Introduction to Ratio and Proportions:

The ratio of two quantities a and b in the same units, is the fraction and we write it as a : b.
In the ratio a : b, we call ‘a’ as the first term or antecedent and ‘b’, the second term or consequent.
Eg. The ratio 5 : 9 represents 5/9 with antecedent = 5, consequent = 9.

Proportions is where two ratios are compared and equated.
Where a:b is a ratio and c:d is another ratio, and if they are equal,
then, they can be re-written as a:b :: c:d. { the ‘::’ sign means ‘equal to’}
Therefore, a:b = c:d

Properties of proportions:

(i) a:b = c:d
can be written as a/b = c/d
which implies, axd = bxc, or, ad = bc
this property helps in solving many questions

(ii) if a:b = b:c, which means this proportions between three numbers is in the form of
‘continued proportions’, as all three numbers are having a connection.
so, a/b=b/c or,
ac=bxb or,