Ratios give the relation between two quantities. For example, if two quantities A and B have a ratio of 1:3, it means that for every quantity of A, B has three times as much. Ratios can be represented in various formats, such as 1:3, 1/3 or "1 to 3." If two numbers are known, here are some simple steps to find the ratio between them.

### Determine if the two numbers have a common factor

Ratios are usually the simplest representation of two quantities. The numbers that form the ratio should therefore be reduced to their simplest terms by dividing the numbers by their greatest common factor, if they have one. For example, for the ratio of 20 red balloons to 15 blue balloons, the numbers would be divided by 5. The number 5 is their greatest common factor, and it reduces the quantities to their equivalents of 4 red balloons and 3 blue balloons.

### Arrange your numbers in the desired ratio format

Choose the format in which the ratio is to be represented. In the example of red and blue balloons stated above, there are various forms of representation. For example, it can be stated that "the ratio of red to blue balloons is 4:3," "the ratio is 4/3" or "the ratio of red to blue balloons is 4 to 3."

### Manipulate the ratio (if necessary)

This step is optional. Ratios can be expanded to calculate the desired number of an object in a given scenario. In the balloon example, assume a birthday party is being planned so the ratio of red to blue balloons is 4:3 in all rooms and 70 balloons are to be used. Now knowing the required ratio, it can be calculated that 40 balloons need to be red and 30 need to be blue to maintain the ratio.