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Home > Ratio

Examples:

• If a school has a twenty-to-one student-teacher ratio, that means that there are twenty times as many students as teachers.
• In a benzene ring, atoms of carbon and hydrogen exist in a one-to-one ratio with each other; there are the same number of each. The carbon:hydrogen ratio in naphthalene is 5:4. The ratio of oxygen atoms to hydrogen atoms in water is 1:2.
• Jupiter is 318 times the size of Earth.
• To mix a Bloody Mary, combine 2 parts vodka, 1/2 part lemon juice, and 3 parts tomato juice.
• 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.

Note the use of words such as "times", "parts", "number", etc. This occurs because ratios are unitless; the units cancel out of the ratio. e.g. 3 kg /5 kg = 3 000 g. /5 000 g = 3/5.

Ratios are not exactly the same thing as fractionIn common usage a fraction is any part of a unit. In mathematics: A vulgar fraction is a rational number written as one integer (the numerator divided by a non-zero integer (the denominator . The line that separates the numerator and the denominator is cas. For example, if I have three penniesA penny (pl. pence or pennies is a unit of currency or a coin used in several English-speaking countries: 1/100 of the British Pound Sterling or the Irish pound ( 1971- 2001), or a coin with that value: see history of the English penny. 1/240 of the Briti and five nickelThe United States five cent coin commonly called a nickel is a unit of currency equaling one 1/20th of a United States dollar. Nickels are 21. 21 mm in diameter, 1. 95 mm thick, with a plain edge. With the exception of a period during World War II, nickels, then the ratio of pennies to nickels is 3:5 or 3/5 (this indicates that there are three fifths as many pennies as nickels, but the fraction of coins which are pennies is 3/(3+5) = 3/8 (this indicates that the chances of a randomly selected coinThis article is about monetary coins. For alternative meaning see see word coinage. euro coin A coin is generally a piece of hard material, traditionally metal and usually in the shape of a disc, which is used as a form of money. With banknotes, coins mak being a penny are three in eight).

The most common thing to do with ratios is multiply them. For example, if there are two snorts for every giggle, and three giggles for every guffaw, then (since 2sn/1gig × 3gig/guf = 6sn/guf) there are six snorts for every guffaw. Note that the intermediate unit "giggle" canceled out of the expression. Note also that each fraction in the expression was equal to one, which is how we know that their product (6sn/guf) is also equal to one. Similarly, if I know there are two guffaws, then I can multiply by 6 snorts per guffaw (6sn/guf = one, the multiplicative identity) to learn that there are 12 snorts.

Ratio equality is expressed with :: for example:

would imply x=6.

See also

• proportionality (mathematics)This article is about proportionality, the mathematical relation. For other uses of the term proportionality see proportionality (disambiguation). In mathematics, two related quantities x and y are called proportional (or directly proportional if there ex
• rational numberIn mathematics, a rational number (or informally fraction is a ratio of two integers, usually written as the vulgar fraction a ''b where b is not zero. The set of all rational numbers is denoted by Q or in blackboard bold. Using the set-builder notation i
• oddsIn probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1 − p , where p is the probability of the event or proposition. The logarithm of the odds is the logit of the probability. Odds have long been
• golden ratio
• financial ratio

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Topics: Ratio Snorts Pennies Times Atoms Nickels Number Ratios Parts...

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