It’s time for another round of arithmetic assignments. You despise the scenario, yet you have no choice but to sit down and work. You will not benefit from procrastination in any manner. There are, however, products that we specifically designed to make your life easier while also supporting your study. We can provide you with Distributive property calculators to help you simplify and solve complicated arithmetic issues. Let’s take a closer look at how it functions and how it can assist you.
Welcome to our distributive property calculator, where we’ll learn about the distributive property of multiplication over addition, one of the most basic mathematics skills. In fact, if we’re cautious, we can extend it to division (under certain conditions) and subtraction. But don’t worry: the definition of the distributive property isn’t the only thing you’ll find here. We’ll offer a few great distributive property instances after we explain what it is.
“So, what precisely is the distributive property in math?” you might wonder. How fortuitous that the first section’s title is exactly that.
We also know the distributive property formula as the multiplication distributive law. It denotes that the procedure entails the division or distribution of something. The distributive property of addition over multiplication is another name for this expression.
Table of Contents
This characteristic comes in handy for solving issues, particularly equations and inequalities. It works with polynomials of any degree. It’s all about spreading one or more terms above others in this property. To put it another way, it’s all about opening brackets and multiplying, adding, subtracting, and dividing the expression’s terms.
This doesn’t appear to be a difficult task, does it? It isn’t, but the chances of making mistakes like skipping a phrase or using a plus sign instead of a minus sign are high, especially when the statement is extensive. When the expression contains variables of varying degrees and/or fractions, things can get a little more difficult.
There’s no need to be discouraged because the distributive property solver is free to use and may be found immediately online. You can access it from any connected device at any time. To use it, there is no need to pay a fee or even register a separate account.
It is the property that allows you to solve an equation; the fundamental form of distributive property is a(b+c). The simplified expression value ab+ac is then returned.
The Distributive Law of Multiplication and Division is another name for distributed property. We must first multiply before proceeding with the addition operation. There is a connection between distributive law and addition and multiplication operations in mathematics.
a(b+c) = ab+ac
On the left side, we can multiply the Factor a with (b+c) and give the left side result in the form of ab+ac.
Some examples for Distributive property are given below:-
1(2+3) = 1*2 + 1*3
= 2 + 3
4(2+6) = 4*2 + 4*6
= 8 + 24
Distributive Property Calculator Application
In the output side, the Distributive Property Calculator returns the simplified expression value.
In the Distributive Property Calculator, enter the expression and get the result as follows:
Enter the expression value for the Distributive property in the Input box.
Then, in the Distributive property’s presented window, click the submit button to get the simplified output result.
How does the Distributive Property Calculator works
To put it another way, the distributive property allows us to break down a large, complex expression into multiple smaller, simpler ones. It must always consist of two distinct procedures (hence, the long name distributive property of multiplication over addition).
Let’s look at and examine a symbolic distribution property definition:
x * (a + b + c + d + …) = x*a + x*b + x*c + x*d + …
So, in arithmetic, what is the distributive property? As you can see, it’s all about taking a single * symbol and multiplying it by a large number of them. That is the essence of multiplication over addition’s distributive property: we spread the multiplication sign * over all phrases separated by the addition sign +. As a result, we go from a complex phrase to one that is much more complex but considerably simpler.
It’s vital to keep in mind that the above distributive property description can be extended in a few different ways. We’ve listed them all nicely here as the good people that we are.
In the Distributive property calculator, multiplication is commutative.
Therefore, x * (a + b + c + d + …) is the same as (a + b + c + d + …) * x. What is more, the same property lets us change the order of multiplication on the right side of the distributive property definition: x*a + x*b + x*c + x*d + … = a*x + b*x + c*x + d*x + …
In the Distributive property calculator, subtraction is similar to addition.
In other words, we can define the distributive property using subtraction instead of addition, or a combination of both. Make certain, however, that the signage are well-maintained. For instance, x * (a – b – c + d + …) = x*a – x*b – x*c + x*d + …
In the Distributive property calculator, division is somewhat similar to multiplication.
We can sometimes have division instead of multiplication, as shown above. However, we must proceed with caution because division is not commutative, and hence the distributive property of division only works in one direction: (a + b + c + d + …) / x = a/x + b/x + c/x + d/x + …. In other words, we cannot use a similar formula for x / (a + b + c + d + …). Nevertheless, point 2. still applies: we can have both pluses and minuses inside the bracket.
The distributive property calculator appears in many areas of mathematics.
It applies to more intricate operations performed not only on numbers but also on objects such as function sequences. It characterizes well-structured spaces in some ways, and strange things happen when it fails. Fortunately, we don’t need to worry about it too much: the distributive property of multiplication over addition is all we need for the time being (and most likely the rest of your life)!
Read Also:Rationalize the denominator calculator
That seems to be the end of the mathematical jargon. Let’s go from symbols to numbers and explore how distributive property works in practice. We’ll tackle a few issues, but we’ll take our time and go through them completely. After all, we promised you some good instances of distributive properties, and you will receive some nice ones!
Distributive Property Calculator step by step
Please follow the below steps to use the distributive property calculator:
Step 1: Enter the values in the given input boxes.
Then, step 2: Click on the “Solve” button to find the value of the expression a(b + c).
Then, step 3: Click on the “Reset” button to clear the fields and enter new values.
Distributive Property Calculator with Steps
In this section, we’ll look at a variety of distributive property examples in increasing difficulty. Note how you can enter any of these into Omni’s distributive property calculator to receive a step-by-step result identical to the one we’ve provided here.
Let’s start with the most basic scenario.
3 * (2 + 4 + 11 + 0) = 3*2 + 3*4 + 3*11 + 3*0 = 6 + 12 + 33 + 0 = 51
We simply computed each item using the distributive property definition from the previous section.
Let’s shake things up a bit. Now, instead of multiplication, we’ll use division and some minuses in the brackets (remember that division’s distributive property only works from one side!).
(13 – 1 + 7 + 3 – 2) / 4 = 13/4 – 1/4 + 7/4 + 3/4 – 2/4 = 3.25 – 0.25 + 1.75 + 0.75 – 0.5 = 5
Observe how we copied the pluses and minuses in the corresponding places.
Now let’s try multiplying by a negative number.
(-2) * (3 + 1 – 9 – 5) = (-2)*3 + (-2)*1 + (-2)*(-9) + (-2)*(-5) = -6 – 2 + 18 + 10 = 20
How we have -2 in every term, i.e., we copied the number with its sign. What is more, the -9 and -5 also appeared with their sign. Alternatively, we could have written
(-2) * (3 + 1 – 9 – 5) = (-2)*3 + (-2)*1 – (-2)*9 – (-2)*5 = 6 – 2 + 18 + 10 = 20.
In such computations, signs are crucial: pay attention to them and make sure you don’t miss any!
Finally, we show how to use nested brackets in a more difficult example. In such circumstances, recall the order of operations in mathematics and see how to apply the distributive property.
(3 + 2*(4 – 5)) * ((11 – 1)/5 + 2) = (3 + 2*4 – 2*5) * (11/5 – 1/5 + 2)
= (3 + 8 – 10) * (2.2 – 0.2+2)
Then, 3 * (2.2 – 0.2 + 2) + 8 * (2.2 – 0.2 + 2) – 10 * (2.2 – 0.2 + 2)
= 3*2.2 – 3*0.2 + 3*2 + 8*2.2 – 8*0.2 + 8*2 – 10*2.2 – 10*(-0.2) – 10*2
= 6.6 – 0.6 + 6 + 17.6 – 1.6 + 16 – 22 + 2 – 20
When both components are sums, we employ the distributive property of multiplication over addition in the third line. Of course, we could have added up one of the brackets and used the formula from the previous section instead, for example,
(3 + 8 – 10) * (2.2 – 0.2 + 2) = (3 + 8 – 10) * 4.
Distributive Property Calculator Algebra
Even the youngest students can use the calculator with ease. It contains two fields that you must complete. The first thing to do is enter the expression that needs to be dispersed. It can be made up of several terms. You must input the expression in the second field, which must be dispersed across the first. There is virtually little possibility for misinterpretation because the two will appear in the same order and will usually be separated by brackets. It’s crucial to double-check that you’ve entered all phrases correctly, even if they’re only numbers. Then all you have to do is press the submit button, and the software will handle the rest.
In a matter of seconds, you’ll have the proper answer. In most cases, it’s clear where it came from, although this isn’t always the case with more complicated polynomials. As a result, it’s a good idea to use the distributive property calculator for free as a reference tool. It will assist you in determining whether you have correctly answered the question while also saving you time. It allows you to practice different types of problems at home in order to improve your arithmetic skills. It’s fantastic to be able to see the answer and know if you got it right or if you made a mistake and need to go back and correct it.
To get the hang of solving arithmetic problems, make full use of this and other internet calculators. They aren’t as difficult as you might believe.
Distributive Property Calculator Formula
The distributive property formula of a given value is expressed as,
a(b+c) = ab + ac
Let us discuss the distributive property of multiplication over addition and subtraction in detail with examples.
Distributive Property Calculator of Multiplication over Addition
When we need to multiply a number by the sum of two numbers, we use the distributive property of multiplication over addition. Let’s multiply 7 by the sum of 20 + 3 as an example. This can be expressed mathematically as 7(20 + 3).
Example: Using the distributive property of multiplication over addition, solve the formula 7(20 + 3).
When utilizing the distributive property to calculate the expression 7(20 + 3), we multiply each addend by 7. This is known as spreading the number 7 across the two addends, after which the products can be added. This signifies that the addition will be performed before the multiplication of 7(20) and 7(3). This leads to 7(20) + 7(3) = 140 + 21 = 161.
Distributive Property Calculator of Multiplication over Subtraction
Except for the operations of addition and subtraction, the distributive property of multiplication over subtraction is equivalent to the distributive property of multiplication over addition. Consider the distributive property of multiplication over subtraction as an example.
Example: Using the distributive property of multiplication over subtraction, solve the expression 7(20 – 3).
Solution: We may solve the expression using the distributive property of multiplication as follows: 7 × (20 – 3) = (7 × 20) – (7 × 3) = 140 – 21 = 119
Verification of Distributive Property Calculator
Let’s look at how the distributive property works for various operations. We’ll use the distributive law to apply to the two basic operations of addition and subtraction separately.
Addition Distributive Property Calculator:
A (B + C) = AB + AC expresses the distributive property of multiplication over addition. Let’s use an example to demonstrate this characteristic.
Example: Using the distributive law of multiplication over addition, solve the expression 2(1 + 4).
Solution: 2(1 + 4) = (2 × 1) + (2 × 4)
⇒ 2 + 8 = 10
If we try to solve the expression using the BODMAS law, we get the following result. We’ll start by adding the numbers in brackets, and then multiply that total by the number outside the brackets.
2(1 + 4) 2 5 = 10
As a result, both procedures get the same outcome.
Subtraction’s Distributive Property: A (B – C) = AB – AC expresses the distributive law of multiplication over subtraction. Let’s look at an example to see if this is true.
Example: Use the distributive law of multiplication over subtraction to solve the expression 2(4 – 1).
Solution: 2(4 – 1) = (2 × 4) – (2 × 1)
⇒ 8 – 2 = 6
If we try to solve the expression with the order of operations, we get the following result. We’ll start by subtracting the numbers in brackets, then multiplying the difference with the number outside the brackets. This equates to 2(4 – 1), 2 × 3 = 6.
Distributive Property Calculator of Division
We can use the distributive property to show the division of larger numbers by splitting the larger number into two or more smaller parts. Let’s look at an example to better grasp this.
Example: Divide 24 ÷ 6 using the distributive property of division.
Solution: We can write 24 as 18 + 6
24 ÷ 6 = (18 + 6) ÷ 6
Now, let us distribute the division operation for each factor (18 and 6) in the bracket.
⇒ (18 ÷ 6) + (6 ÷ 6)
⇒ 3 + 1
Therefore, the answer is 4.
Distributive Property Calculator Examples
Example 1: Solve the expression 3(4 + 5) by using the distributive property.
Using the distributive property formula,
a × (b + c) = (a × b) + (a × c)
We will multiply the outside term by both the terms inside the brackets.
3(4 + 5)
= (3 × 4) + (3 × 5)
= 12 + 15
Therefore, the value of 3(4 + 5) = 27
Example 2: Solve 6(7 + 9) by using the distributive property formula.
The distributive property formula is expressed as,
a × (b + c) = (a × b) + (a × c)
Now, let us multiply the outside term by both the terms inside the brackets.
= 6(7 + 9)
= (6 × 7) + (6 × 9)
= 42 + 54
Therefore, the solution of 6(7 + 9) is 96.
Example 3: Rewrite the expression 10(12 + 15) using the distributive property formula and solve it.
The distributive property formula is expressed as,
a × (b + c) = (a × b) + (a × c)
Let us multiply the outside term by both the terms inside the parenthesis,
10(12 + 15)
= (10 × 12) + (10 × 15)
= 120 + 150
Therefore, the value of 10(12 + 15) = 270
Frequently Asked Questions about Distributive Property Calculator
What is the Distributive Property in Math?
The distributive property is also known as the multiplication distributive law. Multiplication’s distributive property applies to both addition and subtraction. The distributive property is denoted as: a × (b + c) = (a × b) + (a × c).
What is the Formula for Distributive Property?
The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands.
How Does the Distributive Property Work?
We multiply the outside term with the words inside the brackets and then add the terms to get the solution when we utilize the distributive property formula. Let’s look at 15(4 + 3) as an example. To get the solution, multiply 15 by 4, then multiply 15 by 3, and then sum the products. This means 15 × (4 + 3) = (15 × 4) + (15 × 3) = 60 + 45 = 105.
Use the Distributive Property Formula to Solve the Equation 2(m + 2) = 22.
Using the distributive property formula, a × (b + c) = (a × b) + (a × c), we will multiply the outside term by both the terms inside the brackets. This means 2(m + 2) = 22 ⇒ 2m + 4 = 22. Now, the value of ‘m’ can be calculated. That is, 2m = 22 – 4 which can be further solved as, m = 9.
What is the Distributive Property of Multiplication in Math?
When we need to multiply a number by the sum of two or more addends, we apply the distributive property of multiplication. Multiplication’s distributive property applies to addition and subtraction of two or more numbers. It is used to simplify the solution of formulas by spreading a number among the numbers in brackets. For example, to solve the expression 4(2 + 4) using the distributive property of multiplication, we would do so as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24.
What is the Distributive Property for Rational Numbers?
The distributive property states, if p, q, and r are three rational numbers, then the relation between the three is given as, p × (q + r) = (p × q) + (p × r). For example, 1/3(1/2 + 1/5) = (1/3 × 1/2) + (1/3 × 1/5) = 7/30.
Where is the Distributive Property Used?
When adding, subtracting, multiplying, and dividing large numbers, the distributive property is applied. We can break down larger equations into smaller ones by grouping the numbers, regardless of their sequence. It facilitates and accelerates calculations.
How to Use the Distributive Property with Variables?
The distributive property is applied to variables in the same way as it is done for numbers. For example, let us find the value of ‘x’ in the equation -4(x – 3) = 8 using the distributive property. We will first multiply -4 with x and then with -3. This means, -4(x – 3) = 8 ⇒ -4x + 12 = 8. So, the value of x = 1.
How to Use the Distributive Property with Fractions?
In the same manner that the distributive property applies to numbers and variables, it also applies to fractions. Let us use the distributive property to solve the expression 1/3(2/6 + 4/6). First, we’ll multiply 1/3 by 2/6, then by 4/6. This means, 1/3(2/6 + 4/6) ⇒ (1/3 × 2/6) + (1/3 × 4/6) = 2/18 + 4/18 = 6/18 = 1/3.