Four quantities w, x, y, & z are said to be in proportion if w : x = y : z
It also can be expressed as w : x :: y : z
It’s not necessary for all the four quantities forming a proportion to be of the same kind, the two quantities forming the first ratio must be of the same kind and so should be the two quantities forming the second ratio.
There are some Types & Rules are discussed below -
Cross Product Rules -
Suppose, w, x, y, and z are the 1st, 2nd, 3rd, and 4th terms of the proportion respectively then the equation would be w : x = y : z . The 1st & 4th terms are called EXTREMES and 2nd & 3rd terms are called MEANS.
The 4th term z is also called the Fourth Proportional to w, x, y
1st Term 3rd Term w y
So, ----------- = ------------ ; ------- = -------
2nd Term 4th Term x z
CONTINUED PROPORTION –
When three quantities x, y, z are said to be in Continued Proportion or Continued Ratio then the equation would be x : y = y : z .
The term y is called the Mean Proportional between x & z while the term z is called Third Proportional to x & y.
In this case , --------- = --------- , xz = y²