Step 1: Determine the fraction of pineapple Mwesigwa ate. Mwesigwa ate one fifth of a pineapple. $$\text{Mwesigwa's share} = \frac{1}{5}$$ Step 2: Calculate the fraction of pineapple remaining after Mwesigwa ate his share. The whole pineapple is represented by $1$. $$\text{Remaining pineapple} = 1 - \frac{1}{5} = \frac{5}{5} - \frac{1}{5} = \frac{4}{5}$$ Step 3: Calculate the fraction of the remaining pineapple that his sister ate. His sister ate three quarters of what was left. $$\text{Sister's share (of remaining)} = \frac{3}{4} \times \text{Remaining pineapple}$$ $$\text{Sister's share (of remaining)} = \frac{3}{4} \times \frac{4}{5}$$ Step 4: Calculate the actual fraction of the whole pineapple that his sister ate. $$\text{Sister's share (of whole)} = \frac{3 \times 4}{4 \times 5} = \frac{12}{20} = \frac{3}{5}$$ Step 5: Calculate the total fraction of pineapple eaten altogether. Total eaten is the sum of Mwesigwa's share and his sister's share. $$\text{Total eaten} = \text{Mwesigwa's share} + \text{Sister's share (of whole)}$$ $$\text{Total eaten} = \frac{1}{5} + \frac{3}{5}$$ $$\text{Total eaten} = \frac{1+3}{5} = \frac{4}{5}$$ The fraction of a pineapple eaten altogether is $\boxed{\frac{4}{5}}$. That's 2 down. 3 left today — send the next one.