Math Calculators ▶ Distributive Property Calculator

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**Table of Content**

A distributive property calculator is designed to solve any simple mathematical equation by following the basic distribution law. By using this tool, we will get each step solved in a proper manner. Before we move further, let us discuss the basics of distributive property.

**Did you know!**

“By multiplying any number with parenthesis set, we will get the exact and same answer as we multiply that number with each value contained in the parenthesis individually and then adding them”

A distributive property or simply distribution law is a key method to simplify each and every ordinary mathematical equation. The general expression for distribution property is as follows:

**a*(b+c)**

The above expression gives us the step by step detailed and exact answer in the form of:

**a*b +a*c**

The distributive property calculator follows the same expression mentioned above to simply the equations whether they are in simple or fraction form.

Distribution property is categorized in two ways:

**Left Hand Distributive Property:**

The general expression for left hand distributive property is given as;

**a*(b+c) = a*b +a*c**

**Right Hand Distribution Property:**

The generic equation for right hand distribution property is as follows:

**(a+b)*c = a*c + b*c**

The distributive property calculator simplifies the given problem by following either of the above two methods of distribution property and yields the answer with no error.

Involving fractions in any expression increases the complexity of that expression. But the basic way to simplify that expression by following the distributive property remains the same.

Let us discuss the general form of distributive law with fractions as follows:

**a/b*(c+d) = a/b*c + a/b*d (Left distributive property)**

**(a+b)*c/d = a*c/d +b*c/d (Right distributive property)**

Distributive properties with fractions can easily be solved with the help of distribute calculator.

However, you can also use algebra calculator to solve expressions for variables following the phenomenon of distributive property.

Let us have a look of some unique directions about how to use the distributive property.

**1)Commutative Property w.r.t Multiplication:**

As** a*(b+c)=(b+c)*a**, we can say that multiplication is commutative as it yields the same results In the following expanded form:

**a*b+a*c=b*a+c*a**

The distribution property solver always work on this property when subjected to any expression with such condition.

**2)Subtraction is same as Addition:**

In practice, subtraction is a same operation as of addition but with negative sign. We can use subtraction instead of addition in distributive property calculator or even a combination of both these operations by implementing the correct sign usage. Feeding the distributor calculator with opposite signs equation results in proper answer within seconds.

**3)Division equals Multiplication:**

Always keep in mind that division is equal to that of multiplication even when we are dealing with distributive property with fractions. Different mathematical expressions can be easily simplified by multiplying using this way.

We can use distributive property to simplify the expression. Let us have a look of some examples to have a hands on grip on how to use the distributive property.

**Example # 01:**

Simplify the expression using distributive law:

**19*(67 + 3)**

**Solution:**

As we know that distribution property is given as:

**(a+b)*c = a*c + b*c**

So, we have;

**19*(67 + 3)**

**=19*67 +19*3**

**=1273 + 57**

**=1330**

You can authenticate your answer with the help of distribute calculator for double check.

**Example # 02:**

Solve for distribution property:

**(7-5)*9**

Solution:

As we know that distribution property is given as:

**(a+b)*c = a*c + b*c**

It is clear that addition is similar to subtraction with opposite signs. So, we have;

**(7-5)*9**

**=7*9 -5*9**

**=63 – 45**

**=18**

Using distributive calculator, you can get detailed implementation of proper use of distributive property to generate the desired results.

**Example # 03:**

Solve the following expression using distribution law:

**(3+9-12)*(22-0.2+2)**

Solution:

Following the basic rule of distributive property, we have;

**(3+9-12)*(22-0.2+2)**

**=3*22 – 3*0.2 + 3*2 + 9*22 – 9*0.2 + 9*2 – 12*22 + 12*0.2 – 12*2**

For instance 0.2 can also be written as 2/10. so, we have;

**=3*22 – 3*2/10 + 3*2 + 9*22 – 9*2/10 + 9*2 – 12*22 + 12*2/10 – 12*2**

**=66 – 6/10 + 6 + 198 – 18/10 + 18 – 264 + 24/10 – 24**

**=66 + 6 + 198 + 18 – 264 – 24 – 6/10 – 18/10 + 24/10**

**=0 – 6/10 – 18/10 + 24/10**

**=-6-18+24/10**

**=0/10**

**=0**

You can also verify the results by putting the expression in distributive calculator

**Example # 04:**

Solve the expression using distributive property only:

**1/8(8-2(6+7))**

Solution:

By using distributive property, we have;

**1/8(8-2(6+7))**

**=1/8(8-12+14)**

**=1/8*8-1/8*12+1/8*14**

**=1-3/2+7/4**

**=4-6+7/4**

**=-9/4**

Absolute results can easily be obtained along with detailed arithmetic operations performed by using distributive property with variables calculator.

Input:

- Write your expression in the given box.
- Click on ‘calculate’.

Output:

The calculator gives:

- Exact answer along with each step explained corresponding to the distributive law.

The distribution rule is another term used for distribution law having the same procedure as of distributive property.

Distributive law always follow the basic rule defined for distributive property to solve each problem step by step without any error in calculations.

We can solve any expression containing variables by following the distributive property with variables.

Use of distributive property is very vast in the field of mathematics and engineering. Distributive property calculator always provide assistance to perform massive calculations in a couple of seconds.

When you distribute something, you try to divide it into parts. In mathematics, the distributive property helps you to simplify various complicated problems because it solves the expressions by breaking down into the sum or difference of two numbers.

From the source of wikipedia: Distributivity and rounding, __Distributive Property__

From the source of lumen: __The Distributive Property__, The distributive property of multiplication, Use the Distributive Property to Simplify, Combo Meal Distributive Property, Absolute Value

From the source of splashlearn: Distributive Property Definition, Distributive Property with Variables, Distributive Property of Multiplication Over Addition, __Distributive Property of Division.__