Select The Correct Answer.Mark Transferred Songs From His Computer Onto His Portable Music Player. He Transferred 2 6 7 2 \frac{6}{7} 2 7 6 ​ Songs In 1 2 3 1 \frac{2}{3} 1 3 2 ​ Minutes. How Many Songs Did He Transfer Per Minute?A. 7 12 \frac{7}{12} 12 7 ​

by ADMIN 258 views

Understanding the Problem

To find the number of songs transferred per minute, we need to calculate the transfer rate of songs. This involves dividing the total number of songs transferred by the total time taken to transfer them.

Breaking Down the Problem

We are given that Mark transferred 2672 \frac{6}{7} songs in 1231 \frac{2}{3} minutes. To make calculations easier, we can convert the mixed fractions into improper fractions.

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, we multiply the whole number part by the denominator and then add the numerator. The result becomes the new numerator, while the denominator remains the same.

  • 2672 \frac{6}{7} can be converted to an improper fraction as follows: 267=(2×7)+67=14+67=207{ 2 \frac{6}{7} = \frac{(2 \times 7) + 6}{7} = \frac{14 + 6}{7} = \frac{20}{7} }

  • 1231 \frac{2}{3} can be converted to an improper fraction as follows: 123=(1×3)+23=3+23=53{ 1 \frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3} }

Calculating the Transfer Rate

Now that we have the total number of songs transferred and the total time taken, we can calculate the transfer rate by dividing the total number of songs by the total time.

  • Transfer rate = Total number of songs / Total time
  • Transfer rate = 207\frac{20}{7} / 53\frac{5}{3}
  • Transfer rate = 207×35\frac{20}{7} \times \frac{3}{5}
  • Transfer rate = 20×37×5\frac{20 \times 3}{7 \times 5}
  • Transfer rate = 6035\frac{60}{35}
  • Transfer rate = 127\frac{12}{7}

Simplifying the Answer

The transfer rate is 127\frac{12}{7} songs per minute.

Conclusion

To find the number of songs transferred per minute, we need to calculate the transfer rate by dividing the total number of songs transferred by the total time taken. By converting the mixed fractions to improper fractions and then performing the division, we can find the transfer rate.

Answer

The correct answer is 127\frac{12}{7} songs per minute.

Comparison with Other Options

Let's compare our answer with the other options given:

  • A. 712\frac{7}{12}

Our answer, 127\frac{12}{7}, is not equal to 712\frac{7}{12}. Therefore, option A is incorrect.

Final Answer

The final answer is 127\boxed{\frac{12}{7}}.

Q: What is the transfer rate of songs per minute?

A: The transfer rate of songs per minute is the number of songs transferred in one minute. To calculate this, we need to divide the total number of songs transferred by the total time taken.

Q: How do I convert mixed fractions to improper fractions?

A: To convert a mixed fraction to an improper fraction, we multiply the whole number part by the denominator and then add the numerator. The result becomes the new numerator, while the denominator remains the same.

Q: What is the formula for calculating the transfer rate?

A: The formula for calculating the transfer rate is: Transfer rate = Total number of songs / Total time

Q: How do I simplify the answer after calculating the transfer rate?

A: To simplify the answer, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the correct answer for the given problem?

A: The correct answer is 127\frac{12}{7} songs per minute.

Q: Why is option A incorrect?

A: Option A is incorrect because it is equal to 712\frac{7}{12}, which is not the correct answer.

Q: What is the final answer for the given problem?

A: The final answer is 127\boxed{\frac{12}{7}}.

Q: Can I use a calculator to calculate the transfer rate?

A: Yes, you can use a calculator to calculate the transfer rate. However, it's always a good idea to understand the concept and formula behind the calculation.

Q: How do I apply this concept to real-life situations?

A: This concept can be applied to real-life situations where you need to calculate the rate of transfer of items, such as data transfer rates in computer networks or the rate of transfer of goods in a warehouse.

Q: What are some common mistakes to avoid when calculating the transfer rate?

A: Some common mistakes to avoid when calculating the transfer rate include:

  • Not converting mixed fractions to improper fractions
  • Not simplifying the answer after calculation
  • Not using the correct formula for calculating the transfer rate

Q: Can I use this concept to calculate the transfer rate of other items?

A: Yes, you can use this concept to calculate the transfer rate of other items, such as data transfer rates, goods transfer rates, or even the rate of transfer of people in a crowd.

Q: What are some real-life applications of this concept?

A: Some real-life applications of this concept include:

  • Calculating data transfer rates in computer networks
  • Calculating the rate of transfer of goods in a warehouse
  • Calculating the rate of transfer of people in a crowd
  • Calculating the rate of transfer of energy in a system

Q: How can I practice calculating the transfer rate?

A: You can practice calculating the transfer rate by using online calculators, worksheets, or by creating your own problems and solving them.