What's with the Portugese Reis coinage?

I have befor asked about the British £sd currency in their colonies and the usage of denominations like 3 and 15 in the Soviet and former satelite states.

Now my question is, what's with the Portugese and it's colonies (especialy Brazil) coinage?

I was looking at some auctions on Facebook and ran into a 37½ reis(?!)

Considering I've seen a 300 Reis coin, it makes sense as 1/8 of a 300 reis..?

But could someone explain the reis-coinage to me? Is it just like a theory about the Soviet coins? Making accounting more easy? 

Been confused over it for a long time and Google haven't been to much help, haha.

Thanks! :D

Example of 37½:

N#125919

Very weird coin, I have no idea why they would do something like this, but I would guess its just a weird coin used for some weird purpose.

Most Reis coins appear to be in multiples of 10s and 20s, so my guess its either something like Guineas (a coin worth £1 and 1 shilling) 

or maybe it was a failed type of coin seeing how theres not many years like the 4 Reichspfennig coin of the 1930s or the Double Florin

Ah, basic maths foils me again. Turns out 37.5 goes into 300 8 times. So it does work in the Reis system, if a little oddly. I wouldn't be surprised when the coin existed it wasn't a very popular one. 

Would it be possible that this coin was created to be equal to a popular coin from another country to make commerce easy for sailors paid in these coins to do business with Spanish or English ships or ports?

Oh! That would make sense.

Like if we had a 7½ and 15 kroner coin in Denmark. Would make exchanging to euros more easy in daily purchases around the border.

That's a nice one. I love this kind of numismatic discussions.

It all goes back (perhaps even earlier by other kingdom houses) to king Pedro II of Portugal “principe regente” 1667-1683) and King of Portugal (1683-1706) after the death of his brother  (King Afonso VI).

King Pedro II was the first Portuguese King to struck mechanical coins. His coins currency system was a mix of pre-decimal and decimal systems which developed several times through his reign. 

It all started with the 1 ½ real, 3 reis (twice 1 ½ real).  It went wrong with the struck of 5 and 10 reis coins that couldn't fit the division with the pre decimal system. 

Pedro II did't struck any 37 ½ reais coin, but 37 ½  can be divided by 1 ½ . This results in 25 which perfectly fits the decimal system of reis, vinténs (20 reis), tostão (100 reis), cruzado (400 reis), quartinho (1000 reis) e moeda (4000 reis).

King Pedro IV of Portugal (1826-1828) King Pedro 1 do Brazil till 1831, mixed both systems too. The 37 ½ it's thus a kind of linking pin between both systems.

As a collector from Brazil, I know this coins is very difficult to find.

The link below is an detailed explanation why this coin was minted, it is in portuguese but I guess google translator can do a good job:

http://www.moedasdobrasil.com.br/moedas/vintem.asp