Put simply, a ratio is a comparison of two numbers. Ratios are generally used to relate the magnitude of two like parameters of an object (or two or more similar objects) relative to one another. For example, the parameters used in a ratio may describe the same object, such as the length and width of a cardboard box, or differing objects, such as the weight, in pounds, of two bags of fruit. Alternatively, a ratio may provide a means to convert units of measurement that describe the same object, such as 12 inches of string equaling 1 foot of string or 100 centimeters of pavement equaling 1 meter of pavement. The magnitude may represent size, distance, weight, amount, or any other quantifiable parameter of the object(s); the parameters being compared within the ratio are generally quantities (such as the number of red marbles compared to the number of blue marbles in a jar), measurements (such the length of a rowboat compared to the length of a cruise ship), or conversion factors (such as 1000 grams equaling one kilogram). In each case, the ratio provides a means of comparison for two or more values.
Ratios are most often written in one of three forms. If a and b are the values to be compared, the ratio can be written as a fraction (that is, a / b). In fact, all fractions can be considered ratios, and in fact, ratios extend the concept of fractions to a more general form. Alternatively, the ratio may be written in the shorthand notation of a:b, or the language construct of "a to b." Expressing ratios as fractions, however, is feasible only when two values are being compared; writing a / b / c makes no sense. When three or more values are compared, the shorthand notation a:b:c is normally used.
Like fractions, ratios are often reduced to the lowest form possible, based on the greatest common factor. If a piggybank contains 10 quarters, six dimes, and eight pennies, for example, a reasonable ratio is 10:6:8. Since two is a common factor to all three numbers, an equal ratio is 5:3:4--for every five quarters in the piggyback, there are three dimes and four pennies. Reducing the ratio, however, results in a loss of information--one still knows how many quarters are in the bank relative to the number of dimes, but one does not know exactly how many quarters are in the bank. The statement that "the ratio of adults to children attending the soccer match was 5:3," for example, means that five adults attended the match for every three children present; it does not mean that only five adults and three children attended the match. For ease of use, ratios are commonly reduced to some number x relative to 1, that is x:1. Intuitively, an event described by the ratio 1:100 seems more likely to occur than an event described by the ratio 1:10,000; these two ratios are easily compared. Although exactly similar to these two ratios, comparisons between the ratios 20:2,000 and 0.1:1,000 are not intuitive.
Two of the most useful ratios are scale and rate. As a two-dimensional representation of a particular area, a map will not be accurate unless it uses a standard scale to represent distances--such as one inch to 10 miles--in both latitude and longitude. Using this ratio, any two objects that are 10 miles apart on the earth will appear one inch apart on the map, ensuring easy comprehension by the reader and application to his environment. Similarly, construction blueprints must have an accurate scale applied throughout in order to be of practical use to a builder. Using scale also applies to three-dimensional modeling. Aeronautical engineers, for example, often build scale models of design aircraft--that is, models made in the exact shape of the proposed aircraft that have been equally reduced in height, width, and length--for use in wind tunnels.
Rate is another special ratio; it relates distance to time. It is an especially useful tool that enables cone to compare speeds objects as well as estimate how much time will be required to travel a particular distance at a particular speed. If a truck travels 225 miles in 5 hours, for example, the rate is 225 miles per 5 hours, or more commonly, an average speed of 45 miles per hour. Rates can be either instantaneous--that is, the speed of an object at an event moment in time--or it can be a mean, as in the truck example above. It is likely that the truck did not travel at exactly 45 miles per hour during the entire five hours, perhaps stopping for fuel or slowing during periods of heavy traffic.
This is the complete article, containing 777 words
(approx. 3 pages at 300 words per page).
