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