What Is The Quotient Of The Fractions Below?${ \frac{1}{3} \div \frac{5}{8} }$A. { \frac{15}{8}$}$ B. { \frac{5}{24}$}$ C. { \frac{24}{5}$}$ D. { \frac{8}{15}$}$

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Understanding the Concept of Division of Fractions

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 a clear understanding of the steps involved, you'll be able to tackle even the most challenging division problems with ease.

The Formula for Dividing Fractions

To divide one fraction by another, you need to follow a simple formula:

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

In this formula, a and b are the numerator and denominator of the first fraction, while c and d are the numerator and denominator of the second fraction.

Applying the Formula to the Given Problem

Now that we have the formula, let's apply it to the given problem:

13÷58\frac{1}{3} \div \frac{5}{8}

Using the formula, we can rewrite the division as a multiplication:

13×85\frac{1}{3} \times \frac{8}{5}

Simplifying the Expression

To simplify the expression, we need to multiply the numerators and denominators separately:

Numerator: 1×8=81 \times 8 = 8 Denominator: 3×5=153 \times 5 = 15

So, the simplified expression is:

815\frac{8}{15}

Evaluating the Answer Choices

Now that we have the simplified expression, let's evaluate the answer choices:

A. 158\frac{15}{8} B. 524\frac{5}{24} C. 245\frac{24}{5} D. 815\frac{8}{15}

Based on our calculation, the correct answer is:

D. 815\frac{8}{15}

Conclusion

In conclusion, dividing fractions involves inverting the second fraction and then multiplying. By following the formula and simplifying the expression, we can arrive at the correct answer. Remember, practice makes perfect, so be sure to try out different division problems to reinforce your understanding of this concept.

Common Mistakes to Avoid

When dividing fractions, it's essential to avoid common mistakes such as:

  • Not inverting the second fraction: Make sure to invert the second fraction before multiplying.
  • Not multiplying the numerators and denominators separately: Multiply the numerators and denominators separately to simplify the expression.
  • Not simplifying the expression: Simplify the expression to arrive at the correct answer.

Real-World Applications

Dividing fractions has numerous real-world applications, such as:

  • Cooking: When measuring ingredients, you may need to divide fractions to get the correct amount.
  • Science: In scientific experiments, you may need to divide fractions to calculate the results.
  • Finance: In finance, you may need to divide fractions to calculate interest rates or investment returns.

Tips and Tricks

Here are some tips and tricks to help you master dividing fractions:

  • Practice, practice, practice: The more you practice, the more comfortable you'll become with dividing fractions.
  • Use visual aids: Visual aids such as diagrams or charts can help you understand the concept of dividing fractions.
  • Break down complex problems: Break down complex problems into simpler steps to make them more manageable.

Conclusion

In conclusion, dividing fractions is a fundamental concept in mathematics that requires a clear understanding of the formula and the steps involved. By following the formula, simplifying the expression, and avoiding common mistakes, you'll be able to tackle even the most challenging division problems with ease. Remember to practice regularly and use visual aids to reinforce your understanding of this concept.

Q: What is the formula for dividing fractions?

A: The formula for dividing fractions is: ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Q: How do I invert the second fraction?

A: To invert the second fraction, you need to swap the numerator and denominator. For example, if the second fraction is 58\frac{5}{8}, the inverted fraction would be 85\frac{8}{5}.

Q: What happens if the numerator and denominator of the first fraction are the same?

A: If the numerator and denominator of the first fraction are the same, the fraction is equal to 1. For example, 11=1\frac{1}{1} = 1.

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, 12÷3=12×13=16\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}.

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, 4÷12=4×2=84 \div \frac{1}{2} = 4 \times 2 = 8.

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

A: Dividing fractions involves inverting the second fraction and then multiplying, while multiplying fractions involves multiplying the numerators and denominators separately.

Q: Can I simplify a fraction after dividing?

A: Yes, you can simplify a fraction after dividing. To do this, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

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 12\frac{1}{2} is 21\frac{2}{1}.

Q: Can I divide a negative fraction by a positive fraction?

A: Yes, you can divide a negative fraction by a positive fraction. To do this, you need to follow the same steps as dividing positive fractions, but be aware that the result will be negative.

Q: Can I divide a positive fraction by a negative fraction?

A: Yes, you can divide a positive fraction by a negative fraction. To do this, you need to follow the same steps as dividing positive fractions, but be aware that the result will be negative.

Q: What is the result of dividing a fraction by zero?

A: Dividing a fraction by zero is undefined, as it results in an infinite value.

Q: Can I divide a fraction by a fraction with a zero denominator?

A: No, you cannot divide a fraction by a fraction with a zero denominator, as it results in an undefined value.

Q: Can I divide a fraction by a fraction with a zero numerator?

A: No, you cannot divide a fraction by a fraction with a zero numerator, as it results in an undefined value.

Conclusion

In conclusion, dividing fractions is a fundamental concept in mathematics that requires a clear understanding of the formula and the steps involved. By following the formula, simplifying the expression, and avoiding common mistakes, you'll be able to tackle even the most challenging division problems with ease. Remember to practice regularly and use visual aids to reinforce your understanding of this concept.