Ratios express several relationships among numbers. In the marble example, the ratio of 7-to-6 is the number of blue marbles compared with the number of red marbles. The ratio can be reversed - that is it can be written as 6-to-7 - as long as it’s clear that the ratio now expresses red marbles to blue. Ratios can also express part of something to the whole. In the marbles example, the ratio 7-to-13 represents the number of blue marbles to the total number of marbles. The ratio 6-to-13 represents the number of red marbles to the total number of marbles. In these cases, the first number can be divided by the second to determine the percentage of blue marbles and the percentage of red marbles.
Ratios written as fractions represent the same relationships as ratios written using the word “to.” In a classroom with 10 girls and 15 boys, the ratio of girls to boys expressed as a fraction is 10/15. The ratio of boys to girls is 15/10. The ratio of girls to the total number of students is 10/25, or 40 percent. The ratio of boys to the total number of students is 15/25, or 60 percent.
Using fractions to express ratios can make it easier to see numbers in context. For example, in the classroom with 10 girls and 15 boys, the ratio of girls to boys is 10/15. Simplify that by dividing each number by the greatest common factor -- in this case 5 -- just as you would any other fraction. The result is a ratio of 2/3. In simpler terms, for every two girls in the classroom, there are three boys.
Use a colon to express ratios as odds. In this case, the ratio of blue marbles to red marbles is 7:6. The ratio of boys to girls is 15:10. When possible, the ratios can still be simplified and expressed as smaller numbers.