Symbols should always be pronounced to denote their intended meaning. For example, the ampersand symbol (&) means "and", and so is pronounced that way:
eg "Smith & Jones" would be read as "Smith and Jones".
You would not expect someone to pronounce the symbol as "ampersand" when encountering it in a text.
The "slash" symbols (/ and \) are described by the terms "forward slash" and "backslash" but as mathematical symbols they can denote a number of things. Therefore the reader needs to understand their intended meaning before they can be read properly.
In your example...
There is another common business type of partnership 51% / 49%.
... it seems to me that this is representing a ratio.
A ratio expressed using the format "51:49" would normally be pronounced:
Fifty-one to forty-nine.
However, when it comes to percentages it is quite common to omit the ratio altogether. You may be familiar with the expression "50/50" (fifty-fifty) meaning an equal split two-ways. It may, therefore, be acceptable to say:
Fifty-one forty-nine.
There are other uses for the slash symbol, for example, a fraction. Although fractions are traditionally displayed vertically with the numerator above the denominator, it is also common for some to display these on one line using a slash due to the limitations of a computer keyboard. Whatever the symbol, you should consider what it means in context before attempting to pronounce it.