Newport Township Is Building A New Playground Area For Neighborhood Kids. The Playground Will Be A Square With A Perimeter Of $56+\frac{8}{3} X$. An Equivalent Expression Is $56+8\left(\frac{1}{3} X\right$\].Which Expression Represents

Introduction

Newport Township is building a new playground area for neighborhood kids. The playground will be a square with a perimeter of $56+\frac{8}{3} x$. In this article, we will explore the mathematical concept of equivalent expressions and determine which expression represents the perimeter of the playground.

Understanding Perimeter

The perimeter of a square is the sum of the lengths of all its sides. Since a square has four equal sides, the perimeter can be calculated by multiplying the length of one side by 4. In this case, the perimeter is given as $56+\frac{8}{3} x$.

Equivalent Expressions

Equivalent expressions are mathematical expressions that have the same value, but may be written in different ways. In this case, we are given two expressions:

1. $56+\frac{8}{3} x$
2. $56+8\left(\frac{1}{3} x\right)$

We need to determine which expression represents the perimeter of the playground.

Simplifying the First Expression

The first expression is $56+\frac{8}{3} x$. To simplify this expression, we can multiply the fraction by the variable $x$. This gives us:

$$56+\frac{8}{3} x = 56 + \frac{8x}{3}$$

Simplifying the Second Expression

The second expression is $56+8\left(\frac{1}{3} x\right)$. To simplify this expression, we can multiply the fraction by the variable $x$. This gives us:

$$56+8\left(\frac{1}{3} x\right) = 56 + \frac{8x}{3}$$

Comparing the Expressions

Now that we have simplified both expressions, we can compare them to determine which one represents the perimeter of the playground. Both expressions are equal to $56 + \frac{8x}{3}$, which means they are equivalent.

Conclusion

In conclusion, the expression that represents the perimeter of the playground is $56+8\left(\frac{1}{3} x\right)$. This expression is equivalent to the first expression, $56+\frac{8}{3} x$, and both expressions have the same value.

Why is this Important?

Understanding equivalent expressions is an important concept in mathematics. It allows us to simplify complex expressions and make it easier to solve problems. In this case, the equivalent expression $56+8\left(\frac{1}{3} x\right)$ makes it easier to understand the perimeter of the playground.

Real-World Applications

The concept of equivalent expressions has many real-world applications. For example, in engineering, equivalent expressions can be used to simplify complex mathematical models and make it easier to design and build structures. In finance, equivalent expressions can be used to simplify complex financial models and make it easier to make investment decisions.

Final Thoughts

In conclusion, the expression that represents the perimeter of the playground is $56+8\left(\frac{1}{3} x\right)$. This expression is equivalent to the first expression, $56+\frac{8}{3} x$, and both expressions have the same value. Understanding equivalent expressions is an important concept in mathematics and has many real-world applications.

References

• [1] "Mathematics for Engineers and Scientists" by Donald R. Hill
• [2] "Calculus" by Michael Spivak
• [3] "Algebra" by Michael Artin

Glossary

• Equivalent Expressions: Mathematical expressions that have the same value, but may be written in different ways.
• Perimeter: The sum of the lengths of all the sides of a shape.
• Variable: A symbol that represents a value that can change.
• Fraction: A way of expressing a part of a whole as a ratio of two numbers.
  Newport Township Playground Area: A Mathematical Approach - Q&A ===========================================================

Introduction

In our previous article, we explored the mathematical concept of equivalent expressions and determined which expression represents the perimeter of the playground. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is the perimeter of the playground?

A: The perimeter of the playground is $56+\frac{8}{3} x$.

Q: What is the equivalent expression for the perimeter?

A: The equivalent expression for the perimeter is $56+8\left(\frac{1}{3} x\right)$.

Q: Why is it important to understand equivalent expressions?

A: Understanding equivalent expressions is important because it allows us to simplify complex expressions and make it easier to solve problems. In this case, the equivalent expression $56+8\left(\frac{1}{3} x\right)$ makes it easier to understand the perimeter of the playground.

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

A: The concept of equivalent expressions has many real-world applications. For example, in engineering, equivalent expressions can be used to simplify complex mathematical models and make it easier to design and build structures. In finance, equivalent expressions can be used to simplify complex financial models and make it easier to make investment decisions.

Q: How can I simplify complex expressions?

A: To simplify complex expressions, you can use the following steps:

1. Identify the equivalent expression.
2. Simplify the expression by combining like terms.
3. Check your work by plugging in a value for the variable.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change. A constant is a value that does not change.

Q: How can I determine if two expressions are equivalent?

A: To determine if two expressions are equivalent, you can use the following steps:

1. Simplify both expressions.
2. Check if the simplified expressions are equal.
3. If the simplified expressions are equal, then the original expressions are equivalent.

Q: What is the importance of understanding fractions?

A: Understanding fractions is important because it allows us to express a part of a whole as a ratio of two numbers. In this case, the fraction $\frac{8}{3}$ represents a part of the perimeter.

Q: How can I use equivalent expressions in real-world problems?

A: You can use equivalent expressions in real-world problems by simplifying complex expressions and making it easier to solve problems. For example, in engineering, equivalent expressions can be used to simplify complex mathematical models and make it easier to design and build structures.

Conclusion

In conclusion, understanding equivalent expressions is an important concept in mathematics. It allows us to simplify complex expressions and make it easier to solve problems. In this article, we answered some frequently asked questions related to the topic and provided some real-world applications of equivalent expressions.

References

• [1] "Mathematics for Engineers and Scientists" by Donald R. Hill
• [2] "Calculus" by Michael Spivak
• [3] "Algebra" by Michael Artin

Glossary

• Equivalent Expressions: Mathematical expressions that have the same value, but may be written in different ways.
• Perimeter: The sum of the lengths of all the sides of a shape.
• Variable: A symbol that represents a value that can change.
• Fraction: A way of expressing a part of a whole as a ratio of two numbers.
• Constant: A value that does not change.