A ratio demonstrates the relationship between two numbers. The relationship can exist between categories, such as proportions of milk to flour in a recipe, or between a category and a whole, such as proportion of deaths in a population. Ratios can be expressed as fractions, explains Ann Xavier Gantert in her textbook, "Amsco's Integrated Algebra I." The order is very important. The ratio 1:10, one of the simplest to calculate, is not the same as 10:1. Expressing the ratio as a fraction makes the importance of order obvious; one-tenth does not equal 10 wholes.

### Part-to-Part Relationship

You can express the quantitative relationship between two categories in a group or mixture with ratios. Using an adaptation of the recipe example provided by Sybilla Beckmann in her math education textbook, 1 tablespoon of cinnamon to 10 tablespoons of sugar yields a ratio of 1:10. If the amounts increase proportionally, the ratio stays the same. For instance, if there are 4 tablespoons of cinnamon and 40 tablespoons of sugar, the ratio is 4:40. Simplify the ratio in the same way you would a fraction. The common denominator is four; divide four into both sides of ratio to get the simplified ratio 1:10. There is 10 times as much sugar as cinnamon.

### Part-to-Whole Relationship

Fractional expression of a ratio may be easier to visualize when it describes the relationship between a part and whole. If a zoo has 10 gibbons, one of which is male, the ratio of gibbon males to the zoo's gibbon population is 1:10; one-tenth of the gibbons are male. Tenths can be converted directly to percentages: one-tenth, expressed as a decimal, equals the proportion 0.1, which equals 10 percent. Therefore, 10 percent of the gibbons are male.