Proportions

When we find the fraction of the related terms, we call it ratio. Word Ratio means to represent the data in form of fraction such that the units of the two terms are equal. We can no find ratio or proportion for any two terms which are unlike. In this session we will study how to solve proportions. Let’s first see what all proportions are. Any four Numbers are said to be I proportion, if p: q = r : s and we write  the relation of proportion as follows: p: q:: r : s. Now if we are given that the four terms p, q, r, s are in proportion, then it means p: q:: r : s.
 In order to solve the terms which are given in the proportion, we Mean that:
a)       p, q, r and s are called first, second, third and the fourth terms of the proportion.
b)       Here in proportion we say ‘p’ and ‘s’ are the extremes or we say them as extreme terms and  ‘q’ and ‘r’ are called the mean terms or we also call them the means.
c)       We must always remember that in case of proportions, we must have product of means = product of extremes.
d)        We also call‘s’ as the fourth proportion to the terms p, q, and r terms.
e)        In case we are given p: q:: r : s, then  p, q, and r are said to be in continued proportions.
f)        Here we call ‘r’ as the third proportion to ‘p’ and ‘q’ also we say that ‘r’ is the fourth proportion to p, q, q.
g)        Also the Point to be remembered in this continued proportion is that p/q = r / s.
Thus we say that q² = p * r.
Or we say that b = root (p * r).