Evaluate The Expression:$ -17 \div \left(-\frac{1}{3}\right) = $

Mar 12, 2025 by ADMIN 65 views

$Evaluate the Expression: $-17 \div \left(-\frac{1}{3}\right) = $$

Introduction

When it comes to evaluating mathematical expressions, it's essential to understand the rules and operations involved. In this article, we will focus on evaluating the expression $-17 \div \left(-\frac{1}{3}\right)$ . This expression involves division, which can be a bit tricky, especially when dealing with negative numbers and fractions. We will break down the steps involved in evaluating this expression and provide a clear explanation of the process.

Understanding the Division Operation

Before we dive into evaluating the expression, let's take a closer look at the division operation. Division is the inverse operation of multiplication, which means that it involves finding the quotient of two numbers. In the case of the expression $-17 \div \left(-\frac{1}{3}\right)$ , we are dividing a negative number by a negative fraction.

Evaluating the Expression

To evaluate the expression $-17 \div \left(-\frac{1}{3}\right)$ , we need to follow the order of operations (PEMDAS):

Parentheses: Evaluate the expression inside the parentheses first. In this case, we have a fraction $-\frac{1}{3}$ .
Exponents: There are no exponents in this expression.
Multiplication and Division: Evaluate the division operation next. When dividing two numbers, we can multiply the first number by the reciprocal of the second number.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations.

Step 1: Evaluate the Fraction

The expression inside the parentheses is $-\frac{1}{3}$ . This is a fraction with a negative sign. To evaluate this fraction, we can simply write it as $-\frac{1}{3}$ .

Step 2: Multiply the First Number by the Reciprocal of the Second Number

Now that we have evaluated the fraction, we can multiply the first number $-17$ by the reciprocal of the second number $-\frac{1}{3}$ . The reciprocal of $-\frac{1}{3}$ is $-3$ . So, we can multiply $-17$ by $-3$ .

Step 3: Evaluate the Multiplication Operation

To evaluate the multiplication operation, we can multiply the two numbers together. $-17 \times -3 = 51$ .

Step 4: Write the Final Answer

Now that we have evaluated the expression, we can write the final answer. The expression $-17 \div \left(-\frac{1}{3}\right)$ is equal to $51$ .

Conclusion

Evaluating the expression $-17 \div \left(-\frac{1}{3}\right)$ involves following the order of operations and understanding the division operation. By breaking down the steps involved in evaluating this expression, we can see that the final answer is $51$ . This expression is a great example of how division can be used to solve real-world problems.

Frequently Asked Questions

Q: What is the order of operations? A: The order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I evaluate a division operation? A: To evaluate a division operation, you can multiply the first number by the reciprocal of the second number.
Q: What is the reciprocal of a fraction? A: The reciprocal of a fraction is obtained by swapping the numerator and denominator.

Additional Resources

Khan Academy: Division
Mathway: Division
Wolfram Alpha: Division

Final Answer

The final answer to the expression $-17 \div \left(-\frac{1}{3}\right)$ is $\boxed{51}$ .

Introduction

In our previous article, we discussed how to evaluate the expression $-17 \div \left(-\frac{1}{3}\right)$ . We broke down the steps involved in evaluating this expression and provided a clear explanation of the process. In this article, we will answer some frequently asked questions related to evaluating expressions with division.

Q&A

Q: What is the order of operations?

A: The order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This order of operations helps us to evaluate mathematical expressions in the correct order.

Q: How do I evaluate a division operation?

A: To evaluate a division operation, you can multiply the first number by the reciprocal of the second number. For example, to evaluate the expression $-17 \div \left(-\frac{1}{3}\right)$ , you can multiply $-17$ by the reciprocal of $-\frac{1}{3}$ , which is $-3$ .

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and denominator. For example, the reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$ , and the reciprocal of $-\frac{1}{3}$ is $-\frac{3}{1}$ .

Q: How do I handle negative numbers in division?

A: When dividing two negative numbers, the result is positive. When dividing a negative number by a positive number, the result is negative. When dividing a positive number by a negative number, the result is negative.

Q: Can I use a calculator to evaluate expressions with division?

A: Yes, you can use a calculator to evaluate expressions with division. However, it's always a good idea to understand the underlying math and to check your work to ensure that you get the correct answer.

Q: What if I have a fraction with a negative exponent?

A: If you have a fraction with a negative exponent, you can rewrite the fraction with a positive exponent by taking the reciprocal of the fraction. For example, $\left(-\frac{1}{3}\right)^{-2}$ can be rewritten as $\left(\frac{3}{-1}\right)^2$ .

Q: Can I use a calculator to evaluate expressions with negative exponents?

A: Yes, you can use a calculator to evaluate expressions with negative exponents. However, it's always a good idea to understand the underlying math and to check your work to ensure that you get the correct answer.