You are mixing a textured additive into paint and each liter of paint requires \( \frac{1}{8} \) kilogram (kg) of additive. You need \( \frac{1}{2} \) liter of paint with \( \frac{1}{16} \mathrm{~kg} \) of additive for the trim, and 2 liters of paint with \( \frac{1}{4} \mathrm{~kg} \) of additive for the walls. How much additive will you require altogether? Your answer should be in the form of a fraction reduced to its lowest terms. You need \( \square \mathrm{kg} \) of additive.

To solve the problem, let's calculate the amount of additive needed for each part of the painting project and then add those amounts together. 1. **Additive for the trim:** The trim requires \( \frac{1}{2} \) liter of paint. Since each liter requires \( \frac{1}{8} \) kg of additive, the amount of additive needed for the trim is: \[ \text{Additive for trim} = \frac{1}{2} \text{ liter} \times \frac{1}{8} \text{ kg/liter} = \frac{1}{16} \text{ kg} \] 2. **Additive for the walls:** The walls require 2 liters of paint. The additive needed here is: \[ \text{Additive for walls} = 2 \text{ liters} \times \frac{1}{8} \text{ kg/liter} = \frac{2}{8} \text{ kg} = \frac{1}{4} \text{ kg} \] Now, we add the amounts of additive required for the trim and the walls: \[ \text{Total additive} = \text{Additive for trim} + \text{Additive for walls} = \frac{1}{16} \text{ kg} + \frac{1}{4} \text{ kg} \] To add these fractions, we need a common denominator. The least common denominator of 16 and 4 is 16: \[ \frac{1}{4} = \frac{4}{16} \] So, \[ \text{Total additive} = \frac{1}{16} + \frac{4}{16} = \frac{5}{16} \text{ kg} \] In total, you need \(\frac{5}{16} \text{ kg}\) of additive.