Divide And Write Your Answer As A Fraction Or Mixed Number In Simplest Form.$\frac{4}{3} \div \left(-\frac{8}{9}\right$\]

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When it comes to dividing fractions, it's essential to understand the concept of inverting the second fraction and then multiplying. This process may seem complex, but with practice, you'll become proficient in dividing fractions in no time.

What is Dividing Fractions?

Dividing fractions involves taking one fraction and dividing it by another fraction. This operation is also known as a division of fractions. To divide fractions, we need to follow a specific set of rules that will be discussed in this article.

The Rule for Dividing Fractions

The rule for dividing fractions is as follows:

  • Invert the second fraction (i.e., flip the numerator and denominator).
  • Multiply the first fraction by the inverted second fraction.

Example: Dividing Fractions

Let's take the example of dividing 43\frac{4}{3} by −89-\frac{8}{9}. To do this, we need to follow the rule for dividing fractions.

Step 1: Invert the Second Fraction

The second fraction is −89-\frac{8}{9}. To invert this fraction, we need to flip the numerator and denominator. The inverted fraction is 9−8\frac{9}{-8}.

Step 2: Multiply the First Fraction by the Inverted Second Fraction

Now that we have the inverted second fraction, we can multiply the first fraction by the inverted second fraction. The first fraction is 43\frac{4}{3}, and the inverted second fraction is 9−8\frac{9}{-8}. To multiply these fractions, we need to multiply the numerators and denominators separately.

43×9−8=4×93×−8\frac{4}{3} \times \frac{9}{-8} = \frac{4 \times 9}{3 \times -8}

Step 3: Simplify the Result

Now that we have the product of the two fractions, we need to simplify the result. To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.

The GCD of 36 and -24 is 12. We can divide both the numerator and denominator by 12 to simplify the fraction.

36−24=36÷12−24÷12=3−2\frac{36}{-24} = \frac{36 \div 12}{-24 \div 12} = \frac{3}{-2}

Step 4: Write the Result as a Mixed Number

Now that we have the simplified fraction, we can write the result as a mixed number. To write the fraction as a mixed number, we need to divide the numerator by the denominator.

−2÷3=−0.67-2 \div 3 = -0.67

The mixed number is −113-1\frac{1}{3}.

Conclusion

Dividing fractions may seem complex, but with practice, you'll become proficient in dividing fractions in no time. Remember to invert the second fraction and then multiply the first fraction by the inverted second fraction. Simplify the result by finding the greatest common divisor of the numerator and denominator, and write the result as a mixed number.

Common Mistakes to Avoid

When dividing fractions, it's essential to avoid common mistakes. Here are a few common mistakes to avoid:

  • Not inverting the second fraction: Make sure to invert the second fraction before multiplying the first fraction by the inverted second fraction.
  • Not simplifying the result: Make sure to simplify the result by finding the greatest common divisor of the numerator and denominator.
  • Not writing the result as a mixed number: Make sure to write the result as a mixed number by dividing the numerator by the denominator.

Practice Problems

Here are a few practice problems to help you become proficient in dividing fractions:

  • 23÷(−68)\frac{2}{3} \div \left(-\frac{6}{8}\right)
  • 56÷(34)\frac{5}{6} \div \left(\frac{3}{4}\right)
  • 78÷(−910)\frac{7}{8} \div \left(-\frac{9}{10}\right)

Answer Key

Here are the answers to the practice problems:

  • 23÷(−68)=−43\frac{2}{3} \div \left(-\frac{6}{8}\right) = -\frac{4}{3}
  • 56÷(34)=56×43=2018=109\frac{5}{6} \div \left(\frac{3}{4}\right) = \frac{5}{6} \times \frac{4}{3} = \frac{20}{18} = \frac{10}{9}
  • 78÷(−910)=−78×109=−7072=−3536\frac{7}{8} \div \left(-\frac{9}{10}\right) = -\frac{7}{8} \times \frac{10}{9} = -\frac{70}{72} = -\frac{35}{36}
    Dividing Fractions: A Q&A Guide =====================================

In the previous article, we discussed the concept of dividing fractions and provided a step-by-step guide on how to divide fractions. In this article, we will answer some frequently asked questions about dividing fractions.

Q: What is the rule for dividing fractions?

A: The rule for dividing fractions is to invert the second fraction (i.e., flip the numerator and denominator) and then multiply the first fraction by the inverted second fraction.

Q: Why do we need to invert the second fraction?

A: We need to invert the second fraction because dividing by a fraction is the same as multiplying by its reciprocal. By inverting the second fraction, we are essentially multiplying by its reciprocal.

Q: How do I simplify the result of a division of fractions?

A: To simplify the result of a division of fractions, you need to find the greatest common divisor (GCD) of the numerator and denominator. Once you have found the GCD, you can divide both the numerator and denominator by the GCD to simplify the fraction.

Q: Can I divide a fraction by a whole number?

A: Yes, you can divide a fraction by a whole number. To do this, you need to multiply the fraction by the reciprocal of the whole number. For example, to divide 12\frac{1}{2} by 3, you need to multiply 12\frac{1}{2} by 13\frac{1}{3}.

Q: Can I divide a whole number by a fraction?

A: Yes, you can divide a whole number by a fraction. To do this, you need to multiply the whole number by the reciprocal of the fraction. For example, to divide 4 by 12\frac{1}{2}, you need to multiply 4 by 2.

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

A: The main difference between dividing fractions and multiplying fractions is the order in which you perform the operations. When dividing fractions, you need to invert the second fraction and then multiply the first fraction by the inverted second fraction. When multiplying fractions, you simply multiply the numerators and denominators separately.

Q: Can I use a calculator to divide fractions?

A: Yes, you can use a calculator to divide fractions. However, it's essential to understand the concept of dividing fractions and how to perform the operation manually. Using a calculator can help you check your work and ensure that you are getting the correct answer.

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

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

  • Not inverting the second fraction
  • Not simplifying the result
  • Not writing the result as a mixed number
  • Not using the correct order of operations

Q: How can I practice dividing fractions?

A: You can practice dividing fractions by working through a series of problems. Start with simple problems and gradually move on to more complex ones. You can also use online resources or math apps to practice dividing fractions.

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

A: Dividing fractions has many real-world applications, including:

  • Cooking: When you are cooking, you may need to divide a recipe by a fraction to get the correct amount of ingredients.
  • Science: In science, you may need to divide a measurement by a fraction to get the correct value.
  • Finance: In finance, you may need to divide a investment by a fraction to get the correct return on investment.

Conclusion

Dividing fractions may seem complex, but with practice, you'll become proficient in dividing fractions in no time. Remember to invert the second fraction and then multiply the first fraction by the inverted second fraction. Simplify the result by finding the greatest common divisor of the numerator and denominator, and write the result as a mixed number. With this guide, you'll be able to divide fractions with confidence and accuracy.