During a checker game there are 16 pieces left. the ratio of black to red is 3: 5. how many black pieces are left on the board?

We know that there are 16 pieces left and that the ratio is 3 : 5. The ratio teels us there are 8 "parts" inside (because 3 + 5 = 8), so now we may just divide 16 by 8 to find out how much is one such "part":

16 ÷ 8 = 2

Now we can see that one "part" of the ratio is for 2 pieces. So if the ratio of black to red pieces is 3 : 5, then there are 3 * 2 = 6 red pieces and 5 * 2 = 10 black bieces.

Are you asking for 6 or 15?