To determine how many songs Mark transferred per minute, we need to calculate the rate of transfer in terms of songs per minute.
1. First, we express the mixed numbers as improper fractions.
- Mark transferred [tex]\(2 \frac{6}{7}\)[/tex] songs. This can be converted to an improper fraction:
[tex]\[
2 \frac{6}{7} = \frac{2 \times 7 + 6}{7} = \frac{14 + 6}{7} = \frac{20}{7}
\][/tex]
- The time taken was [tex]\(1 \frac{2}{3}\)[/tex] minutes. This can be converted to an improper fraction:
[tex]\[
1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}
\][/tex]
2. Next, we need to divide the number of songs by the time to find the rate of transfer (songs per minute):
[tex]\[
\text{songs per minute} = \frac{\frac{20}{7}}{\frac{5}{3}}
\][/tex]
3. Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
\text{songs per minute} = \frac{20}{7} \times \frac{3}{5}
\][/tex]
4. Multiply the numerators together and the denominators together:
[tex]\[
\text{songs per minute} = \frac{20 \times 3}{7 \times 5} = \frac{60}{35}
\][/tex]
5. Simplify the fraction [tex]\(\frac{60}{35}\)[/tex]:
- The greatest common divisor (GCD) of 60 and 35 is 5. Divide both the numerator and denominator by 5:
[tex]\[
\frac{60}{35} = \frac{60 \div 5}{35 \div 5} = \frac{12}{7}
\][/tex]
6. Convert the improper fraction back to a mixed number for better understanding:
- [tex]\( \frac{12}{7} \)[/tex] as a mixed number:
[tex]\[
\frac{12}{7} = 1 \frac{5}{7}
\][/tex]
Therefore, Mark transferred [tex]\(1 \frac{5}{7}\)[/tex] songs per minute.
The correct answer is:
B. [tex]\(1 \frac{5}{7}\)[/tex] songs per minute
