# Distributive Property Worksheet, Formula, and Definition

Get the free Distributive Property Worksheet and other resources for teaching & understanding the Distributive Property

### Key Points

- The distributive property is a fundamental concept in mathematics, particularly in algebra.
- The distributive property of multiplication over addition and subtraction is known as the distributive law.
- The distributive property is a powerful tool that can be used to simplify expressions and solve equations.

## What is Distributive Property in Math?

The Distributive Property is a way to simplify expressions. The Distributive Property is used when you are given a number, or constant, on the outside of a set of parenthesis with at least two terms on the inside of the parenthesis. When using the Distributive Property you must take the term on the outside of the parenthesis and distributive it to everything on the inside of the parenthesis.

When distributing, you must include the signs on the terms that are being multiplied together. You can tell if you did the Distributive Property correctly because there should be no parenthesis left in the expression. You can try the practice problems on our Distributive Property worksheets by downloading them on the right side of this page.

The distributive property is a fundamental concept in mathematics, particularly in algebra. It is a property that allows us to simplify multiplication equations by distributing the multiplier to each number in the parentheses and then adding those products together to get the answer. The distributive property is used in everyday life, from calculating the total cost of items on a shopping list to understanding how to solve complex mathematical problems.

In math, the distributive property of multiplication over addition and subtraction is known as the distributive law. The distributive property is a powerful tool that can be used to simplify expressions and solve equations. It is a property that allows us to break up complex problems into simpler ones, making it easier to solve them. The distributive property is one of the most used properties in mathematics, and it is a cornerstone of algebra.

**Common Core Standard: **7.NS.1**Related Topics:** Combining Like Terms, Two Step Equations, One Step Inequalities, Two Step Inequalities, Multi Step Inequalities**Return To: **Home, 7th Grade

## How to do the Distributive Property

Distributive property is a fundamental concept in mathematics that is used to simplify algebraic expressions. It is a property of multiplication that allows us to break down a complex multiplication problem into simpler ones. The distributive property states that when multiplying a number by a sum or difference of two or more numbers, we can distribute the multiplication over each term and then add or subtract the products.

For instance, let’s say we have to find the product of 3 and (7 + 2). By applying the distributive property, we can distribute 3 over the sum of 7 and 2, and then add the products. This gives us:

```
3 x (7 + 2) = (3 x 7) + (3 x 2) = 21 + 6 = 27
```

As we can see, the distributive property makes the calculation much simpler and straightforward. It is a powerful tool that helps us solve complex algebraic expressions with ease.

The distributive property is also used in reverse to factorize algebraic expressions. For instance, if we have to factorize the expression 6x + 12, we can use the distributive property to write it as:

```
6x + 12 = 6(x + 2)
```

In this case, we have distributed the common factor of 6 over the sum of x and 2, which gives us the factored expression.

Overall, the distributive property is a crucial concept in mathematics that is used extensively in algebra and other branches of mathematics. It is a powerful tool that simplifies complex expressions and helps us solve problems with ease.

## Distributive Property of Multiplication

The distributive property of multiplication is a fundamental concept in arithmetic and algebra that allows us to simplify multiplication problems. It states that when one factor is multiplied by the sum of two numbers, we can distribute the multiplication over each of the two numbers and add the resulting products. In other words, we can break down a larger multiplication problem into two simpler problems.

For example, consider the expression 4 x (8 + 12). Using the distributive property, we can rewrite this as (4 x 8) + (4 x 12) = 32 + 48 = 80. This is much easier to solve than the original expression, especially when dealing with larger numbers.

The distributive property of multiplication is a specific case of the distributive law, which states that multiplication can be distributed over addition and subtraction. The distributive law is a fundamental property of real numbers and is used extensively in algebraic equations.

It is important to note that the distributive property only applies to multiplication, not division. However, there is a distributive property of division that allows us to simplify division problems in a similar way.

When using the distributive property, it is important to follow the order of operations and simplify like terms before adding or subtracting. It can also be helpful to use the FOIL method, which stands for First, Outer, Inner, Last, to simplify multiplication problems with two terms.

Here are some solved examples of the distributive property of multiplication:

- 3 x (2 + 4) = (3 x 2) + (3 x 4) = 6 + 12 = 18
- (5 + 2) x 8 = (5 x 8) + (2 x 8) = 40 + 16 = 56
- 2 x (3x – 5) = (2 x 3x) – (2 x 5) = 6x – 10

It is also important to note that the distributive property holds true even when dealing with negative signs. For example, -2 x (3 + 5) = (-2 x 3) + (-2 x 5) = -6 – 10 = -16.

Overall, the distributive property of multiplication is a powerful tool that makes solving arithmetic and algebraic expressions much easier. By breaking down larger multiplication problems into simpler ones, we can solve equations more efficiently and accurately.

## Distributive Property Formula

The distributive property is a fundamental concept in mathematics that describes how multiplication is distributed over addition. It states that multiplying a sum by a number is the same as multiplying each addend by that number and then adding the products. The formula for the distributive property can be expressed as follows:

```
a(b + c) = ab + ac
```

In this formula, `a`

, `b`

, and `c`

are variables that can represent any real numbers or algebraic expressions. The distributive property can be used to solve problems and simplify equations in a variety of contexts.

### Solving Problems

One of the most common applications of the distributive property is in solving problems that involve multiplication and addition. For example, consider the following problem:

```
3(4 + 2)
```

To solve this problem using the distributive property, you would first distribute the `3`

to each addend inside the parentheses:

```
3(4) + 3(2)
```

Then, you would simplify each multiplication problem:

```
12 + 6
```

Finally, you would add the two products together to get the final answer:

```
18
```

### Simplifying Equations

The distributive property can also be used to simplify equations by removing parentheses and combining like terms. For example, consider the following equation:

```
4(x + 2) + 3(x + 5)
```

To simplify this equation using the distributive property, you would first distribute the `4`

and `3`

to each addend inside the parentheses:

```
4x + 8 + 3x + 15
```

Then, you would combine like terms by adding the coefficients of `x`

and the constants:

```
7x + 23
```

The distributive property is a powerful tool that is used extensively in algebra and other branches of mathematics. It is essential for understanding the relationships between addition and multiplication and for solving a wide variety of problems. By mastering the distributive property formula and its applications, students can gain a deeper understanding of mathematical concepts and develop the skills they need to succeed in more advanced courses.

## Distributive Property Examples: 5 Easy Steps to Solve

- When an expression has a term on the outside of a set of parenthesis you use the Distributive Property.
- You take the term on the outside of the parenthesis and distribute it to everything on the inside of the parenthesis.
- To distribute you must multiply the terms together.
- Make sure you include the signs of the terms when multiplying them together.
- You are finished when there are no parenthesis left.

The distributive property is a fundamental concept in mathematics that allows for the simplification of complex equations. Here are some examples to help illustrate how it works.

### Example 1

Suppose you have the equation:

```
3(4 + 5)
```

Using the distributive property, you can simplify this equation as follows:

```
3(4) + 3(5) = 12 + 15 = 27
```

### Example 2

Now, let’s consider a slightly more complex equation:

```
2(x + 3) - 4(x - 1)
```

Using the distributive property, we can simplify this equation as follows:

```
2x + 6 - 4x + 4 = -2x + 10
```

### Example 3

Here’s another example:

```
5(2x + 3y) - 2(3x - y)
```

Using the distributive property, we can simplify this equation as follows:

```
10x + 15y - 6x + 2y = 4x + 17y
```

### Example 4

Let’s consider one more example:

```
-2(a - 3b) + 4(2a + b)
```

Using the distributive property, we can simplify this equation as follows:

```
-2a + 6b + 8a + 4b = 6a + 10b
```

As you can see from these examples, the distributive property can be used to simplify complex equations and make them easier to solve. By breaking down an equation into smaller parts and then combining them, you can arrive at a solution more quickly and easily.

## 5 Quick Distributive Property Practice Problems

## Distributive Property Definition

The distributive property is a fundamental concept in mathematics that deals with the distribution of a number or variable over a sum or difference of terms. In other words, it allows us to simplify expressions by breaking them down into smaller parts that are easier to work with.

Specifically, the distributive property states that the product of a number or variable and a sum or difference of terms is equal to the sum or difference of the products of the number or variable with each term separately. This can be represented using the following formula:

```
a(b + c) = ab + ac
```

where `a`

, `b`

, and `c`

are any numbers or variables.

For example, if we have the expression `3(x + 2)`

, we can use the distributive property to simplify it as follows:

```
3(x + 2) = 3x + 6
```

This is because we can distribute the `3`

over the sum of `x`

and `2`

, giving us `3x + 6`

.

The distributive property is a powerful tool that allows us to simplify complex expressions and solve equations more easily. It is used extensively in algebra, calculus, and other branches of mathematics, and is an essential concept for anyone studying these subjects.

## What does Distributive Property mean?

The Distributive Property is a fundamental concept in mathematics that is used to simplify expressions involving multiplication and addition. It states that when a number is multiplied by a sum of two or more numbers, the result is the same as if each of those numbers were multiplied by the original number and then added together. In other words, the Distributive Property allows us to distribute a factor to each term in a sum or difference.

For example, consider the expression 3(x + 2). Using the Distributive Property, we can distribute the factor 3 to each term in the parentheses, giving us:

3(x + 2) = 3x + 6

This is equivalent to first multiplying x by 3 and then adding 6 to the result.

The Distributive Property is a powerful tool for simplifying expressions and solving equations. It is especially useful in algebra, where it is used to manipulate equations and solve for unknown variables. By applying the Distributive Property, we can often transform complex expressions into simpler forms that are easier to work with.

Overall, the Distributive Property is a fundamental concept in mathematics that plays a critical role in algebra and other areas of mathematics. Understanding this concept is essential for anyone who wants to excel in mathematics and related fields.

## Solve Using Distributive Property FAQ

### What is the Distributive Property used for?

The Distributive Property is a mathematical property that is used to simplify algebraic expressions. It allows the multiplication of a single term to be distributed across two or more terms inside a set of parentheses. This property is widely used in algebra and helps in solving complex equations.

### How can you apply the Distributive Property in algebraic expressions?

To apply the Distributive Property in algebraic expressions, you need to multiply the term outside the parentheses with each term inside the parentheses. For example, if you have an expression 3(x+2), you need to multiply 3 with x and 3 with 2. The expression will then become 3x+6.

### What are some real-world applications of the Distributive Property?

The Distributive Property is used in various fields such as engineering, physics, and economics. It helps in simplifying complex equations and makes calculations easier.

### Can the Distributive Property be used with fractions?

Yes, the Distributive Property can be used with fractions. You can distribute a fraction across two or more terms inside a set of parentheses. For example, if you have an expression 2(1/3 + 1/4), you can distribute 2 across 1/3 and 1/4. The expression will then become 2/3 + 1/2.

### What are some common mistakes when using the Distributive Property?

One common mistake is forgetting to distribute the term outside the parentheses with each term inside the parentheses. Another mistake is not simplifying the expression after distributing the term.

### How do you simplify expressions using the Distributive Property?

To simplify expressions using the Distributive Property, you need to distribute the term outside the parentheses with each term inside the parentheses. Then, you need to combine like terms. Finally, you need to simplify the expression by performing any necessary operations.

### What are 2 examples of distributive property?

Two examples of the Distributive Property are:

- 3(x+2) = 3x+6
- 2(4y-5) = 8y-10

### What are the 4 steps for distributive property?

The 4 steps for using the Distributive Property are:

- Identify the term outside the parentheses.
- Distribute the term across each term inside the parentheses.
- Combine like terms.
- Simplify the expression.

### What does a distributive property look like?

The Distributive Property looks like this: a(b+c) = ab + ac. It shows that the multiplication of a term a with the sum of two terms b and c is equal to the sum of the multiplication of a with b and a with c.

### How do I solve distributive property?

To solve distributive property, you need to distribute the term outside the parentheses with each term inside the parentheses. Then, you need to combine like terms. Finally, you need to simplify the expression by performing any necessary operations.

## Distributive Property Worksheet Video Explanation

Watch our free video on how to do the Distributive Property. This video shows how to solve problems that are on our free Distributive Property worksheet 7th grade that you can get by submitting your email above.

**Watch the free Distributive Property video on YouTube here: How to do Distributive Property Video**

**Video Transcript:**

This video is about how to do the distributive property. You can get the 7th grade distributive property worksheet used in this video for free by clicking on the link in the description below. The first part in figuring out how to do the distributive property is understanding that the distributive property states that if you’re given an expression in the form of this expression, where you have a times the quantity b plus c, you can take this a and distribute it by multiplying it by everything inside of the parentheses.

In the case of this first example that gives us 5 times the quantity 5x minus 5. The distributive property states that you need to use a distributive law of multiplication to take the term that is on the outside of the parentheses and distribute it to everything inside of the parentheses using multiplication. We’re going to take this term that is on the outside of the parentheses and distribute it to everything inside the parentheses. We take this term in this case which is 5 and we multiply it times the first term inside of the parentheses which is 5x.

Then we bring down the symbol in the middle which is our minus symbol and then we take the term on the outside which is 5 and multiply it times the second term on the inside which is also 5. Our 5 has now been distributed to both the 5x and the 5 inside of the parentheses. Now you follow order of operations, which is to multiply before you subtract. So, we’re going to multiply 5 times 5x and get 25x. Leep the sign in the middle the same, which is minus and then 5 times 5 which is 25. 25x and 25 are not like terms so you do not combine them. Our final solution is 25x minus 25.

Let’s do a couple practice problems on our distributive property worksheet. Jumping to the first problem on our distributive property works it gives us 2 times the quantity x minus 1. We know that we’re supposed to take the term that is outside the parentheses and distribute it through multiplication to everything inside of the parentheses. We’re going to take this 2 and we’re going to multiply it times the first term, in this case is x.

We’re going to multiply it times x then we bring the symbol straight down that’s in the middle then we take the term which is on the outside, 2 again and we multiply it times the last term inside of the parenthesis which is 1. Finally, according to order of operations we simplify by doing multiplication before addition or subtraction. We do 2 times x which is 2x minus the sign in the middle stays the same and then 2 times 1 which is 2. Our final solution will be 2x minus 2.

Moving on to number three on our distributive property worksheet. This problem gives us negative 10 times the quantity x plus eight. Again, we take the term that is outside of the parentheses and we use multiplication to distribute it to everything that is on the inside of the parentheses. The term negative 10 is going to be multiplied by our first term inside of the parenthesis in this case is x.

We bring down the plus symbol in the middle then we take negative 10 and multiply it by positive 8 which is our last term in the parentheses. Negative 10 times x is negative 10x and then negative 10 times 8 is negative 80. Our final solution is negative 10x minus 80.

The last problem we’re going to complete on our distributive property worksheet is number eight. This problem gives us negative seven times the quantity five x minus ten. We take this negative seven, just like we did in the other problems, and we distribute it to everything that is inside of the parentheses. In the case of this problem, we do negative 7 times 5x, that’s going to be the first thing we multiply by.

The symbol in the middle comes down, which is minus, and then we do negative 7 again times in this case the last term is going to be 10. Then we simplify following order of operations negative 7 times 5x is negative 35 x. The symbol in the middle stays the same and then negative 7 times 10 is negative 70. Now what’s unique about this problem is that we have two negatives that are next to each other.

When you have two negatives next to each other the two negatives cancel. We’re going to cancel them and they become a positive. Our final answer will be negative 35 x plus 70 because the two negatives cancel. Hopefully this video helped you better understand what is the distributive property in math. Try the practice problems on the Distributive Property quiz above or download the distributive property 7th grade worksheet and try those problems.

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