To determine how many cakes John can bake, we first need to know how much sugar he has and how much sugar is required for each cake.
John has \( \frac{5}{2} \) kg of sugar. The recipe requires \( \frac{1}{4} \) kg of sugar per cake.
Now, we can calculate the number of cakes he can bake by dividing the total sugar he has by the sugar required per cake:
\[ \text{Number of cakes} = \frac{\text{Total sugar}}{\text{Sugar per cake}} = \frac{\frac{5}{2}}{\frac{1}{4}} \]
To divide by a fraction, we multiply by the reciprocal:
\[ \text{Number of cakes} = \frac{5}{2} \times \frac{4}{1} = \frac{5 \times 4}{2 \times 1} = \frac{20}{2} = 10 \]
Therefore, John can bake 10 cakes.