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What is the definition of ratio?
Relation of two quantities of the same kind
Relation of two quantities of the different kind
Equality between two ratios
Inequality between two ratios
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Answers
- Defination of ratio (the relation between two numbers which shows how much bigger one quantity is than another)
A Ratio is the relation between two quantities of the same kind. This relation indicates how many times one quantity is equal to the other. ... The numbers forming the ratio are called terms. The numerator, i.e. "12", is known as the antecedent and the denominator, i.e. "13", in this case, is known as the consequent.
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Answer:
In comparing two quantities of the same kind, the fraction, which expresses by how many times the first quantity is greater or smaller than the second quantity is called the ‘ratio’ between the first quantity and the second quantity.
The mathematical symbol of ratio is ‘:‘
It is written as say, 1:4 and read as 1 “is to” 4. The first of the two quantities forming a ratio is called the antecedent and the second is called the consequent of the ratio. The two together are called the terms of the ratio.
Points to Note:
1. Since the quotient of two quantities of the same kind is an abstract number, the ratio involving two quantities of the same kind is abstract. It has no unit.
2. In determining the ratio, the quantities are to be expressed in the same unit.
For example, the ratio between 2Kg and 1 tonne is 2 Kg : 1000 Kg = 1 : 500.
3. The ratio of two quantities of different kinds is not possible.
For example, 4 metres : Rs 6 is inadmissible as the comparison is not possible.
4. Inverse ratio: If two ratios, the antecedent and the consequent of one are respectively the consequent and antecedent of the other, they are said to be ‘inverse ratio’ or ‘reciprocal’ to one another.
For example, the inverse ratio of 3: 4 is 4: 3 and the inverse ratio of 4: 3 is 3: 4 . The reciprocal of \dfrac{2}{3} is \dfrac{3}{2} and the reciprocal of 3 is \dfrac{1}{3} .
Corollary: The product of a ratio and its inverse is always unity.
Types of Ratio
Ratios are mainly of two types:
Simple Ratio
Compound Ratio
The ratio between two quantities of the same kind is called ‘simple ratio‘.
Example, Rs \: 4 : Rs \: 5 = 4 : 5
When the product of the antecedents of two or more simple ratios is considered as the antecedent and the product of their consequents is considered as the consequent, the ratio thus formed is known as a ‘compound ratio‘.
Thus, the compound ratio of 4 : 5 , 6 : 7 and 5 : 6 is (4 \times 6 \times 5 ) : ( 5 \times 7 \times 6 ) = 4 : 7
There are three kinds of simple ratios:
Ratio of greater inequality
Ratio of equality and
Ratio of lesser inequality
1. In ratio of greater inequality, the antecedent is greater than the consequent.
For example, 20 : 13. Its value is always greater than 1.
2. In the ratio of equality, the antecedent is equal to the consequent.
For example, 3 : 3. Its value is always equal to 1.
3. In the ratio of lesser inequality, the antecedent is smaller than the consequent.
For example, 5 : 18. Its value is always less than 1 .
Ratio of greater inequality and ratio of lesser inequality are called ‘ratios of inequality’. Evidently, inverse ratio or reciprocal of a ratio of greater inequality is a ratio of lesser inequality.
Summing up important points
The ratio of two quantities = \dfrac{Antecedent}{Consequent}
Antecedent and Consequent are similar quantities and in determining the ratio, they are to be expressed in the same unit.
maybe a whole number or a fraction.
a ratio is an abstract number, it has no unit.
Since a ratio is expressed as a fraction, its value is not changed when both its antecedent and consequent are multiplied or divided by the same number except 0.
they can be expressed in reduced form.
Conversion into the same denominator etc. can also be applied in the case of ratios.