I was given a 4 kg bag of rice to take to my grandmother's house. On the way there the bag tore and a quarter of it spilled out. How many kilograms of rice will my grandmother have to cook?

The bag initially contained $4 \text{ kg}$ of rice, and a quarter of it spilled.

$$\text{Spilled rice} = \frac{1}{4} \times 4 \text{ kg} = 1 \text{ kg}$$

Subtract the spilled amount from the initial amount.

$$\text{Remaining rice} = 4 \text{ kg} - 1 \text{ kg} = 3 \text{ kg}$$

The grandmother will have to cook $\boxed{3 \text{ kg}}$ of rice.

j)

One cake needs $445 \text{ g}$ of flour, and the aunt wants to bake 20 cakes.

$$\text{Total flour} = 445 \text{ g/cake} \times 20 \text{ cakes} = 8900 \text{ g}$$

Since $1 \text{ kg} = 1000 \text{ g}$:

$$\text{Total flour} = \frac{8900}{1000} \text{ kg} = 8.9 \text{ kg}$$

She will need $\boxed{8900 \text{ g}}$ or $\boxed{8.9 \text{ kg}}$ of flour.

k)

One school book weighs $25 \text{ g}$, and there are 12 books in the bag.

$$\text{Total weight} = 25 \text{ g/book} \times 12 \text{ books} = 300 \text{ g}$$

The books weigh $\boxed{300 \text{ g}}$.