Determine the fraction of pineapple Mwesigwa ate.

Mwesigwa ate one fifth of a pineapple.

$$\text{Mwesigwa's share} = \frac{1}{5}$$

The whole pineapple is represented by 1.

$$\text{Remaining pineapple} = 1 - \frac{1}{5} = \frac{5}{5} - \frac{1}{5} = \frac{4}{5}$$

His sister ate three quarters of what was left.

$$\text{Sister's share (of remaining)} = \frac{3}{4} \times \text{Remaining pineapple}$$ $$\text{Sister's share (of remaining)} = \frac{3}{4} \times \frac{4}{5}$$

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 $\frac{4}{5}$.