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 [tex]$\frac{6}{7}$[/tex] of the book. What fraction of the book did he read each night?

A. [tex]$\frac{1}{56}$[/tex] of the book
B. [tex][tex]$\frac{3}{28}$[/tex][/tex] of the book
C. [tex]$\frac{7}{48}$[/tex] of the book
D. [tex]$\frac{1}{8}$[/tex] of the book



Answer :

To determine what fraction of the book James read each night, we start with the information given:

- James read a total of [tex]\(\frac{6}{7}\)[/tex] of the book over 8 nights.

We need to find the fraction of the book he read each night. To do this, we divide the total fraction of the book he read by the number of nights he spent reading:

[tex]\[ \text{Fraction read per night} = \frac{\frac{6}{7}}{8} \][/tex]

Dividing a fraction by a whole number involves multiplying the fraction by the reciprocal of the whole number. So:

[tex]\[ \frac{\frac{6}{7}}{8} = \frac{6}{7} \times \frac{1}{8} \][/tex]

Multiplying these fractions together:

[tex]\[ \frac{6 \times 1}{7 \times 8} = \frac{6}{56} \][/tex]

Next, we simplify [tex]\(\frac{6}{56}\)[/tex] by finding the greatest common divisor (GCD) of 6 and 56. The GCD is 2, so we divide both the numerator and the denominator by 2:

[tex]\[ \frac{6 \div 2}{56 \div 2} = \frac{3}{28} \][/tex]

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

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

From the given options, the correct answer is:

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