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

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Introduction

In this problem, we are given the number of songs transferred and the time taken to transfer them. We need to find the rate at which Mark transferred songs per minute. This problem involves converting mixed numbers to improper fractions and then performing division to find the rate.

Step 1: Convert Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and add the numerator. Then, we write the result as the new numerator over the denominator.

  • 2 \frac{6}{7}$ can be converted to an improper fraction as follows: * Multiply the whole number part (2) by the denominator (7): 2 × 7 = 14 * Add the numerator (6) to the result: 14 + 6 = 20 * Write the result as the new numerator over the denominator: $\frac{20}{7}

  • 1 \frac{2}{3}$ can be converted to an improper fraction as follows: * Multiply the whole number part (1) by the denominator (3): 1 × 3 = 3 * Add the numerator (2) to the result: 3 + 2 = 5 * Write the result as the new numerator over the denominator: $\frac{5}{3}

Step 2: Divide the Number of Songs by the Time Taken

Now that we have the number of songs transferred as an improper fraction ($\frac{20}{7}$) and the time taken as an improper fraction ($\frac{5}{3}$), we can divide the number of songs by the time taken to find the rate.

To divide fractions, we invert the second fraction (i.e., flip the numerator and denominator) and multiply:

207÷53=207×35\frac{20}{7} \div \frac{5}{3} = \frac{20}{7} \times \frac{3}{5}

Now, we multiply the numerators and denominators:

20×37×5=6035\frac{20 \times 3}{7 \times 5} = \frac{60}{35}

Step 3: Simplify the Result

To simplify the result, we can divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 60 and 35 is 5.

6035=60÷535÷5=127\frac{60}{35} = \frac{60 ÷ 5}{35 ÷ 5} = \frac{12}{7}

Conclusion

Mark transferred $\frac{12}{7}$ songs per minute. To convert this improper fraction to a mixed number, we can divide the numerator (12) by the denominator (7):

127=157\frac{12}{7} = 1 \frac{5}{7}

Therefore, Mark transferred $1 \frac{5}{7}$ songs per minute.

Answer

Q: What is the formula to find the rate of song transfer?

A: The formula to find the rate of song transfer is:

Rate = Number of songs ÷ Time taken

In this problem, we converted the mixed numbers to improper fractions and then performed division to find the rate.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, follow these steps:

  1. Multiply the whole number part by the denominator.
  2. Add the numerator to the result.
  3. Write the result as the new numerator over the denominator.

For example, to convert $2 \frac{6}{7}$ to an improper fraction:

  1. Multiply the whole number part (2) by the denominator (7): 2 × 7 = 14
  2. Add the numerator (6) to the result: 14 + 6 = 20
  3. Write the result as the new numerator over the denominator: $\frac{20}{7}$

Q: How do I divide fractions?

A: To divide fractions, follow these steps:

  1. Invert the second fraction (i.e., flip the numerator and denominator).
  2. Multiply the fractions.

For example, to divide $\frac{20}{7}$ by $\frac{5}{3}$:

  1. Invert the second fraction: $\frac{5}{3}$ becomes $\frac{3}{5}$
  2. Multiply the fractions: $\frac{20}{7} \times \frac{3}{5}$

Q: How do I simplify a fraction?

A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD.

For example, to simplify $\frac{60}{35}$:

  1. Find the GCD of 60 and 35: 5
  2. Divide both the numerator and denominator by the GCD: $\frac{60 ÷ 5}{35 ÷ 5} = \frac{12}{7}$

Q: What is the rate of song transfer in this problem?

A: The rate of song transfer is $\frac{12}{7}$ songs per minute, which can be converted to a mixed number as $1 \frac{5}{7}$ songs per minute.

Q: How do I apply this problem to real-life scenarios?

A: This problem can be applied to real-life scenarios where you need to find the rate of transfer of items, such as:

  • Transferring files from a computer to a portable storage device
  • Transferring data from one database to another
  • Transferring items from one location to another

In each of these scenarios, you can use the same formula and steps to find the rate of transfer.

Conclusion

In this article, we covered a problem where Mark transferred songs from his computer to a portable music player. We converted mixed numbers to improper fractions, performed division to find the rate, and simplified the result. We also answered frequently asked questions related to the problem and provided examples of how to apply the problem to real-life scenarios.