When you divide the mass of a solute by the mass of the solution does that yield the mass %, or do we then ...

Multiply that number by 100 to get a percentage?

You have to multiply by 100. Try it:
Mass of solute = 25g
Mass of solution = 100g
Now in any logic you know that this is a 25%m/m solution:
Mathematically, if you divide mass of solute by mass of solution only , you get
25/100 = 0.25
This cannot be the answer - the solution is not a 0.25% m/m solution
But if you do:
25/100 *100 = 25 you have the correct answer.