Changing Subject of the Formula; Examples & Tricks

Changing the subject of a formula deals with inverting the subject of an equation with the given one. Given the equation x = 2y + 6, x is the subject of the formula.

What if we want to make y the subject, then

	
	2y +6 = x
	2y = x -6
	y = (x -6)/ 2

Some tricks and rules

• When dividing an expression by a fraction, invert the fraction such that the denominator multiples the top expression and the numerator becomes the denominator.
  

  		
  			2/3x = 4y
  			x = 4y/(2/3)
  			x = 3(4y)/2 (Notice 2 is now the denominator)
  			x = 12y/2 = 6y
  		

• When the subject has a power of 2, introduce a square root to both sides. The power will cancel with the square root.
  x@2 = 4y; √x@2 = √4y; x = √4y = 2√y
• When the subject has a power of 3, introduce a cube root to both sides.
  x@3 = 4y; x = @3√4y

Example 1

Given w = ac + k. Make c the subject

	w -k = ac
	c = (w -k) /a

Example 2

Given p = st - q. Make s the subject

p = st-q
	st = p + q
	s = (p +q)/t

Example 3

Given P = 2a+ 2b. Make a the subject

	P = 2a + 2b
	P -2b = 2a (isolate the subject)
	2a = P - 2b (rearrange)
	a = (P - 2b)/2

Example 4

Given V = 4/3πr@2. Make r the subject

Example 5

Given H = mp +1/2f@2p. Make f the subject