# Distributive Property Definition, Formula, Examples

The distributive property is a math rule that states that the distribution of a multiplication problem can be reversed. So, if you have a multiplication problem like 4×15, you can divide it into two parts: 4×10 and 4×5, which would give you the answer 40+20=60. This article will explain the distributive property in more depth so that you can apply it to other math problems!

## What is the Distribution Property?

The distributive property is a mathematical rule that allows you to multiply a single term and two terms inside of parentheses. The distributive property is written as: a(b + c) = ab + ac. This property is used to simplify equations and make them easier to solve.

For example, let’s say you want to multiply 3x(4+5). You could do this by multiplying 3×4 and then adding that to 3×5, or you could use the distributive property and multiply 3×4+3×5. This would give you the same answer, but using the distributive property is often quicker and simpler.

The distributive property can also be used with division. For example, if you wanted to divide 10 ÷ (2+3), you could first divide 10 ÷ 2 to get 5 and then add 5 ÷ 3 to get 2. Or, you could use the distributive property and divide 10 ÷ (2+3) = 10 ÷ 2+10 ÷ 3 which would give you the same answer of 2.

Hopefully, this gives you a better understanding of the distributive property and how it can be used!

### Distribution Property Formula

The distributive property is a mathematical rule that allows you to simplify expressions that contain multiple terms. In its most basic form, the distributive property states that when you multiply a number by a group of numbers, you can multiply each number in the group individually and then add up the results. For example, if you wanted to calculate 4 times (2 + 3), you could multiply 4 by 2 to get 8, then multiply 4 by 3 to get 12, and then add 8 and 12 together to get 20. Using the distributive property saves you time and effort when working with complex math problems.

The distributive property can also be used to divide numbers. For instance, if you wanted to divide 10 by (2 + 3), you could first divide 10 by 2 to get 5, then divide 10 by 3 to get 3.33, and then add 5 and 3.33 together to get 8.33.

The distributive property is a powerful tool that can be used to simplify a wide variety of math problems. Next time you’re stuck on a math problem, see if the distributive property can help you out!

#### Distribution Property Examples

The distributive property is a math rule that allows you to simplify expressions involving multiplication. It states that for any numbers a, b, and c, the following equation holds:

a (b + c) = ab + ac

This rule can be applied to addition and subtraction as well, by simply reversing the order of the terms:

(a + b) c = ac + bc

The property is extremely useful when simplifying complex algebraic expressions. It’s one of the first rules you’ll learn in algebra. Let’s take a look at a few examples of how the property can be used.

#### Distribution Property of Division

The property is the same as the distributive law of multiplication, with only the multiplication sign changing to division along with the operation. The larger term is divided into smaller factors (added), and the divisor acts as the operand. You will understand this better with the example given below.

Example: Using the distributive property of division, solve 36 ÷ 12.

Solution: 36 can be written as 24 + 12

Therefore we can write 36 ÷ 12 = (24 + 12) ÷ 12

Now, let us distribute 12 inside the bracket

⇒ (24 ÷ 12) + (12 ÷ 12)

⇒ 2 + 1

This gives us the answer as 3.

#### When to use the Distribution Property

The Distributive Property is a powerful tool that can be used to simplify algebraic expressions. However, it’s important to know when to use it and when not to use it. In this blog post, we’ll discuss when the  Property can be used and when it can’t be used.

The  Property can be used whenever you’re dealing with a linear expression. A linear expression is an expression that can be written in the form ax + b, where a and b are constants and x is a variable. The  Property allows you to rewrite this expression as an (x + b), which is often much simpler to work with.

There are some situations where the  Property cannot be used. One such situation is when you’re dealing with an exponential expression. An exponential expression is an expression of the form ax ^n, where a and n are constants and x is a variable. The Property cannot be used to simplify this type of expression.

Another situation where the Property cannot be used is when you’re dealing with a polynomial expression. A polynomial expression is an expression that can be written in the form ax ^n + BX ^m

##### Why the distribution Property is important

The  Property is one of the most important properties in mathematics. It allows us to simplify equations and make calculations easier. In this blog post, we’ll explore why the  Property is so important and some of the different ways it can be used.

One of the most important uses of the  Property is simplifying equations. Oftentimes, an equation can be made much simpler by using the Property to remove parentheses. For example, consider the equation 4x + 3(2x – 5). This equation can be simplified using the  Property to 4x + 6x – 15, which is much easier to solve.

Another common use of the  Property is solving problems with variables. For example, suppose you are asked to find the value of x is 3(x + 2) = 21. We can use the Property to simplify this equation to 3x + 6 = 21. Then, we can solve for x by subtracting 6 from both sides, which gives us 3x = 15. Therefore, x = 5.

###### Conclusion

The distributive property is an algebraic property that allows you to multiply a single term and distribute the product to multiple terms. This property is essential when solving equations and can be used to simplify algebraic expressions. While the distributive property may seem daunting at first, it’s quite simple once you understand the concept. With a little practice, you’ll be able to use the property like a pro!

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