Question

What can you say about density if volume increase and mass stays the same

Answer 1

Density = mass
              volume 

For the sake of explanation, let's pretend the mass is 2g and the volume is 1 ml

Density = 2 g = 2 g/ml
              1 ml

Now if we increase the volume, and leave the mass the same then mass is still 2g, but we can increase the volume to 2 ml 

Density = 2 g   = 1 g/ml
              2 ml

Therefore we can say that if volume increases and mass stays the same, then density will decrease.

Answer 2

Well we know that density is equal to mass by volume, written scientifically as such:
ρ = m/v
Let's plug in some numbers to see how this looks, we'll say the object weighs 1 kg and it's volume is 2 cm^3
Thus, ρ = 1 kg / 2 cm^3
So, density in this case is equal to 1/2 kg for every cm^3.
Now let's increase the volume and keep the mass. We'll double the volume.
ρ = 1 kg / 4 cm^3
Now the density comes out to 1/4 kg for every cm^3, which is obviously less. 
We've come to the conclusion, then, that as volume increases and mass stays the same, density decreases. Therefore volume and density are inversely proportioned.

This makes sense mathematically, but does it make sense if we just think about it? It invariably does.
What is density? Density is just how much mass is stuck in a certain space. As such, when you increase that space, but keep the mass, the mass will be more sparsely distributed.
Think of it like this, you've a small room filled to the brim with toys, should you increase the room size, but keep the same amount of toys, then the toys would be further spread apart.
It is the same way with mass and volume.
Hope this helps :)