Find the remaining cake after keeping some for the party, then divide equally among the children.<br><br>
&bull; Kept \( \frac{2}{5} \) for office party → remaining = \( 1 - \frac{2}{5} = \frac{3}{5} \)<br>
&bull; Shared equally among 6 children: each child gets \( \frac{3}{5} \div 6 \)<br>
&bull; \( \frac{3}{5} \div 6 = \frac{3}{5} \times \frac{1}{6} = \frac{3}{30} \)<br>
&bull; Simplify: divide numerator and denominator by 3.<br>
&bull; \( \frac{3}{30} = \frac{3 \div 3}{30 \div 3} = \frac{1}{10} \)<br><br>
Final Answer: \( \frac{1}{10} \)