## Ratios

The knowledge of ratio and proportion is necessary for a family to run. The belongings of father must be divided among children proportionally. Or in other words the ratio should be the same.

The ratio is found of quantities

- of the same kind
- in the same units

A ratio of two quantities is the fraction that one quantity is of the other and is expressed in its lowest terms.

- The ratio a:b is the fraction a/b. a:b is read as a is to b.
**Terms of a ratio**: In the ratio a:b, a is the first term and is called **antecedent** and b is second term and is called **consequent**.
- A ratio remains unchanged if both of its terms are multiplied or divided by the same non-zero quantity.

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**Simplest form:**

A ratio is said to be in the simplest form if H.C.F. of the antecedent and consequent is 1.

## Comparison of ratios:

To compare two ratios, compare its decimal fraction.

**Ratio of equality:**

- If antecedent of a ratio is equal to its consequent, then the ratio is called the ratio of equality.

**Ratio of greater Inequality:**

- If antecedent of a ratio is greater than its consequent, then the ratio is called the ratio of greater inequality..

**Ratio of lesser inequality:**

- If antecedent of a ratio is less than its consequent, then the ratio is called the ratio of lesser inequality.

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**Compounded ratios:**

The compounded ratios of a:b and c:d is ac:bd.In compounded ratios the result is the term wise multiplication. The compounded ratios of a:b ,c:d and e:f is ace:bdf.

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**Reciprocal Ratio:**

If a≠0 and b≠0 then the reciprocal ratios of a:b ia 1/a:1/b i.e. b:a.

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**Duplicate Ratio:**

It is the compounded ratios of two equal ratios. Thus the duplicate ratios of a:b is aa:bb i.e. a

^{2}:b

^{2}.

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**Sub-Duplicate Ratio:**

√a:√b is sub-duplicate ratio of a:b.

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**Triplicate Ratio:**

It is the compounded ratios of three equal ratios. Thus the Triplicate ratios of a:b is aaa:bbb i.e. a

^{3}:b

^{3}.

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**Sub-Triplicate Ratio:**

∛a:

∛b is sub-Triplicate ratio of a:b.

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**Continued Ratio:**

If A:B and B:C then A,B,C are said to be continued ratio A:B:C.

## Proportion

If two ratios are equal then it is called a proportion.

a:b::c:d