How to Multiply Numbers Using the Distributive Property

Oct 13, 2025 by miodeya.com 126 views

Introduction

In mathematics, the distributive property is a fundamental concept that allows us to simplify complex expressions and find the product of numbers. It is a powerful tool that helps us to break down a problem into smaller, more manageable parts. In this article, we will explore how to multiply numbers using the distributive property, and provide a step-by-step guide on how to use this property to find the product.

What is the Distributive Property?

The distributive property is a mathematical concept that states that for any numbers a, b, and c, the following equation holds true:

a(b + c) = ab + ac

This property allows us to distribute a single number (a) to two or more numbers (b and c) inside a set of parentheses. In other words, it allows us to break down a complex expression into simpler parts.

How to Multiply Numbers Using the Distributive Property

To multiply numbers using the distributive property, we need to follow these steps:

Identify the numbers: Identify the numbers that we want to multiply. In this case, we have 5 and 44.
Break down the numbers: Break down the numbers into their individual parts. In this case, we can break down 44 into 40 + 4.
Apply the distributive property: Apply the distributive property by distributing the first number (5) to the individual parts of the second number (40 + 4).
Simplify the expression: Simplify the expression by multiplying the numbers together.

Let's apply these steps to the example above:

Step 1: Identify the numbers

We have two numbers: 5 and 44.

Step 2: Break down the numbers

We can break down 44 into 40 + 4.

Step 3: Apply the distributive property

We apply the distributive property by distributing 5 to the individual parts of 44:

5(40 + 4) = 5(40) + 5(4)

Step 4: Simplify the expression

We simplify the expression by multiplying the numbers together:

5(40) = 200 5(4) = 20

Therefore, 5(40 + 4) = 200 + 20 = 220.

Example 2: Multiply 3(24 + 5)

Let's apply the distributive property to multiply 3(24 + 5):

Step 1: Identify the numbers

We have two numbers: 3 and 24 + 5.

Step 2: Break down the numbers

We can break down 24 + 5 into 24 and 5.

Step 3: Apply the distributive property

We apply the distributive property by distributing 3 to the individual parts of 24 + 5:

3(24 + 5) = 3(24) + 3(5)

Step 4: Simplify the expression

We simplify the expression by multiplying the numbers together:

3(24) = 72 3(5) = 15

Therefore, 3(24 + 5) = 72 + 15 = 87.

Benefits of Using the Distributive Property

The distributive property is a powerful tool that helps us to simplify complex expressions and find the product of numbers. Some of the benefits of using the distributive property include:

Simplifying complex expressions: The distributive property allows us to break down complex expressions into simpler parts, making it easier to solve problems.
Finding the product of numbers: The distributive property helps us to find the product of numbers by distributing a single number to two or more numbers inside a set of parentheses.
Improving problem-solving skills: The distributive property helps us to develop problem-solving skills by breaking down complex problems into smaller, more manageable parts.

Conclusion

In conclusion, the distributive property is a fundamental concept in mathematics that allows us to simplify complex expressions and find the product of numbers. By following the steps outlined in this article, we can multiply numbers using the distributive property and simplify complex expressions. The benefits of using the distributive property include simplifying complex expressions, finding the product of numbers, and improving problem-solving skills. With practice and patience, we can master the distributive property and become proficient in solving complex mathematical problems.

Frequently Asked Questions

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any numbers a, b, and c, the following equation holds true: a(b + c) = ab + ac.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to follow these steps: identify the numbers, break down the numbers, apply the distributive property, and simplify the expression.

Q: What are the benefits of using the distributive property?

A: The benefits of using the distributive property include simplifying complex expressions, finding the product of numbers, and improving problem-solving skills.

Q: Can I use the distributive property to multiply fractions?

A: Yes, you can use the distributive property to multiply fractions. However, you need to follow the rules of multiplying fractions, which include multiplying the numerators and denominators separately.

Q: Can I use the distributive property to multiply decimals?

A: Yes, you can use the distributive property to multiply decimals. However, you need to follow the rules of multiplying decimals, which include multiplying the numbers as if they were whole numbers and then placing the decimal point in the correct position.

Additional Resources

For more information on the distributive property, you can check out the following resources:

Khan Academy: Distributive Property
Mathway: Distributive Property
Wolfram Alpha: Distributive Property

Conclusion

Introduction

The distributive property is a fundamental concept in mathematics that allows us to simplify complex expressions and find the product of numbers. In this article, we will answer some of the most frequently asked questions about the distributive property, including how to apply it, its benefits, and how to use it with fractions and decimals.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any numbers a, b, and c, the following equation holds true: a(b + c) = ab + ac.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to follow these steps:

Identify the numbers: Identify the numbers that you want to multiply.
Break down the numbers: Break down the numbers into their individual parts.
Apply the distributive property: Apply the distributive property by distributing a single number to two or more numbers inside a set of parentheses.
Simplify the expression: Simplify the expression by multiplying the numbers together.

Q: What are the benefits of using the distributive property?

A: The benefits of using the distributive property include:

Simplifying complex expressions: The distributive property allows us to break down complex expressions into simpler parts, making it easier to solve problems.
Finding the product of numbers: The distributive property helps us to find the product of numbers by distributing a single number to two or more numbers inside a set of parentheses.
Improving problem-solving skills: The distributive property helps us to develop problem-solving skills by breaking down complex problems into smaller, more manageable parts.

Q: Can I use the distributive property to multiply fractions?

Q: Can I use the distributive property to multiply decimals?

Q: How do I apply the distributive property to a problem like 3(24 + 5)?

A: To apply the distributive property to a problem like 3(24 + 5), you need to follow these steps:

Identify the numbers: Identify the numbers that you want to multiply, which are 3 and 24 + 5.
Break down the numbers: Break down 24 + 5 into 24 and 5.
Apply the distributive property: Apply the distributive property by distributing 3 to the individual parts of 24 + 5, which gives you 3(24) + 3(5).
Simplify the expression: Simplify the expression by multiplying the numbers together, which gives you 72 + 15 = 87.

Q: How do I apply the distributive property to a problem like 2(3x + 4)?

A: To apply the distributive property to a problem like 2(3x + 4), you need to follow these steps:

Identify the numbers: Identify the numbers that you want to multiply, which are 2 and 3x + 4.
Break down the numbers: Break down 3x + 4 into 3x and 4.
Apply the distributive property: Apply the distributive property by distributing 2 to the individual parts of 3x + 4, which gives you 2(3x) + 2(4).
Simplify the expression: Simplify the expression by multiplying the numbers together, which gives you 6x + 8.

Q: Can I use the distributive property to simplify expressions with exponents?

A: Yes, you can use the distributive property to simplify expressions with exponents. However, you need to follow the rules of working with exponents, which include multiplying the exponents when you multiply the same base.

Q: Can I use the distributive property to simplify expressions with variables?

A: Yes, you can use the distributive property to simplify expressions with variables. However, you need to follow the rules of working with variables, which include using the distributive property to break down complex expressions into simpler parts.

Conclusion

In conclusion, the distributive property is a fundamental concept in mathematics that allows us to simplify complex expressions and find the product of numbers. By following the steps outlined in this article, we can apply the distributive property to a variety of problems, including those with fractions, decimals, and variables. The benefits of using the distributive property include simplifying complex expressions, finding the product of numbers, and improving problem-solving skills. With practice and patience, we can master the distributive property and become proficient in solving complex mathematical problems.

Additional Resources

For more information on the distributive property, you can check out the following resources:

Khan Academy: Distributive Property
Mathway: Distributive Property
Wolfram Alpha: Distributive Property

Practice Problems

To practice applying the distributive property, try solving the following problems:

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

Answer Key

8x + 12
15x - 6
6x + 8
10x - 15
6x + 15