To determine how many pages Charlie reads per minute, we need to calculate his reading rate in pages per minute.
1. Converting the mixed number to an improper fraction:
Charlie reads [tex]\(1 \frac{3}{7}\)[/tex] pages. To convert this mixed number to an improper fraction:
[tex]\[
1 \frac{3}{7} = 1 + \frac{3}{7}
\][/tex]
First, convert the integer part to a fraction with the same denominator:
[tex]\[
1 = \frac{7}{7}
\][/tex]
Now, add the fractions:
[tex]\[
1 \frac{3}{7} = \frac{7}{7} + \frac{3}{7} = \frac{7 + 3}{7} = \frac{10}{7}
\][/tex]
So, Charlie reads [tex]\(\frac{10}{7}\)[/tex] pages.
2. Finding the rate in pages per minute:
Time taken is [tex]\(\frac{2}{3}\)[/tex] minutes. We need to find how many pages Charlie reads per minute by dividing the number of pages by the time taken.
[tex]\[
\text{Rate} = \frac{\text{Pages read}}{\text{Time in minutes}} = \frac{\frac{10}{7}}{\frac{2}{3}}
\][/tex]
To divide by a fraction, we multiply by its reciprocal:
[tex]\[
\frac{\frac{10}{7}}{\frac{2}{3}} = \frac{10}{7} \times \frac{3}{2}
\][/tex]
Multiply the numerators and denominators:
[tex]\[
\frac{10 \times 3}{7 \times 2} = \frac{30}{14}
\][/tex]
Simplify the fraction:
[tex]\[
\frac{30}{14} = \frac{15}{7}
\][/tex]
3. Simplifying the improper fraction:
Convert the improper fraction [tex]\(\frac{15}{7}\)[/tex] to a decimal by performing the division:
[tex]\[
\frac{15}{7} \approx 2.142857142857143
\][/tex]
Therefore, Charlie reads approximately [tex]\(2.142857142857143\)[/tex] pages per minute.
