Question

James read an equal number of pages of his book each night for 8 nights to prepare for his upcoming exam. During this time, he has read a total of StartFraction 6 Over 7 EndFraction of the book. What fraction of the book did he read each night?
StartFraction 1 Over 56 EndFraction of the book
StartFraction 3 Over 28 EndFraction of the book
StartFraction 7 Over 48 EndFraction of the book
One-eighth of the book

Answer 1

To find the fraction of the book James read each night, we start by dividing the total fraction of the book he read, which is \( \frac{6}{7} \), by the number of nights he read, which is 8.

The amount he read each night can be calculated as:

\[
\text{Fraction read each night} = \frac{\frac{6}{7}}{8}
\]

We can express 8 as a fraction:

\[
\text{Fraction read each night} = \frac{6}{7} \div 8 = \frac{6}{7} \times \frac{1}{8}
\]

Now we multiply the fractions:

\[
\text{Fraction read each night} = \frac{6 \times 1}{7 \times 8} = \frac{6}{56}
\]

Next, we simplify \( \frac{6}{56} \):

\[
\frac{6}{56} = \frac{3}{28}
\]

Thus, the fraction of the book that James read each night is:

\[
\frac{3}{28}
\]

Therefore, the answer is:

\[
\boxed{\frac{3}{28}}
\]