# What is Distributive Property

## Distributive property equations and definition:

We have been using **distributive property equations **since long for solving simple problems of algebra. Even we might have used it without knowing the **definition of distributive property**. So we'll **define distributive property **and learn the **algebra behind distributive property**.** **Distributive property is similar to distributing something in general life. We can process numbers easily using this property. The **Distributive Property** helps to multiply a sum by simply multiplying each number and adding their products. Once you understand **distributive property definition** and solve some related examples, multiplication of numbers becomes easier and can even carried out in mind. The simplest form of distributive law is a * (b+c) = (a * b) + (a * c), where a, b and c could be any real number. Thus the multiplication of real numbers can be expressed as addition of real numbers. The commutative property also holds true for above equation and another form of the equation is (b+c) * a = (b * a) + (c * a). Let's have an example of it.

*Find product of 6 * 54:

6 * 54 = 6 * (50 + 4) = (6 * 50) + (6 * 4) = 300 + 24 =324

*Find product of 5 * 19:

5 * 19 = 5 * (20 – 1) = (5 * 20) - (5 * 1) = 100 - 5 = 95

Above example shows that distributive property also holds true in case there is a need of subtraction of numbers. Distributive property is not only limited to arithmetic operations and can also be written for logical operations. One such logical operation is (a & (b | c)) = ((a & b) | (a & c)). If we apply commutative property to logical equation, we have ((b | c) & a) = ((b & a) | (c & a)) which yields same results as the previous one. Thus once you know **what is distributive property**, you can solve many problems related to algebra as well as Boolean logic.

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