (5 × 4) + (5 × 1)

=> LHS = 5(4 + 1) = 5 * 5 = 25

=> RHS = (5 × 4) + (5 × 1) = 20 + 5 = 25

=> LHS = RHS

=> So, this statement shows distributive property.

Problem 3: Using the distributive property, evaluate x(y + 2), for x = 3 and y = 4.

Solution: Given: x = 3 and y = 4

=> Use distributive property a( b + c) = a *b + a * c

=> Substitute the values in x (y + 2) = 3 (4 + 2) = 3 * 4 + 3 * 2= 12 + 6 = 18.