Simplify The Expression: -\frac{3}{5} \div \left(-\frac{1}{6}\right ]

Introduction

When it comes to simplifying expressions involving fractions, it's essential to understand the rules and procedures for dividing fractions. In this article, we'll delve into the world of fraction division and provide a step-by-step guide on how to simplify the expression: $-\frac{3}{5} \div \left(-\frac{1}{6}\right)$. By the end of this article, you'll be equipped with the knowledge and skills to tackle similar problems with confidence.

Understanding Fraction Division

Before we dive into the solution, let's take a moment to understand the concept of fraction division. When we divide one fraction by another, we're essentially asking how many times the second fraction fits into the first fraction. In other words, we're looking for the quotient of the two fractions.

The Rule for Dividing Fractions

The rule for dividing fractions is straightforward: to divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction. In mathematical terms, this can be represented as:

$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$

Applying the Rule to the Given Expression

Now that we've covered the basics of fraction division, let's apply the rule to the given expression: $-\frac{3}{5} \div \left(-\frac{1}{6}\right)$. To simplify this expression, we'll multiply the first fraction by the reciprocal of the second fraction.

$$-\frac{3}{5} \div \left(-\frac{1}{6}\right) = -\frac{3}{5} \times \left(-\frac{6}{1}\right)$$

Simplifying the Expression

Now that we've applied the rule, let's simplify the expression by multiplying the numerators and denominators.

$$-\frac{3}{5} \times \left(-\frac{6}{1}\right) = \frac{3 \times (-6)}{5 \times 1}$$

Evaluating the Numerator and Denominator

Let's evaluate the numerator and denominator separately.

$$3 \times (-6) = -18$$

$$5 \times 1 = 5$$

Combining the Results

Now that we've evaluated the numerator and denominator, let's combine the results to simplify the expression.

$$\frac{-18}{5} = -\frac{18}{5}$$

Conclusion

In this article, we've explored the concept of fraction division and provided a step-by-step guide on how to simplify the expression: $-\frac{3}{5} \div \left(-\frac{1}{6}\right)$. By applying the rule for dividing fractions and simplifying the expression, we arrived at the final answer: $-\frac{18}{5}$. With this knowledge and skill, you'll be well-equipped to tackle similar problems and simplify expressions involving fractions with confidence.

Common Mistakes to Avoid

When simplifying expressions involving fractions, it's essential to avoid common mistakes. Here are a few to watch out for:

• Not applying the rule for dividing fractions: Make sure to multiply the first fraction by the reciprocal of the second fraction.
• Not simplifying the expression: Take the time to simplify the expression by multiplying the numerators and denominators.
• Not evaluating the numerator and denominator separately: Make sure to evaluate the numerator and denominator separately before combining the results.

Practice Problems

To reinforce your understanding of fraction division, try the following practice problems:

• Simplify the expression: $\frac{2}{3} \div \left(\frac{4}{5}\right)$
• Simplify the expression: $-\frac{1}{2} \div \left(-\frac{3}{4}\right)$
• Simplify the expression: $\frac{5}{6} \div \left(\frac{2}{3}\right)$

Conclusion

Introduction

In our previous article, we explored the concept of fraction division and provided a step-by-step guide on how to simplify the expression: $-\frac{3}{5} \div \left(-\frac{1}{6}\right)$. In this article, we'll address some of the most frequently asked questions related to simplifying expressions involving fractions.

Q&A

Q: What is the rule for dividing fractions?

A: The rule for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction. In mathematical terms, this can be represented as:

$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$

Q: How do I simplify an expression involving fractions?

A: To simplify an expression involving fractions, you need to multiply the numerators and denominators, and then simplify the resulting fraction. For example, to simplify the expression $\frac{2}{3} \div \left(\frac{4}{5}\right)$, you would multiply the numerators and denominators as follows:

$$\frac{2}{3} \div \left(\frac{4}{5}\right) = \frac{2}{3} \times \left(\frac{5}{4}\right) = \frac{2 \times 5}{3 \times 4} = \frac{10}{12}$$

Q: What is the difference between dividing fractions and multiplying fractions?

A: Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction, while multiplying fractions involves multiplying the numerators and denominators directly. For example, to multiply the fractions $\frac{2}{3}$ and $\frac{4}{5}$, you would multiply the numerators and denominators as follows:

$$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$$

Q: Can I simplify an expression involving fractions by canceling out common factors?

A: Yes, you can simplify an expression involving fractions by canceling out common factors. For example, to simplify the expression $\frac{6}{8}$, you can cancel out the common factor of 2 as follows:

$$\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}$$

Q: How do I handle negative fractions when simplifying expressions?

A: When simplifying expressions involving negative fractions, you need to remember that a negative sign in the numerator or denominator can change the sign of the resulting fraction. For example, to simplify the expression $-\frac{3}{5} \div \left(-\frac{1}{6}\right)$, you would multiply the numerators and denominators as follows:

$$-\frac{3}{5} \div \left(-\frac{1}{6}\right) = -\frac{3}{5} \times \left(-\frac{6}{1}\right) = \frac{3 \times 6}{5 \times 1} = \frac{18}{5}$$

Q: Can I use a calculator to simplify expressions involving fractions?

A: Yes, you can use a calculator to simplify expressions involving fractions. However, it's essential to understand the underlying math and be able to simplify expressions manually. Using a calculator can help you verify your answers and check for errors.

Conclusion

In this article, we've addressed some of the most frequently asked questions related to simplifying expressions involving fractions. By understanding the rules and procedures for dividing fractions, you can simplify expressions with confidence. Remember to practice regularly and use a calculator to verify your answers. With this knowledge and skill, you'll be well-equipped to tackle similar problems and simplify expressions involving fractions with ease.