# CLASS-8SUBJECT OF A FORMULAE

Subject of a Formula –

When one quantity (or variable) is expressed in terms of other quantities ( or variables), the number (or variable) thus expressed is named the “subject of the formula”.

Examples.1) The area (A) of a square of side a is A = a², here ‘A’ is the subject of the formula.

2)  If P, l & b denote the perimeter, length, and breadth of a rectangle respectively then -

P = 2 ( l + b ).

Here ‘P’ is the subject of the formula.

Changing The Subject of a Formula –

In the formula V = l X b X h for the volume of a cuboid, the subject is ‘V’. to express ‘l’ in terms of the volume ‘V’, breadth ‘b’ and height ‘h’, we write the formula as –                                                                                                       V                                                                                                                                                         l =  -----------

b X h                                                                                                                         The subject of the formula, is now l.

This process of transforming a formula is called “changing the subject of the formula”.

Example.1) – Change the subject of the formula v = u + ft to 1) u , 2) f & 3) t

Ans.)  Given,  v = u + ft

So,  u = v – ft …………………. (1)

Given,  v = u + ft

ft = v – u

v – u

f  =  ----------- ……………………... (2)

t

Given,  v = u + ft

ft = v – u

v – u

t  = ---------- ……………...……… (3)          (Ans.)

f

C           F - 32

Example.2) Change the subject of the formula ------- = ----------- to

5              9

1) C & 2) F.

Ans.)

C           F - 32

Given, ------- = ------------

5              9

5 (F – 32)

C  =  -------------- …………………………… (1)

9

C            F - 32

Given, ------- = ------------

5              9

9C

Or,    F – 32 =  ----------

5

9C

Or,  F  =  --------- + 32

5

9C + 160

Or,  F =  ------------- …………………………. (2)     (Ans.)

5