Question

nikolai has \\(\frac{3}{4}\\) of a sugar pie. he saves \\(\frac{1}{3}\\) of the remaining pie for later and cuts the rest into eight equal pieces. what fraction of the whole pie is each piece?

Explanation:

Step1: Find pie left after saving

First, calculate the fraction of the pie that is not saved. If he saves $\frac{1}{3}$, the remaining fraction to cut is $1 - \frac{1}{3} = \frac{2}{3}$. Multiply this by the amount of pie Nikolai has:
$\frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}$

Step2: Divide into 8 equal pieces

Divide the remaining pie $\frac{1}{2}$ by 8 to find the fraction of the whole pie each piece is:
$\frac{1}{2} \div 8 = \frac{1}{2} \times \frac{1}{8} = \frac{1}{16}$

Answer:

$\frac{1}{16}$