How does MMR work in normals?

I sometimes play with my friends and our ranks are:

normally 1 Gold (me), 1 Diamond, 1 Platinum and 2 Silver.

We often get teams with one solo player (not premade with the others) that is unranked or low bronze) and he gets absolutely destroyed.

How does our MMR from Rankeds come into play in Normals?

Does it come into play at all? Do we have different MMR for Normals/Rankeds?

Is it just random?

In League of Legends, there are seperate Elo scores for each gamemode's matchmaking. This means that your ranked Elo is seperate to your standard (normal game) Elo.

When going into Matchmaking, the matchmaking system uses the Elo that corresponds to the gamemode you're queuing for.
Because Ranked games and standard games are considered two different gamemodes, they have two different scores.

(ie. You have 1000 Elo (it's an estimate, we don't actually get to see this value) in standard games, and 3000 Elo (this value is visable in your Ranked stats) for ranked games on Summoner's Rift. This means that your next standard game will be against those that have a lower skill-level than you, while your next ranked game will be against those that are the same skill-level as you.)

As far as the matchmaking system is concerned: Your ranked Elo (MMR) does not affect the standard Elo (isn't taken into consideration during Standard Game matchmaking).

The point is: Even if you're the top player in Ranked games, and you've never played a single standard game (not possible, since you HAVE to play Standard Games to be able to level up), you will be matched with those close to the starting Elo if you were to play a Standard non-ranked match. The matchmaking system does NOT care about your ranked stats (MMR, Elo, etc.) if you queue for a Standard non-ranked game.

The only thing that will be taken into consideration is your loading screen portrait, which reflects the current league you're in.

You have a MMR for each different queue: normal 5, normal 3, aram, dominion, ranked 5, team ranked 5, team ranked 3, and I believe team builder also has a separate number.

So when you queue up with your friend, the game takes the average MMR of your team, and matches it against another team with the same average MMR. If your players haven't played a lot of normals, your MMR won't be high and you'll be matched against lower level players, or players having played as few games as you. If you keep playing normals, you'll end up playing against better and better players, as your MMR rises.

The only place where your MMR from other queues is taken into account is when you're playing team ranked 5/3. IE, a team of 5 bronze players having never played ranked team and going 5-0 in placement will be placed in silver, wile a team full of diamonds having never played ranked teams and going 5-0 will be placed in gold.