Sure, let's go through this step-by-step to find out how much of the cake each of the 5 members gets.
1. Shyam's Share:
Shyam ate [tex]\(\frac{1}{7}\)[/tex] part of the cake.
2. Remaining Cake:
Since Shyam ate [tex]\(\frac{1}{7}\)[/tex] of the cake, the remaining part of the cake is:
[tex]\[
1 - \frac{1}{7} = \frac{7}{7} - \frac{1}{7} = \frac{6}{7}
\][/tex]
3. Distribution to Members:
Now Shyam distributes the remaining [tex]\(\frac{6}{7}\)[/tex] of the cake equally among 5 members. To find out how much each member gets, we divide the remaining cake by 5:
[tex]\[
\frac{6}{7} \div 5 = \frac{6}{7} \times \frac{1}{5} = \frac{6}{7 \times 5} = \frac{6}{35}
\][/tex]
So, each of the 5 members gets [tex]\(\frac{6}{35}\)[/tex] part of the cake.
To summarize:
- Shyam ate [tex]\(\frac{1}{7}\)[/tex] part of the cake.
- The remaining part of the cake is [tex]\(\frac{6}{7}\)[/tex].
- Each of the 5 members gets [tex]\(\frac{6}{35}\)[/tex] part of the cake.
