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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.
Distributive Property Calculator
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:
- Left Hand Distributive Property: The left-hand distributive property can be expressed as follows;
$$a\times (b+c) = a\times b +a\times c$$
- 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.
- 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.
- 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.
- 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, $$4 = 4$$
$$LHS = RHS$$
Distributive Property Calculator Step-by-step:
The Distributive Property Calculator Step-by-step is a tool that helps you simplify algebraic expressions using the distributive property. The distributive property states that when you multiply a number or term outside a set of parentheses by each term inside the parentheses, you can distribute the multiplication and simplify the expression. This calculator provides a step-by-step breakdown of the process to help you understand how the distributive property is applied and simplify the expression correctly.
Solution:
To use the Distributive Property Calculator Step-by-step, follow these steps:
1. Enter the algebraic expression you want to simplify into the calculator.
2. The calculator will analyze the expression and identify any terms that can be simplified using the distributive property.
3. It will show you the step-by-step process of applying the distributive property to simplify the expression.
4. Each step will demonstrate how the multiplication is distributed across the terms inside the parentheses and how the expression is simplified.
5. The calculator will continue simplifying the expression until no further steps can be taken.
By using this calculator, you can learn and understand the process of applying the distributive property, which is a fundamental concept in algebra. It can be particularly useful when dealing with complex expressions or equations.
Using The Distributive Property Calculator:
The “Using The Distributive Property Calculator” is a tool designed to simplify algebraic expressions by applying the distributive property. This calculator provides an efficient and accurate way to perform calculations involving the distributive property, saving you time and effort.
Solution:
To use the “Using The Distributive Property Calculator,” follow these steps:
1. Enter the algebraic expression you want to simplify into the calculator.
2. The calculator will analyze the expression and identify any terms that can be simplified using the distributive property.
3. It will automatically apply the distributive property and simplify the expression accordingly.
4. The calculator will provide you with the simplified result, showing all the necessary steps and intermediate calculations.
5. You can repeat the process with different expressions as needed.
Using this calculator can help you streamline your algebraic calculations and ensure accurate results. It eliminates the potential for human error in applying the distributive property and saves you time by automating the simplification process.
Multiply Using The Distributive Property Calculator:
The “Multiply Using The Distributive Property Calculator” is a specialized tool that allows you to multiply two or more algebraic expressions by applying the distributive property. It simplifies the multiplication process by breaking it down step-by-step and demonstrates how the distributive property is used to obtain the final result.
Solution:
To use the “Multiply Using The Distributive Property Calculator,” follow these steps:
1. Enter the algebraic expressions you want to multiply into the calculator, separating each expression with the multiplication sign (*) or an appropriate operator.
2. The calculator will analyze the expressions and identify any terms that can be simplified using the distributive property.
3. It will apply the distributive property by multiplying each term in the first expression by each term in the second expression.
4. The calculator will demonstrate the step-by-step process of multiplying each term and combining like terms, if applicable.
5. It will provide you with the final result of the multiplication, simplifying the expression as much as possible.
Using this calculator can be particularly helpful when multiplying polynomials or complex algebraic expressions. It ensures accuracy and helps you understand the underlying principles of the distributive property in multiplication.
Distributive Property Calculator With Shown Work:
The “Distributive Property Calculator With Shown Work” is a tool that not only calculates the result of an algebraic expression using the distributive property but also shows the step-by-step work involved in the simplification process. It provides a detailed breakdown of each step, making it easier to follow along and understand the solution.
Solution:
To use the “Distributive Property Calculator With Shown Work,” follow these steps:
1. Enter the algebraic expression you want to simplify into the calculator.
2. The calculator will analyze the expression and identify any terms that can be simplified using the distributive property.
3. It will apply the distributive property and show the work involved in each step.
4. The calculator will combine like terms, simplify the expression, and provide the final result.
5. Along with the result, it will display a step-by-step breakdown of the simplification process, clearly showing how the distributive property was applied at each stage.
Using this calculator can enhance your understanding of the distributive property and help you grasp the underlying principles of algebraic simplification. It provides a comprehensive view of the solution process and helps you learn by example.
Distributive Property With Variables Calculator:
The “Distributive Property With Variables Calculator” is a tool that simplifies algebraic expressions involving variables using the distributive property. It enables you to simplify expressions that contain variables and constants, making it easier to solve equations and manipulate algebraic formulas.
Solution:
To use the “Distributive Property With Variables Calculator,” follow these steps:
1. Enter the algebraic expression with variables you want to simplify into the calculator.
2. The calculator will analyze the expression and identify any terms that can be simplified using the distributive property.
3. It will apply the distributive property by multiplying each term outside the parentheses by each term inside the parentheses.
4. The calculator will combine like terms and simplify the expression, taking into account the variables and constants involved.
5. It will provide the simplified result, giving you a clearer expression with simplified terms and coefficients.
Using this calculator can be beneficial when dealing with algebraic expressions that contain variables. It helps you simplify and manipulate such expressions, making it easier to solve equations, factor polynomials, or perform other algebraic operations involving variables.
Solve Using Distributive Property:
“Solve Using Distributive Property” refers to the process of solving equations or expressions by applying the distributive property. This technique is commonly used in algebra to simplify equations, isolate variables, or solve for unknowns.
Solution:
To solve an equation or expression using the distributive property, follow these steps:
1. Identify the equation or expression that needs to be solved.
2. Determine if there is any part of the equation or expression that can be simplified using the distributive property.
3. If so, apply the distributive property by multiplying the term outside the parentheses by each term inside the parentheses.
4. Simplify the resulting expression by combining like terms, if applicable.
5. Continue simplifying or solving the equation using other algebraic techniques or methods, depending on the specific problem.
Using the distributive property as part of the solution process can help simplify expressions, isolate variables, or transform equations into a more manageable form. It is a valuable tool in algebraic problem-solving.
Distributive Property Simplify:
“Distributive Property Simplify” refers to the process of simplifying algebraic expressions using the distributive property. By applying the distributive property, you can simplify complex expressions, eliminate parentheses, and combine like terms, resulting in a more concise and manageable form.
Solution:
To simplify an algebraic expression using the distributive property, follow these steps:
1. Identify the expression that needs to be simplified.
2. Identify any terms or factors that can be simplified using the distributive property.
3. Apply the distributive property by multiplying the term outside the parentheses by each term inside the parentheses.
4. Simplify the resulting expression by combining like terms, if applicable.
5. Repeat the process if there are multiple instances where the distributive property can be applied.
6. Continue simplifying the expression until no further simplifications can be made.
The distributive property simplifies complex expressions by distributing the multiplication and reducing redundancy. This technique is widely used in algebra to make expressions more manageable and easier to work with.
The Distributive Property Answers:
“The Distributive Property Answers” refers to the solutions or results obtained after applying the distributive property to algebraic expressions. When using the distributive property, the answers represent the simplified form of the expression, obtained by distributing the multiplication and combining like terms.
Solution:
To obtain the distributive property answers, follow these steps:
1. Identify the algebraic expression for which you need the answers.
2. Apply the distributive property by multiplying the term outside the parentheses by each term inside the parentheses.
3. Simplify the expression by combining like terms, if applicable.
4. Continue applying the distributive property and simplifying the expression until no further simplifications can be made.
5. The final result represents the distributive property answers, which provide the simplified form of the expression.
The distributive property answers help express complex expressions in a simplified and concise form, making it easier to analyze, solve equations, or perform further algebraic operations.
Distributive Property Simplify Calculator:
The “Distributive Property Simplify Calculator” is a specialized tool that simplifies algebraic expressions by applying the distributive property. It automates the process of distributing multiplication and simplifying expressions, providing the final simplified form of the expression.
Solution:
To use the “Distributive Property Simplify Calculator,” follow these steps:
1. Enter the algebraic expression you want to simplify into the calculator.
2. The calculator will analyze the expression and identify any terms that can be simplified using the distributive property.
3. It will automatically apply the distributive property, distribute the multiplication, and simplify the expression.
4. The calculator will provide the final simplified result, showing all the necessary steps and combining like terms.
5. You can repeat the process with different expressions as needed.
Using this calculator saves time and effort by automating the simplification process. It ensures accuracy and provides clear, simplified expressions that are easier to work with in algebraic calculations.
GCF Distributive Property Calculator:
The “GCF Distributive Property Calculator” is a tool that simplifies algebraic expressions by applying the distributive property in combination with the greatest common factor (GCF). The GCF is the largest number or term that divides evenly into all the terms of an expression. By factoring out the GCF and applying the distributive property, expressions can be simplified further.
Solution:
To use the “GCF Distributive Property Calculator,” follow these steps:
1. Enter the algebraic expression you want to simplify into the calculator.
2. The calculator will analyze the expression and identify the GCF of the terms involved.
3. It will factor out the GCF from each term and apply the distributive property.
4. The calculator will distribute the GCF and simplify the expression by combining like terms.
5. It will provide the final result, which represents the expression simplified with the GCF and the distributive property.
Using this calculator can help you identify and factor out the GCF from expressions, leading to further simplification. It streamlines the process and ensures accurate results when applying the distributive property in combination with the GCF.
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, $$(2×5)^2 = (2^2)(5^2)$$
$$(3x)^6 = 3^6x^6$$
$$3(4xy)^5 = 3(4^5)x^5y^5.$$
How To Do Distributive Property Calculator?
To use a Distributive Property Calculator, follow these steps:
Step 1: Find a reliable Distributive Property Calculator online. There are several options available on various math websites or calculator platforms.
Step 2: Once you have accessed the calculator, look for a clear input field where you can enter your algebraic expression.
Step 3: Enter the algebraic expression that you want to simplify or solve using the distributive property. Make sure to input the expression correctly, including any parentheses or variables.
Step 4: After entering the expression, double-check for any errors or typos to ensure accurate results.
Step 5: Click on the “Calculate” or “Simplify” button, depending on the specific calculator you are using.
Step 6: The calculator will process the expression and apply the distributive property to simplify or solve it step-by-step. It will show you the intermediate steps and the final result.
Step 7: Review the simplified or solved expression provided by the calculator. Take note of any important details or further steps you may need to follow.
Step 8: If necessary, copy or save the results for future reference.
Remember that using a Distributive Property Calculator can be a helpful tool, but it is also essential to understand the underlying concepts and steps involved. Use the calculator as a learning aid and refer to the solutions to enhance your understanding of the distributive property in algebra.
What Is The Distributive Property Calculator?
A Distributive Property Calculator is an online tool or software that simplifies or solves algebraic expressions using the distributive property. It automates the process of applying the distributive property, saving time and effort in manual calculations.
The distributive property is a fundamental concept in algebra that allows you to distribute the multiplication of a term or number outside parentheses to each term inside the parentheses. The calculator uses this property to simplify or solve expressions by breaking down the multiplication and combining like terms.
The calculator takes an algebraic expression as input and applies the distributive property step-by-step. It shows the intermediate steps and provides the final result, simplifying the expression as much as possible. Some calculators may also offer additional features such as factoring or finding the greatest common factor (GCF).
By using a Distributive Property Calculator, you can quickly obtain simplified expressions, which are useful in solving equations, factoring polynomials, or performing other algebraic operations. It eliminates the potential for human error and provides a reliable and efficient solution to algebraic problems involving the distributive property.
Is The Distributive Property Calculator Free?
The availability and pricing of Distributive Property Calculators can vary depending on the platform or website you use. However, many online calculators that simplify or solve algebraic expressions using the distributive property are available for free.
There are numerous math websites, educational platforms, and online calculators that offer free access to Distributive Property Calculators. These calculators are often part of a broader collection of algebraic tools or equation solvers provided as a free resource to students, educators, and individuals seeking assistance with algebraic calculations.
When searching for a Distributive Property Calculator, consider exploring reputable math websites, educational platforms, or online communities dedicated to math and education. These sources are more likely to provide reliable and free calculators for your algebraic needs.
However, it is important to note that some advanced or specialized calculators may offer additional features or functionality at a cost. If you require more advanced capabilities, such as graphing or solving complex systems of equations, you may need to explore premium or subscription-based calculator options.
Where To Find The Best Distributive Property Calculator?
To find the best Distributive Property Calculator, consider the following options:
1. Educational Websites: Reputable educational websites, such as Khan Academy, Mathway, or MathHelp, often offer reliable and user-friendly calculators for various algebraic operations, including the distributive property. These calculators are designed with educational purposes in mind and may provide additional explanations or resources to enhance learning.
2. Math Apps: Check mobile applications that focus on math education. Some apps, like Photomath or Symbolab, provide advanced calculators capable of handling distributive property calculations. These apps often offer step-by-step solutions, graphing capabilities, and additional features that can be beneficial for learning and problem-solving.
3. Online Math Communities: Engage with online math communities and forums where individuals passionate about math share resources and recommendations. Websites like Math Stack Exchange or Reddit’s r/learnmath can be excellent places to seek advice from experienced math enthusiasts who can point you towards reliable calculators.
4. Math Software: Consider exploring math software like Wolfram Mathematica or Maple, which provide comprehensive mathematical functionalities, including distributive property calculations. These software packages are often used in professional settings and offer powerful tools for advanced mathematical operations.
When searching for the best Distributive Property Calculator, prioritize calculators that are user-friendly, accurate, and provide step-by-step explanations. Additionally, consider your specific needs and requirements, such as whether you prefer a web-based calculator, a mobile app, or software installed on your computer.