## RATIO

Ratio : A comparison by division is called ratio. A ratio is usually denoted by the symbol (:). If a and b (b is not equal to 0) are two quantities of the same kind, then the fraction a/b  is called the ratio of a to b, we write it as a : b.
or  = a/b= In the ratio a: b, the first term is 'a' and the second term is 'b'. A ratio is said to be in the simplest form if its two terms have no common factor other than 1.
NOTE :
(i) The ratio of two numbers is usually expressed in its simplest form.
(ii) In a ratio, we compare two quantities. The comparison becomes meaningless if the quantities being compared are not of the same kind i.e. they are not measured in the same units.
(iii) It is just meaningless to comeare 20 bags with 200 crows. Therefore, to find the ratio of two quantities, they must be expressed in the same units.
(iv) Since the ratio of two quantities of the same kind determines how many times one quantity is contained by the other. So the ratio of any two quantities of the same kind is an abstract quantity.
In other words, ratio has no unit or it is independent of the units used in the quantities compared.
(v) The order of the terms in a ratio a : b is very important. The ratio 3 : 2 is different from the ratio 2 : 3.
(vi) We can multiply or divide both the terms of the ratio by a non zero number which does not alter the value of the ratio.

RATIO IN THE SIMPLEST OR LOWEST FORM
A ratio a/b or a : b is said to be in its lowest or simplest form if a and b have no common factors except 1.
For example,
40 : 80 = = 1/2  = 1 : 2
10000 : 8000 = = 5/4  = 5 : 4
STEPS :
(a) Write the ratio as a fraction.
(b) Divide the numerator and the denominator by their HCF.
(c) The answer is a fraction in its lowest form ; so change it to ratio, which will be in the lowest form.

Ex. Express the following ratio in their simplest form :
(a) 150 : 400
(b) 85 : 225
Sol. (a) 150 : 400 = = 3/8 = 3 : 8
(b) 85 : 255 = = 1/3 = 1 : 3

Ex. Find the ratio of the following :
(a) 36 minutes to 2 hours.
(b) 50 cm to 5 metres.
(c) 32 g to 1 kg
(d) 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
36 : 120 = = 3/10 = 3 : 10
(b) First convert both into numbers with the same unit.
50 cm = 50 cm
5 metres = 500 cm
Hence ratio of 50 cm to 5 metes is
= 50 : 500 =