# Ratio

Â**Ratio: **The ratio of two quantities in the same units is the fraction that one quantity is of the other.

Thus, the ratio a to b is the fraction , written as a : b.

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In the ratio a : b, we call â€˜aâ€™ the first term or antecedent and b is called the second term or consequent.

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Â**Rule:Â ***The value of a ratio remains unchanged, if each one of its terms is multiplied or divided by a same non-zero number.*Â

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(i) If a > b, then a : b is called a ratio of greater inequality.

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(ii) If a < b, then a : b is called a ratio of less inequality.

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**Rule 1:Â **If a > b and same positive number is added to each term of a : b, then the ratio is diminished.

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**Rule 2:Â **If a < b and same positive number is added to each term of a : b, then the ratio is increased.

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(i)Â Â a^{2} : b^{2} is called duplicate ratio of a : b.

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(ii)Â a^{3} : b^{3} is called triplicate ratio of a : b.

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(iii) :is called sub-duplicate ratio of a : b.

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(iv) is called sub-triplicate ratio of a : b.

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(v)Â If a : b and c : d are two ratios, then ac : bd is called the ratio compounded of the given ratio.

# Proportion

ÂThe equality of two ratios is called proportion,

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If a : b = c : d, we say that a, b, c, d are proportional and, we write, a : b : : c : d.

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Here a and d are known as extremes and b, c are known as means. We always have:

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Â Â Â Â Â Â Â **Product of Means = Product of Extremes**

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(i)Â Â Â Â In a : b : : c : d, we say that d is the fourth proportional to a, b & c.

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(ii)Â Â Â If x is the third proportional to a, b then a : b : : b : x.

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(iii)Â Â Mean proportional between a and b is .

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(iv)Â Â If then = & .

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