Solutions to Example Problems

Oct 13, 2025 by miodeya.com 138 views

Introduction

In mathematics, division of fractions is a fundamental operation that involves dividing one fraction by another. When we divide a fraction by another fraction, we are essentially multiplying the first fraction by the reciprocal of the second fraction. In this article, we will learn how to perform the operation and reduce the answer fully for the given problem: $\frac{3}{8} \div -\frac{6}{5}$ .

Understanding the Problem

The given problem involves dividing a fraction by another fraction. To solve this problem, we need to follow the rules of division of fractions. The rules state that when we divide a fraction by another fraction, we are essentially multiplying the first fraction by the reciprocal of the second fraction.

Reciprocal of a Fraction

The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$ . Similarly, the reciprocal of $-\frac{6}{5}$ is $-\frac{5}{6}$ .

Step 1: Multiply the First Fraction by the Reciprocal of the Second Fraction

To solve the problem, we need to multiply the first fraction by the reciprocal of the second fraction. The first fraction is $\frac{3}{8}$ and the reciprocal of the second fraction is $-\frac{5}{6}$ . Therefore, we need to multiply $\frac{3}{8}$ by $-\frac{5}{6}$ .

Multiplying Fractions

To multiply fractions, we need to multiply the numerators and the denominators separately. The product of the numerators is $3 \times (-5) = -15$ and the product of the denominators is $8 \times 6 = 48$ . Therefore, the product of the fractions is $\frac{-15}{48}$ .

Reducing the Answer

The answer $\frac{-15}{48}$ can be reduced by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of $-15$ and $48$ is $3$ . Therefore, we can divide both the numerator and the denominator by $3$ to get the reduced answer.

Reduced Answer

The reduced answer is $\frac{-5}{16}$ .

Conclusion

In this article, we learned how to perform the operation and reduce the answer fully for the given problem: $\frac{3}{8} \div -\frac{6}{5}$ . We followed the rules of division of fractions and multiplied the first fraction by the reciprocal of the second fraction. We then reduced the answer by dividing both the numerator and the denominator by their greatest common divisor. The reduced answer is $\frac{-5}{16}$ .

Example Problems

Here are some example problems that involve dividing fractions:

$\frac{2}{3} \div \frac{4}{5}$
$\frac{5}{6} \div -\frac{3}{4}$
$\frac{7}{8} \div \frac{2}{3}$

Solutions to Example Problems

Here are the solutions to the example problems:

$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$
$\frac{5}{6} \div -\frac{3}{4} = \frac{5}{6} \times -\frac{4}{3} = -\frac{20}{18} = -\frac{10}{9}$
$\frac{7}{8} \div \frac{2}{3} = \frac{7}{8} \times \frac{3}{2} = \frac{21}{16}$

Tips and Tricks

Here are some tips and tricks that can help you solve division of fractions problems:

Always follow the rules of division of fractions.
Multiply the first fraction by the reciprocal of the second fraction.
Reduce the answer by dividing both the numerator and the denominator by their greatest common divisor.
Practice, practice, practice! The more you practice, the better you will become at solving division of fractions problems.

Conclusion

$In conclusion, division of fractions is a fundamental operation in mathematics that involves dividing one fraction by another. To solve division of fractions problems, we need to follow the rules of division of fractions and multiply the first fraction by the reciprocal of the second fraction. We then reduce the answer by dividing both the numerator and the denominator by their greatest common divisor. With practice and patience, you can become proficient in solving division of fractions problems.<br/> **Frequently Asked Questions (FAQs) About Division of Fractions**$

Q: What is division of fractions?

A: Division of fractions is a fundamental operation in mathematics that involves dividing one fraction by another. It is a way of finding the quotient of two fractions.

Q: How do I divide fractions?

A: To divide fractions, you need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$ .

Q: How do I multiply fractions?

A: To multiply fractions, you need to multiply the numerators and the denominators separately. The product of the numerators is the numerator of the product, and the product of the denominators is the denominator of the product.

Q: How do I reduce a fraction?

A: To reduce a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers. One way is to list the factors of each number and find the largest factor that is common to both numbers.

Q: What are some common mistakes to avoid when dividing fractions?

A: Some common mistakes to avoid when dividing fractions include:

Not following the rules of division of fractions
Not multiplying the first fraction by the reciprocal of the second fraction
Not reducing the answer by dividing both the numerator and the denominator by their GCD
Not checking for common factors between the numerator and the denominator

Q: How can I practice dividing fractions?

A: There are several ways to practice dividing fractions, including:

Using online resources and practice problems
Working with a tutor or teacher
Practicing with real-world examples and applications
Creating your own practice problems and exercises

Q: What are some real-world applications of division of fractions?

A: Division of fractions has many real-world applications, including:

Cooking and recipe scaling
Building and construction
Finance and banking
Science and engineering

Q: How can I use division of fractions in my everyday life?

A: Division of fractions can be used in many everyday situations, including:

Measuring ingredients for a recipe
Calculating the cost of materials for a project
Determining the amount of time it will take to complete a task
Solving problems in science and engineering

Conclusion

In conclusion, division of fractions is a fundamental operation in mathematics that involves dividing one fraction by another. By following the rules of division of fractions and practicing with real-world examples and applications, you can become proficient in solving division of fractions problems.