Ratio
A ratio is a comparison of two numbers (quantities) by division. A ratio is usually denoted by the symbol (:). The ratio of a to b (b 0) is written as a : b or 

In the ratio a : b, a and b are called terms of the ratio. 'a' is the antecedent and 'b' is the consequent. 
A ratio is a number, so to find the ratio of two quantities they must be expressed in the same units.

Properties of Ratios
(a)     In a ratio, two quantities are compared. So, the quantities must be of the same kind. i.e., they must be expressed in the same units.
(b)     The value of a ratio remains unaltered if the given ratio is multiplied or divided by the same non-zero quantity. 
(c)    The order of the terms in a ratio a : b is very important. The ratio 3 : 2 is different from the ratio 2 : 3.

Ratio in the simplest or lowest form :

Ex.1    Find the ratio of the following :
        (a)     36 minutes to 2 hours.    
        (b)     32 g to 1 kg
        (c)     3 days to 1 years.

Sol.  (a) Change both 36 minutes and 2 hours to the same unit.
            Now, 36 minutes = 36 minutes 
            2 hours = 2 × 60 minutes = 120 minutes 
                Ratio of 36 minutes to 2 hours 

(b)     First convert both into numbers with the same unit.
            32 g = 32 g 
            3kg = 3000 g 

(c)     First , convert both into numbers with the same unit.
            3 days = 3 days  
            1 year = 365 days 
            Ratio = 3 : 365

Ex.2  Find the (i) ratio of M20 to M80   (ii) ratio of 3 km to 600m
Sol.    (i)     20 : 80 or 1 : 4
          (ii)    3000m : 600m or 3000 : 600 or 5 : 1

Comparison of Ratios :
1.    Write the given ratios as fractions in the simplest form.
2.    Find the LCM of the denominators of the fractions.    
3.    Convert them into like fractions with same denominators    .
4.    Compare the numerators and arrange the fractions.
5.    Then respective ratios are also in the same order.

Ex.2    Two numbers are in the ratio 4 : 5. If the sum of the number is 63, then find the numbers.
Sol.    Here 63 is to be divided in the ratio 4 : 5.

Ex.3  Mr. Harry divided Rs. 84,630 between Shinchan and Nimavari in the ratio 3 : 4. How much did each of them get ?
Sol.  Ratio of money between Shinchan and Nimavari = 3 : 4 
        Sum of the terms of the ratio = 3 + 4 = 7

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