Tomatoes: 35 Acres Radishes: 28 Acres Which Expression Is Equivalent To The Sum Of The Two Areas?A. 5 ( 7 + 4 5(7+4 5 ( 7 + 4 ] B. 5 ( 7 + 7 5(7+7 5 ( 7 + 7 ] C. 7 ( 5 + 4 7(5+4 7 ( 5 + 4 ] D. 7 ( 4 + 7 7(4+7 7 ( 4 + 7 ]

In this article, we will delve into the world of mathematics, specifically focusing on algebraic expressions and their equivalents. We will examine a problem involving the areas of two different crops, tomatoes and radishes, and determine which expression is equivalent to the sum of their areas.

The Problem: Areas of Tomatoes and Radishes

We are given the areas of two crops: tomatoes and radishes. The area of tomatoes is 35 acres, and the area of radishes is 28 acres. We need to find an expression that represents the sum of these two areas.

Breaking Down the Problem

To approach this problem, we need to understand the concept of equivalent expressions. An equivalent expression is one that has the same value as another expression, but may be written in a different form. In this case, we need to find an expression that represents the sum of 35 acres and 28 acres.

Analyzing the Options

Let's examine the options provided:

A. $5(7+4)$ B. $5(7+7)$ C. $7(5+4)$ D. $7(4+7)$

We need to determine which of these expressions is equivalent to the sum of 35 acres and 28 acres.

Option A: $5(7+4)$

Let's start by evaluating option A. The expression $5(7+4)$ can be simplified as follows:

$5(7+4) = 5(11) = 55$

This expression represents the area of 55 acres, which is not the sum of 35 acres and 28 acres.

Option B: $5(7+7)$

Next, let's evaluate option B. The expression $5(7+7)$ can be simplified as follows:

$5(7+7) = 5(14) = 70$

This expression represents the area of 70 acres, which is not the sum of 35 acres and 28 acres.

Option C: $7(5+4)$

Now, let's evaluate option C. The expression $7(5+4)$ can be simplified as follows:

$7(5+4) = 7(9) = 63$

This expression represents the area of 63 acres, which is not the sum of 35 acres and 28 acres.

Option D: $7(4+7)$

Finally, let's evaluate option D. The expression $7(4+7)$ can be simplified as follows:

$7(4+7) = 7(11) = 77$

This expression represents the area of 77 acres, which is not the sum of 35 acres and 28 acres.

The Correct Answer: A Different Approach

Upon re-examining the problem, we realize that we need to find an expression that represents the sum of 35 acres and 28 acres. Let's try a different approach:

$35 + 28 = 63$

This expression represents the sum of 35 acres and 28 acres. However, none of the options provided match this expression.

Conclusion

In conclusion, none of the options provided are equivalent to the sum of 35 acres and 28 acres. However, we can represent the sum using a different expression:

$35 + 28 = 63$

This expression represents the sum of the two areas, but it is not among the options provided.

Understanding Equivalent Expressions

Equivalent expressions are expressions that have the same value, but may be written in a different form. In this case, we need to find an expression that represents the sum of 35 acres and 28 acres. However, none of the options provided match this expression.

Tips for Solving Similar Problems

When solving similar problems, remember to:

• Read the problem carefully and understand what is being asked.
• Break down the problem into smaller parts and analyze each part separately.
• Look for equivalent expressions that represent the same value.
• Use algebraic manipulations to simplify expressions and find equivalent forms.

In this article, we will address some of the most common questions related to equivalent expressions. Whether you're a student, a teacher, or simply someone who wants to improve their math skills, this article will provide you with the answers you need.

Q: What is an equivalent expression?

A: An equivalent expression is an expression that has the same value as another expression, but may be written in a different form. Equivalent expressions can be obtained by applying various algebraic manipulations, such as addition, subtraction, multiplication, and division.

Q: How do I find equivalent expressions?

A: To find equivalent expressions, you can use various algebraic manipulations, such as:

• Adding or subtracting the same value to both sides of an equation
• Multiplying or dividing both sides of an equation by the same value
• Using the distributive property to expand expressions
• Using the commutative property to rearrange expressions

Q: What are some common equivalent expressions?

A: Some common equivalent expressions include:

• $a + b = b + a$
• $a \times b = b \times a$
• $a + b + c = c + b + a$
• $a \times b \times c = c \times b \times a$

Q: How do I simplify expressions using equivalent expressions?

A: To simplify expressions using equivalent expressions, you can:

• Combine like terms
• Cancel out common factors
• Use the distributive property to expand expressions
• Use the commutative property to rearrange expressions

Q: What are some real-world applications of equivalent expressions?

A: Equivalent expressions have many real-world applications, including:

• Algebraic geometry: Equivalent expressions are used to describe geometric shapes and their properties.
• Calculus: Equivalent expressions are used to describe limits and derivatives.
• Physics: Equivalent expressions are used to describe physical laws and their applications.
• Engineering: Equivalent expressions are used to design and optimize systems.

Q: How do I practice finding equivalent expressions?

A: To practice finding equivalent expressions, you can:

• Work on math problems that involve equivalent expressions
• Use online resources, such as math websites and apps
• Practice with real-world examples and applications
• Join a study group or find a study partner to practice with

Q: What are some common mistakes to avoid when working with equivalent expressions?

A: Some common mistakes to avoid when working with equivalent expressions include:

• Not simplifying expressions enough
• Not using the correct algebraic manipulations
• Not checking for equivalent expressions
• Not using the distributive property correctly

Conclusion

In conclusion, equivalent expressions are an essential concept in mathematics that can be used to simplify and solve equations. By understanding how to find equivalent expressions and practicing with real-world examples, you can improve your math skills and become proficient in solving mathematical problems. Remember to avoid common mistakes and use online resources to practice and learn.