Calculate The Quotient. Enter The Answer As A Fraction In Lowest Terms, Using The Slash (/) As The Fraction Bar.$\frac{3}{5} \div \frac{9}{10}$Answer Here: ________

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Understanding the Concept of Dividing Fractions

When it comes to dividing fractions, many students struggle to understand the concept and apply it correctly. However, with a clear understanding of the rules and a step-by-step approach, dividing fractions can be a straightforward process. In this article, we will explore the concept of inverting and multiplying to calculate quotients of fractions, and provide a step-by-step guide on how to apply this rule.

The Rule of Inverting and Multiplying

To divide two fractions, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply the two fractions together. This rule is often represented as:

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Where ab\frac{a}{b} and cd\frac{c}{d} are the two fractions being divided.

Applying the Rule to the Given Problem

Now that we have a clear understanding of the rule, let's apply it to the given problem:

35÷910\frac{3}{5} \div \frac{9}{10}

To solve this problem, we need to invert the second fraction and then multiply the two fractions together.

Inverting the Second Fraction

The second fraction is 910\frac{9}{10}. To invert this fraction, we need to flip the numerator and denominator, resulting in:

109\frac{10}{9}

Multiplying the Fractions

Now that we have the inverted second fraction, we can multiply the two fractions together:

35×109\frac{3}{5} \times \frac{10}{9}

To multiply fractions, we need to multiply the numerators together and the denominators together, resulting in:

3×105×9\frac{3 \times 10}{5 \times 9}

Simplifying the Result

Now that we have the product of the two fractions, we need to simplify the result by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 30 and 45 is 15.

3×105×9=3045\frac{3 \times 10}{5 \times 9} = \frac{30}{45}

Dividing both the numerator and denominator by 15, we get:

30÷1545÷15=23\frac{30 \div 15}{45 \div 15} = \frac{2}{3}

Conclusion

In conclusion, dividing fractions can be a straightforward process if we apply the rule of inverting and multiplying. By inverting the second fraction and then multiplying the two fractions together, we can calculate the quotient of two fractions. In this article, we applied this rule to the given problem and arrived at the solution of 23\frac{2}{3}.

Common Mistakes to Avoid

When dividing fractions, there are several common mistakes to avoid. These include:

  • Not inverting the second fraction: Failing to invert the second fraction can result in an incorrect solution.
  • Not multiplying the fractions: Failing to multiply the fractions can result in an incorrect solution.
  • Not simplifying the result: Failing to simplify the result can result in an incorrect solution.

Real-World Applications

Dividing fractions has several real-world applications, including:

  • Cooking: When cooking, we often need to divide ingredients in fractions. For example, if a recipe calls for 3/4 cup of flour and we need to divide it into 4 equal parts, we would need to divide 3/4 by 4.
  • Science: In science, we often need to divide measurements in fractions. For example, if we need to measure the volume of a liquid in milliliters and the measurement is given in fractions, we would need to divide the measurement by the fraction.
  • Finance: In finance, we often need to divide money in fractions. For example, if we need to divide a sum of money into 4 equal parts and the sum is given in fractions, we would need to divide the sum by the fraction.

Practice Problems

To practice dividing fractions, try the following problems:

  • 23÷45\frac{2}{3} \div \frac{4}{5}
  • 34÷23\frac{3}{4} \div \frac{2}{3}
  • 12÷34\frac{1}{2} \div \frac{3}{4}

Conclusion

In conclusion, dividing fractions can be a straightforward process if we apply the rule of inverting and multiplying. By inverting the second fraction and then multiplying the two fractions together, we can calculate the quotient of two fractions. In this article, we applied this rule to the given problem and arrived at the solution of 23\frac{2}{3}. We also discussed common mistakes to avoid and real-world applications of dividing fractions. Finally, we provided practice problems for readers to try.

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 two fractions together.

Q: How do I invert a fraction?

A: To invert a fraction, you need to flip the numerator and denominator. For example, if you have the fraction 34\frac{3}{4}, the inverted fraction would be 43\frac{4}{3}.

Q: How do I multiply fractions?

A: To multiply fractions, you need to multiply the numerators together and the denominators together. For example, if you have the fractions 23\frac{2}{3} and 34\frac{3}{4}, the product would be 2×33×4=612\frac{2 \times 3}{3 \times 4} = \frac{6}{12}.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and denominator by their greatest common divisor (GCD). For example, if you have the fraction 612\frac{6}{12}, the GCD of 6 and 12 is 6. Dividing both the numerator and denominator by 6, you get 6÷612÷6=12\frac{6 \div 6}{12 \div 6} = \frac{1}{2}.

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

A: Dividing fractions is the opposite of multiplying fractions. When you divide fractions, you invert the second fraction and then multiply the two fractions together. When you multiply fractions, you multiply the numerators together and the denominators together.

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 invert the fraction and then multiply the fraction by the whole number. For example, if you have the fraction 12\frac{1}{2} and you want to divide it by 3, you would invert the fraction to get 21\frac{2}{1} and then multiply it by 3 to get 2×31×3=63\frac{2 \times 3}{1 \times 3} = \frac{6}{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 invert the fraction and then multiply the whole number by the inverted fraction. For example, if you have the whole number 6 and you want to divide it by the fraction 12\frac{1}{2}, you would invert the fraction to get 21\frac{2}{1} and then multiply it by 6 to get 6×21=126 \times \frac{2}{1} = 12.

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

A: Dividing fractions has several real-world applications, including cooking, science, and finance. For example, in cooking, you may need to divide ingredients in fractions. In science, you may need to divide measurements in fractions. In finance, you may need to divide money in fractions.

Q: How do I practice dividing fractions?

A: You can practice dividing fractions by trying the following problems:

  • 23÷45\frac{2}{3} \div \frac{4}{5}
  • 34÷23\frac{3}{4} \div \frac{2}{3}
  • 12÷34\frac{1}{2} \div \frac{3}{4}

You can also try dividing fractions with different numerators and denominators to get a feel for the process.

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 multiplying the fractions
  • Not simplifying the result
  • Not using the correct order of operations

By avoiding these mistakes, you can ensure that you get the correct answer when dividing fractions.