Multiplying by $10$'s place voodoo: Why is $30\times 50= 15\times 100$? This is a very trivial question, but I can't seem to reason out why 
$$30\times 50= 15\times 100$$ 
As a kid, I never really thought about why it works, but now I can't figure it out and the idea is really troubling me. I understand that we can break up the problem like this: 
$$3\times 10\times 5\times 10$$ 
but at this point I feel like I've lost the intuitive aspect of the problem. Can someone plz help and provide some intuition?

$$30\cdot50=(3\cdot10)(5\cdot10)=(3\cdot5)(10\cdot10)=15\cdot100$$
It's all just the property that $$(ab)(cd)=(ac)(bd)$$
