Distributive Property Equations Worksheet, Examples, and Formula

What are Distributive Properties in Math?

The distributive property is a fundamental concept in mathematics that explains how to simplify expressions that involve multiplication and addition. It is also known as the distributive law of multiplication and division. Essentially, it states that when you multiply a number by a sum, you can distribute the multiplication across each term in the sum.

For example, consider the expression 2 x (3 + 4). We can apply the distributive property to simplify this expression as follows:

2 x (3 + 4) = 2 x 3 + 2 x 4 = 6 + 8 = 14

Here, we distributed the multiplication of 2 across the terms 3 and 4, and then added the results. This is a simple example, but the distributive property can be applied to much more complex expressions as well.

The distributive property is particularly useful when dealing with algebraic expressions that involve variables. For example, consider the expression 3(x + 2). We can apply the distributive property to simplify this expression as follows:

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

Here, we distributed the multiplication of 3 across the terms x and 2, and then added the results. This gives us a simplified expression that is easier to work with.

In general, the distributive property applies to any expression of the form a(b + c), where a, b, and c are numbers or variables. By distributing the multiplication across the sum, we can simplify the expression and make it easier to work with.

It is important to note that the distributive property only applies to addition within parentheses. If the expression involves subtraction within parentheses, the distributive property does not apply. In such cases, we need to use a different method to simplify the expression.

Solving Distributive Property Equations

When solving distributive property equations, the goal is to isolate the variable on one side of the equation. This is done by using inverse operations to undo any operations that are being performed on the variable. The distributive property is a useful tool in solving equations because it allows us to simplify expressions before isolating the variable.

To solve an equation using the distributive property, first distribute the number outside the parentheses to each term inside the parentheses. Then, combine like terms and simplify the expression. Next, use inverse operations to isolate the variable on one side of the equation. Finally, check the solution by plugging it back into the original equation.

Here is an example of solving an equation using the distributive property:

3(x + 4) = 21

First, distribute the 3 to each term inside the parentheses:

3x + 12 = 21

Next, subtract 12 from both sides to isolate the variable:

3x = 9

Finally, divide both sides by 3 to solve for x:

x = 3

The solution to the equation is x = 3.

It is important to note that the distributive property can also be used in reverse to factor expressions. This can be helpful in simplifying expressions before solving equations. For example, the expression 3x + 9 can be factored as 3(x + 3).

In summary, the distributive property is a powerful tool in solving equations and simplifying expressions. By distributing a number to each term inside parentheses, we can simplify expressions before isolating the variable. This allows us to solve equations more efficiently and accurately.

3 Simple Distributive Property Equation Examples

The distributive property is a fundamental concept in algebra that states that the product of a number and the sum or difference of two other numbers is equal to the sum or difference of the products of the number and each of the other two numbers. In other words, the distributive property allows us to multiply a single term by two or more terms inside a set of parentheses.

Steps for solving the Equation with the Distributive Property above:

1. Distribute the two to the x and one inside the parenthesis.
2. Multiply the two times x and the two times one.
3. Add two to both sides.
4. Divide both sides by two to get the solution of x equals three.

Distributive Property with Addition and Subtraction

One common application of the distributive property is to simplify expressions that involve addition or subtraction. For example, consider the following equation:

3(x + 4) - 2(x - 1) = 11

To solve this equation, we can use the distributive property to expand the parentheses and simplify the resulting expression:

3x + 12 - 2x + 2 = 11

Next, we can combine like terms and solve for x:

x + 14 = 11
x = -3

Distributive Property and Fractions

The distributive property can also be used to simplify expressions that involve fractions. For example, consider the following equation:

2/3(x + 6) = 4

To solve this equation, we can use the distributive property to eliminate the fraction:

2/3x + 4 = 4

Next, we can subtract 4 from both sides and multiply by the reciprocal of 2/3 to solve for x:

2/3x = 0
x = 0

Distributive Property and Order of Operations

The distributive property is also useful for simplifying expressions that involve multiple operations. For example, consider the following equation:

4 + 2(3x - 1) = 10

To solve this equation, we can use the distributive property to simplify the expression inside the parentheses:

4 + 6x - 2 = 10

Next, we can combine like terms and solve for x:

6x + 2 = 10
6x = 8
x = 4/3

In summary, the distributive property is a powerful tool for simplifying algebraic expressions and solving equations. By applying the distributive property correctly, we can eliminate parentheses, combine like terms, and isolate variables to find their values.

Solving Equations with Distributive Property

When solving algebraic equations, the distributive property is a useful tool that can simplify the equation and make it easier to solve. The distributive property states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the products. This property can be used to solve equations that involve variables and expressions with multiple terms.

To solve an equation with the distributive property, the first step is to distribute the coefficient or constant to each term in the parenthesis. This can be done by multiplying the coefficient or constant by each term in the parenthesis. Once this is done, the equation can be simplified by combining like terms and isolating the variable on one side of the equation.

For example, consider the equation 3(x + 2) = 15. To solve this equation, the distributive property can be used to distribute the coefficient 3 to each term in the parenthesis, resulting in 3x + 6 = 15. Next, the equation can be simplified by subtracting 6 from both sides, resulting in 3x = 9. Finally, the variable can be isolated by dividing both sides by 3, resulting in x = 3.

It is important to note that the distributive property can also be used to simplify algebraic expressions with multiple terms. To simplify an expression with the distributive property, the first step is to distribute the coefficient or constant to each term in the expression. Once this is done, the expression can be simplified by combining like terms.

In summary, the distributive property is a powerful tool that can be used to simplify algebraic equations and expressions. By distributing the coefficient or constant to each term in the parenthesis, equations can be simplified and variables can be isolated. With practice, solving equations with the distributive property can become second nature to students learning algebra.

Distributive Property Steps

When solving equations using the distributive property, there are a few steps that need to be followed. These steps are essential to ensure that the equation is solved correctly.

The steps for solving equations using the distributive property are as follows:

1. Distribute the number outside the parentheses to each term inside the parentheses. This means that you multiply the number outside the parentheses by each term inside the parentheses. For example, if you have the equation 3(x+2), you would distribute the 3 to both x and 2, resulting in 3x+6.

2. Combine like terms. This means that you add or subtract terms that have the same variable and exponent. For example, if you have the equation 2x+3x, you would combine the x terms to get 5x.

3. Move all the variable terms to one side of the equation and all the constant terms to the other side. This means that you want to isolate the variable on one side of the equation. For example, if you have the equation 5x+2=17, you would subtract 2 from both sides to get 5x=15.

4. Solve for the variable. This means that you want to find the value of the variable that makes the equation true. For example, if you have the equation 5x=15, you would divide both sides by 5 to get x=3.

It is important to practice solving equations using the distributive property to become proficient in these steps. By practicing, you will become more confident in your ability to solve these types of equations.

Solve Using Distributive Property FAQ

How can you use the distributive property to simplify equations?

The distributive property is a powerful tool for simplifying equations. It allows you to distribute a number or variable to every term inside a set of parentheses. For example, if you have the equation 2(x + 3), you can use the distributive property to simplify it to 2x + 6. This is because you distribute the 2 to both x and 3.

What are some common mistakes to avoid when using the distributive property to solve equations?

One common mistake when using the distributive property is forgetting to distribute the number or variable to every term inside the parentheses. Another mistake is not combining like terms after distributing. It’s important to remember to simplify the equation as much as possible before solving for the variable.

What are some examples of equations that can be solved using the distributive property?

Equations that involve multiplication and addition or subtraction can often be solved using the distributive property. For example, 3(x + 2) = 15 can be solved by distributing the 3 to both x and 2, resulting in 3x + 6 = 15.

What is the difference between solving equations with the distributive property on one side versus both sides?

Solving equations with the distributive property on one side means that you only distribute the number or variable to one side of the equation. For example, 2(x + 3) = 10 can be solved by distributing the 2 to only the left side of the equation, resulting in 2x + 6 = 10. Solving equations with the distributive property on both sides means that you distribute the number or variable to both sides of the equation. For example, 2(x + 3) + 4 = 10 + 2(x - 1) can be solved by distributing the 2 to both sides of the equation, resulting in 2x + 10 = 2x + 0.

What are some strategies for teaching the distributive property to students?

One strategy for teaching the distributive property is to use visual aids, such as manipulatives or diagrams, to help students understand the concept. Another strategy is to provide real-world examples of how the distributive property is used, such as in calculating prices at a store.

How can you check your work when using the distributive property to solve equations?

One way to check your work is to substitute your solution back into the original equation and see if it makes the equation true. Another way is to simplify the equation as much as possible and make sure that both sides are equal.

How do you use distributive property in two step equations?

To use the distributive property in two-step equations, you first simplify any expressions inside parentheses by distributing any coefficients. Then, you use inverse operations to isolate the variable on one side of the equation. For example, 3(x + 2) - 4 = 13 can be solved by distributing the 3 to both x and 2, resulting in 3x + 6 - 4 = 13. Then, you simplify the equation to 3x + 2 = 13, and isolate the variable by subtracting 2 from both sides, resulting in 3x = 11. Finally, you solve for x by dividing both sides by 3, resulting in x = 11/3.