2.6.1 Rearranging formula

2.6 Formula

The formula is a mathematically written fact or rule. It is typically used to connect two or more quantities with an equal sign. When you know the value of one quantity, you can use the formula to find the value of the other. It helps to solve the questions quickly.

2.6.1 Rearranging formulae

Rearranging formulae is also known as changing the subject.

• The subject is the variable that you want to discover or obtain on its own on one side of the equation.
• The procedure for changing the subject is the same as that for solving linear equations.
  • Any fractions or brackets should be removed
  • Use inverse operations to isolate the variable you’re attempting to make the subject of
  • If Equation involves \( x^n \)
    • First make \( x^n \) the subject of the formula
    • Take \( n^{th} \) root and add \( \pm \) sign

Worked example:

\( m=2p+ \sqrt{ \frac{x}{y} } \)Make \( x \) the subject of this formula.Subtract \( 2p \) from both sides\( m-2p=2p-2p+ \sqrt{ \frac{x}{y}} \)\( m-2p= \sqrt{ \frac{x}{y}} \)Remove square root by squaring both sides\( (m-2p)^2=( \sqrt{ \frac{x}{y} } )^2 \)\( (m-2p)^2= \frac{x}{y} \)Isolate \( x \) by multiplying both sides by \( y \)\( y(m-2p)^2= \frac{x}{y} \times y \)\( y(m-2p)^2=x \)\( x=y(m-2p)^2 \)

Test yourself

Question 1:Make \( m\) the subject of the formula \( x=\frac{3m}{2-m} \).[4]Question 2:\( P=2r+πr \)Rearrange the formula to write \( r \) in terms of \( P \) and \( \pi \) .[2]Question 3:\( A=(2 \pi +y)x^2 \)Rearrange the formula to make \( x \) the subject .[2]Question 4:Rearrange \( 2(w+h)=P \) to make \( w \) the subject[2]