# Finding a Part Given Ratio + Whole

## Finding a Part Given Ratio and Whole

**The key to solving almost any ratio problem is figuring out how many of the whole each one in the ratio represents.** In our particular example, the key is going to be to figure out how many marbles of these 360 each one in this ratio represents.

The way we do that in a situation where we’re given the whole and the ratio is we add the two numbers of the ratio together and then divide the whole by the sum of the two ratio numbers. We’re going to add two and seven. 2 + 7 = 9. Then, we’re going to divide the whole, 360, by the sum of the ratios.

We’ll divide 360 by 9. 9 goes into 36 four times. That takes care of the 36, so we just have to add a zero here. So 9 goes into 360 forty times. **Each one in this ratio represents 40 marbles.** Now, we can find the number of each type of marble by multiplying the number that represents that type in the ratio by 40.

To find the number of black marbles, we can multiply 40 by 2 and to find the number of red marbles, we can multiply 40 by 7. The question is asking us how many of the marbles are red. We’ll multiply 40 by 7 to find that. We have 40 x 7 = 280 marbles. Of the 360, there are 280 red marbles.