Ratio

From Exampleproblems

In algebra, a ratio is the relationship between two quantities. It is expressed as the quotient of two numbers, or as two numbers separated by a colon (pronounced "to"). A number that can be written as a ratio of two integers is a rational number. In physics, a ratio between two magnitudes of the same type of quantity gives a positive real number when the magnitudes are expressed relative to an absolute or natural zero. The ratio between a difference of two magnitudes to a third magnitude, such as a unit, gives a real number (i.e. positive or negative).

Examples

• If a school has a twenty-to-one student-teacher ratio, that means that there are twenty times as many students as teachers.
• The ratio of heights of the Eiffel Tower (300m) and the Great Pyramid (137m) is 300:137, so one structure is more than twice the height of the other (or more precisely, 2.2 times).
• The ratio of the mass of Jupiter to the mass of the Earth is approximately 317.8:1.
• The musical interval of a perfect fifth, the pitch ratio 3:2, consists of two pitches, one approximately 1.5 times the frequency of another.
• If two axles are connected by gear wheels, the number of times one axle turns for each turn of the other is known as the gear ratio. The best example being the number of turns of the pedals of a bicycle compared with number of turns of the bicycle's rear wheel.
• The ratio of hydrogen atoms to oxygen in water is 2:1, or two parts to one.

Note the use of words such as "times", "parts", "number", etc. Because two objects are being compared using the same measure, ratios are unitless; the units cancel out of the ratio. For example, the ingredients in a recipe that required 500 grams and 300 grams of each, would be in the ratio of 5:3, with no units.

Note also the difference between ratios and vulgar fractions. For example, if I have three raspberry candies and five blackcurrant candies, then the ratio of raspberry candies to blackcurrant candies is 3:5. This indicates that there are three fifths as many raspberry candies as blackcurrant candies. However the fraction of all the candies that are raspberry is three out of a total of all eight candies or 3/(3+5) = 3/8. Thus the chances of a randomly selected candy being raspberry are three in eight.

See also

• Analogy
• Conversion factor
• Financial ratio
• Golden ratio
• Odds
• Proportionality
• Ratio decidendi — the reasoning for a court of law's decision
• Rational numberda:Forhold

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