Ratio (mathematics)
A ratio in mathematics is a way to express the relationship between two or more values, highlighting how they compare to one another. The first value in a ratio is called the antecedent, while the second is the consequent; the order of these values is crucial for maintaining the ratio's meaning. Ratios can be represented in various forms, including phrases (e.g., "a to b"), colons (e.g., "a:b"), or fractions (e.g., "a/b"). They can be applied to a wide range of contexts, such as comparing quantities, measurements, or relationships.
When two ratios are equivalent, they are said to be in proportion. Ratios can also include different units, such as the ratio of teachers to students in a school or speed measurements like miles per hour, which are referred to as rates. Additionally, ratios can represent scales, such as in model representations where a specific dimension on the model corresponds to a larger dimension in reality. Typically, ratios are simplified to their lowest terms for ease of understanding and application, making complex relationships more manageable.
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Ratio (mathematics)
A ratio is a term in mathematics relating to comparisons between values. Most ratios compare two values, but some may compare more than two. The two main values in a ratio are known as the antecedent and consequent. They must be kept in the same order to retain the meaning and accuracy of the comparison. Ratios may be written in several ways. They can use the word “to” or the colon symbol. They may also be styled as fractions, with the antecedent at the left or top. People may use ratios for almost any task that involves comparing values. Ratios can compare numbers, measurements, or various relationships between values.
Overview
The most basic ratio consists of two values. The first value is the antecedent and the second is the consequent. These values cannot be interchanged. Moving the antecedent into the consequent spot, or vice versa, can change the meaning of the ratio or make it mathematically invalid. More complex ratios can include more than two values. If two ratios are the same, they are said to be in proportion.
The antecedent and consequent may be written in several ways. Using “a” to represent the antecedent and “b” to represent the consequent, the ratio may be written using the word “to,” as in “a to b.” A colon may replace the term “to” in the mathematical equation “a:b.” The ratio may be expressed as the fraction “a/b.” These styles represent the same information and may be read aloud as “the ratio of a to b.”
Ratios may be used to compare almost any values, as long as the values are related in some way. Units are generally added to ratio values. For example, if a school has 25 teachers and 350 students, the ratio of teachers to students is 25 to 350. In this case, the units are “teachers” and “students.” Units may also represent measurements such as weights, speeds, or denominations of currency. They can show relationships, such as the business profits per transaction, or the miles per hour of a vehicle. Saying that a car is traveling at 35 miles per hour makes a ratio of 35 miles to 1 hour, or 35:1. A ratio containing two values with different units is known as a rate. Speed measurements, such as miles or kilometers per hour, and data-rate units, such as megabytes per second (MB/s), are rates.
In some cases, ratios present a scale that does not directly specify the unit. For instance, a model airplane may be advertised as being sized at a 1:75 scale. A consumer may use that ratio by inserting any unit of size measurement. For example, by using inches, one inch on the model represents 75 inches on the real-life airplane. Similarly, one centimeter of the model would represent 75 centimeters of the actual plane.
In most cases, ratios are used after they are reduced to their lowest terms, which makes them easier to use and understand. For example, a school with 250 students and 750 available textbooks has a 250 to 750 students-to-textbooks ratio. For the sake of simplicity, the values can be divided or reduced by the same amount to reach their lowest terms. Here, the students-to-textbooks ratio of 250 to 750 can be reduced to its lowest term by dividing the antecedent and the consequent by 250. Because 250 is one-third of 750, the ratio becomes 1 to 3, or 1:3. This ratio is equal to the original but easier to use.
Bibliography
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