a recipe calls for 1"4 kg of sugar per cake if john has 5/2 kg of sugar, how many cakes can he bake?

To find out how many cakes John can bake, we need to divide the amount of sugar John has by the amount of sugar required per cake.

John has 5/2 kg of sugar, which is the same as 2.5 kg.
If 1 cake requires 1/4 kg of sugar, then dividing the total amount of sugar John has by the amount of sugar required per cake can be expressed as 2.5 kg / 1/4 kg per cake.

To divide by a fraction, we invert the fraction and multiply.
So, 2.5 kg / 1/4 kg per cake = 2.5 kg * 4 kg per cake.

Multiplying these values, we get:
2.5 kg * 4 kg per cake = 10 cakes.

Therefore, John can bake 10 cakes with 2.5 kg of sugar.