The subject of an equation/a formula is a variable that is expressed in terms of other variables. It should have an exponent of 1 and a coefficient of 1

Changing the subject where the variable appears in multiple terms

Maths

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In the prior unit, pupils explored various ways to manipulate and solve various equations and formulae. In this unit, pupils apply these skills to algebraic fractions in order to change the subject and manipulate the algebraic fraction.

Algebraic fractions

What is the most efficient first step to make $$x$$ the subject of $$ax + b = 2x + c$$?

What is the most efficient next step to make $$x$$ the subject of $$ax-2x = c-b$$ ?

Make $$a$$ the subject of $$a(b+c)=3+4(a+2b)$$.

Make $$r$$ the subject of $$p = \frac{r+5}{r+q}$$.

What would be the most efficient first step to make $$a$$ the subject of $$\frac{8a+4b}{6a+3b}+\frac{a+1}{3a+3b}=b$$ ?

Make $$a$$ the subject of $$\frac{4(2a+b)}{3(2a+b)}+\frac{a+1}{3(a+b)}=b$$.

Shown is the formula for the perimeter of a rectangle. Make $$b$$ the subject.

Make $$z$$ the subject of $$\frac{4}{x} +\frac{2}{y} = \frac{3}{z}$$.

Simplify $$\frac{3x-12}{2x-6} + \frac{x}{3x-9}$$

This lesson will be removed by end of Summer Term 2025.

Changing the subject where the variable appears in multiple terms

Lesson outcome

This lesson will be removed by end of Summer Term 2025.