Find The Value Of This Expression If $x = 6$ And $y = -1$: X Y 2 − 5 \frac{x Y^2}{-5} − 5 X Y 2

Jun 1, 2025 by ADMIN 102 views

Finding the Value of a Mathematical Expression

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Introduction

Mathematical expressions are a crucial part of mathematics, and solving them is an essential skill for anyone studying the subject. In this article, we will focus on finding the value of a given mathematical expression when the values of its variables are known. We will use the expression $\frac{x y^2}{-5}$ and substitute the given values of $x$ and $y$ to find the final result.

Understanding the Expression

The given expression is $\frac{x y^2}{-5}$ . This expression involves variables $x$ and $y$ , and we are asked to find its value when $x = 6$ and $y = -1$ . To do this, we need to substitute the given values of $x$ and $y$ into the expression and simplify it.

Substituting the Values of $x$ and $y$

We are given that $x = 6$ and $y = -1$ . We will substitute these values into the expression $\frac{x y^2}{-5}$ .

\frac{(6) (-1)^2}{-5}

Simplifying the Expression

Now that we have substituted the values of $x$ and $y$ into the expression, we need to simplify it. To do this, we will follow the order of operations (PEMDAS):

Evaluate the exponent: $(-1)^2 = 1$
Multiply $x$ and $y^2$ : $6 \times 1 = 6$
Divide the result by $-5$ : $\frac{6}{-5} = -\frac{6}{5}$

Final Result

After simplifying the expression, we get:

\frac{x y^2}{-5} = -\frac{6}{5}

Conclusion

In this article, we found the value of the expression $\frac{x y^2}{-5}$ when $x = 6$ and $y = -1$ . We substituted the given values into the expression and simplified it using the order of operations. The final result is $-\frac{6}{5}$ .

Frequently Asked Questions

Q: What is the value of the expression when $x = 3$ and $y = 2$ ?

A: To find the value of the expression when $x = 3$ and $y = 2$ , we will substitute these values into the expression and simplify it. The final result will be $\frac{12}{-5} = -\frac{12}{5}$ .

Q: How do I simplify a mathematical expression?

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

A: A variable is a value that can change, while a constant is a value that remains the same. In the expression $\frac{x y^2}{-5}$ , $x$ and $y$ are variables, while $-5$ is a constant.

Introduction

Mathematical expressions are a crucial part of mathematics, and solving them is an essential skill for anyone studying the subject. In this article, we will answer some frequently asked questions about mathematical expressions, including how to simplify them, the difference between variables and constants, and more.

Q: What is a mathematical expression?

A: A mathematical expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a result. Examples of mathematical expressions include $2x + 3$ , $\frac{x}{y}$ , and $x^2 + 4x + 4$ .

Q: How do I simplify a mathematical expression?

A: To simplify a mathematical expression, you need to follow the order of operations (PEMDAS). This involves evaluating exponents, multiplying and dividing from left to right, and adding and subtracting from left to right. For example, to simplify the expression $3x^2 + 2x + 5$ , you would first evaluate the exponent, then multiply and divide from left to right, and finally add and subtract from left to right.

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

A: A variable is a value that can change, while a constant is a value that remains the same. In the expression $2x + 3$ , $x$ is a variable, while $2$ and $3$ are constants.

Q: How do I evaluate an exponent?

A: To evaluate an exponent, you need to raise the base number to the power of the exponent. For example, to evaluate the expression $x^2$ , you would raise $x$ to the power of $2$ .

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating a mathematical expression. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate exponents next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate addition and subtraction operations from left to right.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide the numerator and denominator by their greatest common divisor (GCD). For example, to simplify the fraction $\frac{12}{18}$ , you would divide both numbers by their GCD, which is $6$ , to get $\frac{2}{3}$ .

Q: What is the difference between a rational expression and an irrational expression?

A: A rational expression is a fraction that can be simplified to a whole number or a fraction with a finite number of terms. An irrational expression is a fraction that cannot be simplified to a whole number or a fraction with a finite number of terms.

Q: How do I simplify a rational expression?

A: To simplify a rational expression, you need to factor the numerator and denominator, then cancel out any common factors. For, to simplify the expression $\frac{6x}{2x}$ , you would factor the numerator and denominator to get $\frac{3x}{x}$ , then cancel out the common factor of $x$ to get $3$ .

Q: What is the difference between a linear expression and a quadratic expression?

A: A linear expression is an expression that can be written in the form $ax + b$ , where $a$ and $b$ are constants. A quadratic expression is an expression that can be written in the form $ax^2 + bx + c$ , where $a$ , $b$ , and $c$ are constants.

Q: How do I simplify a linear expression?

A: To simplify a linear expression, you need to combine like terms. For example, to simplify the expression $2x + 3x$ , you would combine the like terms to get $5x$ .

Q: What is the difference between a polynomial expression and a non-polynomial expression?

A: A polynomial expression is an expression that can be written in the form $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$ , where $a_n$ , $a_{n-1}$ , $\ldots$ , $a_1$ , and $a_0$ are constants. A non-polynomial expression is an expression that cannot be written in this form.

Q: How do I simplify a polynomial expression?

A: To simplify a polynomial expression, you need to combine like terms. For example, to simplify the expression $2x^2 + 3x + 4x^2$ , you would combine the like terms to get $6x^2 + 3x$ .

Conclusion

In this article, we have answered some frequently asked questions about mathematical expressions, including how to simplify them, the difference between variables and constants, and more. We hope that this article has been helpful in clarifying any confusion you may have had about mathematical expressions.

Find The Value Of This Expression If $x = 6$ And $y = -1$: X Y 2 − 5 \frac{x Y^2}{-5} − 5 X Y 2

Introduction

Understanding the Expression

Substituting the Values of $x$ and $y$

Simplifying the Expression

Final Result

Conclusion

Frequently Asked Questions

Q: What is the value of the expression when $x = 3$ and $y = 2$ ?

Q: How do I simplify a mathematical expression?

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

Further Reading

Introduction

Q: What is a mathematical expression?

Q: How do I simplify a mathematical expression?

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

Q: How do I evaluate an exponent?

Q: What is the order of operations (PEMDAS)?

Q: How do I simplify a fraction?

Q: What is the difference between a rational expression and an irrational expression?

Q: How do I simplify a rational expression?

Q: What is the difference between a linear expression and a quadratic expression?

Q: How do I simplify a linear expression?

Q: What is the difference between a polynomial expression and a non-polynomial expression?

Q: How do I simplify a polynomial expression?

Conclusion

Further Reading

Introduction

Understanding the Expression

Substituting the Values of xxx and yyy

Simplifying the Expression

Final Result

Conclusion

Frequently Asked Questions

Q: What is the value of the expression when x=3x = 3x=3 and y=2y = 2y=2?

Q: How do I simplify a mathematical expression?

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

Further Reading

Introduction

Q: What is a mathematical expression?

Q: How do I simplify a mathematical expression?

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

Q: How do I evaluate an exponent?

Q: What is the order of operations (PEMDAS)?

Q: How do I simplify a fraction?

Q: What is the difference between a rational expression and an irrational expression?

Q: How do I simplify a rational expression?

Q: What is the difference between a linear expression and a quadratic expression?

Q: How do I simplify a linear expression?

Q: What is the difference between a polynomial expression and a non-polynomial expression?

Q: How do I simplify a polynomial expression?

Conclusion

Further Reading

Substituting the Values of $x$ and $y$

Q: What is the value of the expression when $x = 3$ and $y = 2$ ?