Distributive Property of Multiplication

Distributive Property of Multiplication definition states that the product of a number with the sum of two numbers is equal to the sum of individual products of 1st number and each addends. Thus the products of the real numbers can be expressed as sum of the numbers and hence this property is specifically called distributive property of multiplication. The generic property for 3 real numbers x, y and z is x * (y + z) = (x * y) + (x * z). Now if we apply commutative property to it, we get another form of the property, i.e. (y + z) * x = (y * x) + (z * x). Both are same and yields same results. The property also holds true for subtraction of numbers instead of addition. In that case, we have  x * (y – z) = (x * y) – (x * z). Since we have understood what is distributive property of multiplication, it's time to go for an example.

Solve the example of distributive property of multiplication:

            If we understand this property, than it becomes easier dealing with the product of numbers in algebra. Product of many of the numbers can just be carried out in mind within few seconds. Here is an example of distributive property of multiplication.

(i) Find the product of 45 and 52:

            Using the distributive property, 45 * 52 = 45 * (50 + 2) = (45 * 50) + (45 * 2) = 2250 + 90 = 2340.

(ii) Find the product of 11 and 9:

            Using the distributive property, 11 * 9 = (10 + 1) * 9 = (10 * 9) + (1 * 9) = 90 + 9 = 99.  Now try it another way, if you directly find the product, you get the same answer. Thus distributive property of multiplication makes solving algebraic problems easier.

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