# Distributive Property Calculator

With the Distributive Property Calculator, you can display the solutions for any given expression based on the distributive property. With STUDYQUERIES’s online distributive property calculator tool, you can perform calculations faster and see the simplification of numbers in a fraction of a second.

## How do you do distributive property on a calculator?

Following are the instructions for using the distributive property calculator:

• Step 1: Enter the expression a (b + c) in the input box.
• Step 2: Now, click the “Submit” button to get the simplified expression.
• Step 3: When the simplification is complete, it will appear in a new window.

## What Is Distributive Property?

The distributive property is also known as the distributive law that multiplies over additions and subtractions. As the name implies, the operation involves dividing or distributing something. In addition to its name, this formula is also known as the distributive property of addition over multiplication. Here are some examples showing the distributive property in action.

The distributive property states that any expression with three numbers A, B, and C, given in form A (B + C) then it is resolved as $$A × (B + C) = AB + AC$$ or $$A (B – C) = AB – AC$$ This means operand A is distributed among the other two operands. As well as being known as the distributivity of multiplication, this property is also known as the distributivity of addition or subtraction.

With examples, let’s discuss the distributive property of addition over multiplication.

### Types of Distribution Property

Distribution properties can be categorized in two ways:

1. Left Hand Distributive Property: The left-hand distributive property can be expressed as follows;

$$a\times (b+c) = a\times b +a\times c$$

1. Right Hand Distribution Property: The right-hand distribution property can be described as follows:

$$(a+b)\times c = a\times c + b\times c$$

In either of the above two methods of distribution property, the distributive property calculator simplifies the given problem, yielding the correct answer without error.

### Distributive Property with Fractions

When fractions are included in an expression, the complexity increases. Nonetheless, following the distributive property is the most straightforward way to simplify that expression.

We can discuss the general form of distributive law with fractions as follows:

$$\frac{a}{b}\times (c+d) = \frac{a}{b}\times c + \frac{a}{b}\times d$$ (Left distributive property)

$$(a+b)\times \frac{c}{d} = a\times \frac{c}{d} + b\times \frac{c}{d}$$ (Right distributive property)

Using a distributive properties calculator, the distributive properties of fractions can be easily solved.

It is also possible to use an algebra calculator to solve expressions for variables based on the distributive property.

### Characteristics of Distributive Property

Here are some unique ways to use the distributive property.

1. Commutative Property w.r.t Multiplication

As $$a\times (b+c)=(b+c)\times a$$, multiplication is commutative since it results in the same results In the expanded form:

$$a\times b+a\times c=b\times a+c\times a$$

When such conditions are present in an expression, the distribution property solver always works on this property.

1. Subtraction is the same as Addition

Addition and subtraction are the same things in practice, but with the negative sign. In the distributive property calculator, we can use subtraction instead of addition, or a combination of both of these operations by implementing the correct sign. The distributor calculator produces correct answers within seconds when fed with the opposite signs equation.

1. Division equals Multiplication

Even when we are dealing with distributive property with fractions, it is always important to remember that division is the same as multiplication. Various mathematical expressions can be simplified by multiplying this way.

### Distributive Property of Multiplication Over Addition

The distributive property of multiplication over addition is used in such a case where the multiple of one number needs to be multiplied by the sum of two other numbers. As an example, multiply 7 by the sum of 20 + 3. Mathematically we can represent this as $$7(20+3)$$ Using the rules of order of operations, we solve the sum within the parentheses first, followed by multiplying by 7.

$$7(20 + 3) = 7(23) = 161$$ If we solve the expression using the distributive property, we can first multiply every addend by 7. This is known as distributing the number 7 amongst the two addends and then we can add the products.

Before the addition, 7(20) and 7(3) will be multiplied.

$$7(20) + 7(3) = 140 + 21 = 161$$

There is no difference in the result obtained in both cases before and after.

### Distributive Property of Multiplication Over Subtraction

As we discussed above, multiplication over addition has the distributive property. In this section, we’ll discuss subtraction. There is no difference in the process other than a sign. We will now examine an example of multiplication over subtraction as a distributive property. Suppose we have to multiply 7 with a difference of 20 and 3, i.e. $$7(20 – 3)$$

Let us use two different approaches to solve the same problem.

Method 1: $$7 × (20 – 3) = 7 × 17 = 119$$

Method 2: $$7 × (20 – 3) = (7 × 20) – (7 × 3) = 140 – 21 = 119$$

The final result is the same for both methods.

### How to use distribution property?

In this case, we can simplify the expression by using the distributive property. The distributive property can be applied to a few examples so as to have a better understanding of how to use it.

Example: 1 Using distributive law, simplify the expression: $$19\times (67 + 3)$$

Solution: Distributive property can be shown as follows:

$$(a+b)\times c = a\times c + b\times c$$

Therefore, we have;

$$19\times (67 + 3)$$

$$=19\times 67 +19\times 3$$

$$=1273 + 57$$

$$=1330$$

If you are double-checking your answer, you can use a distributive calculator.

Example: 2 Solve for distribution property: $$(7-5)\times 9$$

Solution: We know that distribution property is as follows:

$$(a+b)\times c = a\times c + b\times c$$

Addiction is similar to subtraction with opposite signs. Therefore, we have;

$$(7-5)\times 9$$

$$= 7\times 9 -5\times 9$$

$$= 63 – 45$$

$$= 18$$

A distributive calculator can provide detailed information about how the distributive property is used to generate the desired results.

Example: 3 Use the distribution law to solve the following expression: $$(3+9-12)\times (22-0.2+2)$$

Solution: The basic distributive property requires these values; $$(3+9-12)\times (22-0.2+2)$$

$$= 3\times 22 – 3\times 0.2 + 3\times 2 + 9\times 22 – 9\times 0.2 + 9\times 2 – 12\times 22 + 12\times 0.2 – 12\times 2$$

For instance 0.2 can also be written as $$\frac{2}{10}$$. so, we have;

$$= 3\times 22 – 3\times \frac{2}{10} + 3\times 2 + 9\times 22 – 9\times \frac{2}{10} + 9\times 2 – 12\times 22 + 12\times \frac{2}{10} – 12\times 2$$

$$= 66 – \frac{6}{10} + 6 + 198 – \frac{18}{10} + 18 – 264 + \frac{24}{10} – 24$$

$$= 66 + 6 + 198 + 18 – 264 – 24 – \frac{6}{10} – \frac{18}{10} + \frac{24}{10}$$

$$= 0 – \frac{6}{10} – \frac{18}{10} + \frac{24}{10}$$

$$=\frac{-6-18+24}{10}$$

$$= \frac{0}{10}$$

$$= 0$$

Putting the expression in a distributive calculator will also yield the results.

### Verification of Distributive Property

Let’s try to explain how distributive property works for different operations. The distributive property law will be applied to each of the three basic operations, that is, addition, subtraction, and division.

Distributive Property of Addition: The general distributive property law for addition is expressed as $$A × (B + C) = AB + AC$$ Let us try to fix some numbers in the property to verify the same. For example,

$$= 2(1 + 4) = 2×1 + 2× 8$$

$$⇒ 10 = 10$$

$$LHS = RHS$$

Distributive Property of Subtraction: The general distributive property law for subtraction is expressed as $$A × (B – C) = AB – AC$$ Let us try to fix some numbers in the property to verify the same. For example,

$$= 2(4 – 1) = 2×4 – 2×1$$

$$⇒ 6 = 6$$

$$LHS = RHS$$

Distributive Property of Division: We can show the division of larger numbers by dividing the larger number into two or fewer factors. The following example illustrates the division. Divide $$24 ÷ 6$$

We can write 24 as 18+6

$$24 ÷ 6 = (18 + 6) ÷ 6$$

Here is how we will distribute the division operation for each factor (18 and 6);

$$⇒ 24 ÷ 6 = (18÷6) + (6÷6)$$

$$⇒ 4 = 3 + 1$$

Therefore, $$4 = 4$$

$$LHS = RHS$$

## Conclusion

Distributing something involves dividing it into parts. Distributive property simplifies complex mathematical expressions by breaking them down into sums and differences of two numbers.

## FAQs

How do you find the distributive property?

Property of distribution with exponents

• The equation should be expanded.
• Multiply (distribute) the first numbers in each set, the outer numbers in each set, the inner numbers in each set, and the last numbers in each set.
• Combining like terms.
• If necessary, simplify the equation.

What is a distributive property with fractions?

We can multiply one number or term by a set of terms in parentheses using the distributive property. By multiplying the term outside of the parenthesis by each term inside the parentheses you get the answer. As with any other kind of term in algebra, fractions behave the same way.

What is the distributive property of subtraction?

Multiplication has the distributive property, which is used to add and subtract. According to this property, two or more terms in addition or subtraction with a number are equal to the addition or subtraction of the product of each of those terms with that number.

What is the distributive property of the integer?

The distributive property of integers is that the product of an integer and two integers inside parentheses is equal to the sum of the products of integers separately.

What is the distributive property of multiplication over addition?

The distributive property of multiplication over addition states that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend individually by the number and then adding the products.

What is the distributive property of exponents?

The exponent can be distributed over the term in parentheses if it acts on the singular term. For example, $$(2×5)^2 = (2^2)(5^2)$$

$$(3x)^6 = 3^6x^6$$

$$3(4xy)^5 = 3(4^5)x^5y^5.$$