1. The problem asks to find the fraction of the cake Wetsho left for himself after sharing with his three friends. 2. Wetsho gave Toto \(\frac{1}{6}\), Phatsimo \(\frac{2}{5}\), and Kegone \(\frac{1}{3}\) of the cake. 3. To find how much cake Wetsho left, we need to find the sum of the fractions given away and subtract that sum from 1 (whole cake). 4. Find the least common denominator (LCD) of the fractions \(\frac{1}{6}, \frac{2}{5}, \frac{1}{3}\). The denominators are 6, 5, and 3. 5. The LCD of 6, 5, and 3 is 30. 6. Convert each fraction to have denominator 30: \(\frac{1}{6} = \frac{5}{30}\) \(\frac{2}{5} = \frac{12}{30}\) \(\frac{1}{3} = \frac{10}{30}\) 7. Add the fractions given away: $$\frac{5}{30} + \frac{12}{30} + \frac{10}{30} = \frac{5+12+10}{30} = \frac{27}{30}$$ 8. Simplify \(\frac{27}{30}\) by dividing numerator and denominator by 3: $$\frac{27}{30} = \frac{9}{10}$$ 9. The fraction Wetsho left for himself is: $$1 - \frac{9}{10} = \frac{10}{10} - \frac{9}{10} = \frac{1}{10}$$ 10. Therefore, Wetsho left \(\frac{1}{10}\) of the cake for himself.