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<p><b>New page</b></p><div>[[File:Aspect-ratio-4x3.svg|thumb|Aspect-ratio-4x3.svg]] == Ratio ==<br />
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A '''ratio''' is a quantitative relationship between two numbers, showing how many times one value contains or is contained within the other. Ratios are used in various fields such as [[mathematics]], [[finance]], [[engineering]], and [[statistics]] to compare quantities and express relationships between them.<br />
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== Definition ==<br />
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In its simplest form, a ratio is expressed as "a to b" or a:b, where 'a' and 'b' are any two numbers. For example, the ratio 3:4 means that for every 3 units of the first quantity, there are 4 units of the second quantity. Ratios can also be expressed as fractions, such as 3/4.<br />
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== Types of Ratios ==<br />
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=== Part-to-Part Ratios ===<br />
A part-to-part ratio compares different parts of a whole to each other. For example, in a class with 10 boys and 15 girls, the ratio of boys to girls is 10:15, which can be simplified to 2:3.<br />
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=== Part-to-Whole Ratios ===<br />
A part-to-whole ratio compares one part of a whole to the entire whole. Using the same class example, the ratio of boys to the total number of students (25) is 10:25, which simplifies to 2:5.<br />
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=== Proportions ===<br />
A proportion is an equation that states that two ratios are equal. For example, if the ratio of boys to girls in one class is 2:3 and in another class is 4:6, these ratios are proportional because 2/3 = 4/6.<br />
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== Applications ==<br />
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=== Mathematics ===<br />
In [[mathematics]], ratios are used to solve problems involving proportions, scaling, and rates. They are fundamental in understanding concepts such as [[fractions]], [[percentages]], and [[probability]].<br />
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=== Finance ===<br />
In [[finance]], ratios are used to analyze the financial health of a company. Common financial ratios include the [[price-to-earnings ratio]], [[debt-to-equity ratio]], and [[current ratio]].<br />
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=== Engineering ===<br />
In [[engineering]], ratios are used to design and analyze systems. For example, the gear ratio in a mechanical system determines the relationship between the rotational speeds of two gears.<br />
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=== Statistics ===<br />
In [[statistics]], ratios are used to compare data points and understand relationships between variables. The [[odds ratio]] and [[risk ratio]] are commonly used in [[epidemiology]] and [[public health]].<br />
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== Calculation ==<br />
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To calculate a ratio, divide one quantity by the other. For example, to find the ratio of 8 to 12, divide 8 by 12 to get 2/3 or 0.67. Ratios can be simplified by dividing both terms by their greatest common divisor.<br />
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== See Also ==<br />
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* [[Proportion (mathematics)]]<br />
* [[Fraction (mathematics)]]<br />
* [[Percentage]]<br />
* [[Rate (mathematics)]]<br />
* [[Odds ratio]]<br />
* [[Risk ratio]]<br />
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== References ==<br />
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{{Reflist}}<br />
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== External Links ==<br />
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{{Portal|Mathematics}}<br />
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[[Category:Mathematics]]<br />
[[Category:Finance]]<br />
[[Category:Engineering]]<br />
[[Category:Statistics]]<br />
[[Category:Ratios]]<br />
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