CLASS-7
INTRODUCTION OF PROPORTION

PROPORTION

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 1^st, 2^nd, 3^rd, and 4^th terms of the proportion respectively then the equation would be w : x = y : z. The 1^st & 4^th terms are called EXTREMES and 2^nd & 3^rd terms are called MEANS.

 The 4^th term z is also called the Fourth Proportional to w, x, y

        1^st Term          3^rd Term          w            y

 So, ------------ = ------------ ; ------- = -------    

        2^nd Term          4^th 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.

                      x           y

 In this case,   ------- = -------,  xz = y²

                      y           z