Select The Statement Which Uses The Distributive Property.$\[ \begin{array}{l} \text{A. } 4 \times (7 + 2) = 4 \times 9 \\ \text{B. } 4 \times (7 + 2) = (4 \times 7) + 2 \\ \text{C. } 4 \times (7 + 2) = 4 \times 7 + 7 \times 2 \end{array} \\]

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The distributive property is a fundamental concept in mathematics that allows us to expand expressions involving multiplication and addition. It is a crucial tool for simplifying complex expressions and solving equations. In this article, we will explore the distributive property and learn how to identify and apply it in various mathematical contexts.

What is the Distributive Property?

The distributive property is a mathematical concept that states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In other words, it allows us to distribute a single factor to multiple terms inside a set of parentheses. The distributive property can be expressed mathematically as:

a(b + c) = ab + ac

Applying the Distributive Property

To apply the distributive property, we need to identify the expression that involves multiplication and addition. In the given options, we have three expressions that involve multiplication and addition:

A. 4 × (7 + 2) = 4 × 9 B. 4 × (7 + 2) = (4 × 7) + 2 C. 4 × (7 + 2) = 4 × 7 + 7 × 2

Analyzing Option A

Option A states that 4 × (7 + 2) = 4 × 9. However, this expression does not apply the distributive property correctly. The distributive property requires us to distribute the factor 4 to each term inside the parentheses, not just multiply the entire expression by 4.

Analyzing Option B

Option B states that 4 × (7 + 2) = (4 × 7) + 2. This expression does not apply the distributive property correctly either. The distributive property requires us to distribute the factor 4 to each term inside the parentheses, not just multiply the first term by 4 and leave the second term unchanged.

Analyzing Option C

Option C states that 4 × (7 + 2) = 4 × 7 + 7 × 2. This expression applies the distributive property correctly. We can see that the factor 4 is distributed to each term inside the parentheses, resulting in the sum of the products of 4 and each term.

Conclusion

In conclusion, the correct answer is Option C, which states that 4 × (7 + 2) = 4 × 7 + 7 × 2. This expression applies the distributive property correctly, distributing the factor 4 to each term inside the parentheses.

Real-World Applications of the Distributive Property

The distributive property has numerous real-world applications in various fields, including:

  • Algebra: The distributive property is used extensively in algebra to simplify complex expressions and solve equations.
  • Geometry: The distributive property is used to calculate the area and perimeter of shapes, such as rectangles and triangles.
  • Physics: The distributive property is used to calculate the force and motion of objects, such as projectiles and pendulums.
  • Computer Science: The distributive property is used in computer programming to simplify complex expressions and optimize algorithms.

Tips for Applying the Distributive Property

Here are some tips for applying the distributive property:

  • Identify the expression: Identify the expression that involves multiplication and addition.
  • Distribute the factor: Distribute the factor to each term inside the parentheses.
  • Simplify the expression: Simplify the expression by combining like terms.
  • Check your work: Check your work by plugging in values or using a calculator to verify the result.

Common Mistakes to Avoid

Here are some common mistakes to avoid when applying the distributive property:

  • Not distributing the factor: Failing to distribute the factor to each term inside the parentheses.
  • Not simplifying the expression: Failing to simplify the expression by combining like terms.
  • Not checking your work: Failing to check your work by plugging in values or using a calculator to verify the result.

Conclusion

The distributive property is a fundamental concept in mathematics that can be confusing for many students. In this article, we will answer some frequently asked questions about the distributive property to help you better understand this concept.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In other words, it allows us to distribute a single factor to multiple terms inside a set of parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to identify the expression that involves multiplication and addition. Then, you need to distribute the factor to each term inside the parentheses. Finally, you need to simplify the expression by combining like terms.

Q: What are some common mistakes to avoid when applying the distributive property?

A: Some common mistakes to avoid when applying the distributive property include:

  • Not distributing the factor to each term inside the parentheses.
  • Not simplifying the expression by combining like terms.
  • Not checking your work by plugging in values or using a calculator to verify the result.

Q: How do I simplify expressions using the distributive property?

A: To simplify expressions using the distributive property, you need to follow these steps:

  1. Identify the expression that involves multiplication and addition.
  2. Distribute the factor to each term inside the parentheses.
  3. Simplify the expression by combining like terms.
  4. Check your work by plugging in values or using a calculator to verify the result.

Q: What are some real-world applications of the distributive property?

A: The distributive property has numerous real-world applications in various fields, including:

  • Algebra: The distributive property is used extensively in algebra to simplify complex expressions and solve equations.
  • Geometry: The distributive property is used to calculate the area and perimeter of shapes, such as rectangles and triangles.
  • Physics: The distributive property is used to calculate the force and motion of objects, such as projectiles and pendulums.
  • Computer Science: The distributive property is used in computer programming to simplify complex expressions and optimize algorithms.

Q: How do I check my work when applying the distributive property?

A: To check your work when applying the distributive property, you need to follow these steps:

  1. Plug in values to verify the result.
  2. Use a calculator to verify the result.
  3. Check your work by simplifying the expression and verifying the result.

Q: What are some tips for applying the distributive property?

A: Here are some tips for applying the distributive property:

  • Identify the expression that involves multiplication and addition.
  • Distribute the factor to each term inside the parentheses.
  • Simplify the expression by combining like terms.
  • Check your work by plugging in values or using a calculator to verify the result.

Conclusion

In conclusion, the distributive property is a fundamental concept in mathematics that can be confusing for many students. By understanding and applying the distributive property, you can simplify complex expressions and solve equations. Remember to identify the expression, distribute the factor, simplify the expression, and check your work to ensure accuracy.