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Ratio

 

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.
 

In the ratio a : b, we call ‘a’ the first term or antecedent and b is called the second term or consequent.

 

 

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

 
 

 



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


 

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

 

Rule 1: If a > b and same positive number is added to each term of a : b, then the ratio is diminished.
        
Rule 2: If a < b and same positive number is added to each term of a : b, then the ratio is increased.
 

 

       

 


(i)   a2 : b2 is called duplicate ratio of a : b.
 

(ii)  a3 : b3 is called triplicate ratio of a : b.
 

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

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

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

Proportion

 

The equality of two ratios is called proportion,
 

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

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

 

        Product of Means = Product of Extremes

 

 


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

 

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

 

(iii)   Mean proportional between a and b is .
 

(iv)   If then = & .

 

 





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