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Changing the subject to suit the context

I can evaluate different problems to ascertain when rearranging a formula is beneficial.

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Lesson 10 of 12

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Year 9

Changing the subject to suit the context

I can evaluate different problems to ascertain when rearranging a formula is beneficial.

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Lesson details

Key learning points

Formulae are used in a variety of places, such as the science lab but also in factories.
Rearranging the formula may be beneficial when what you wish to calculate is not the subject.
You can compare rearranging the formula to solving for one unknown.

Keywords

Subject of an equation/formula - 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.

Common misconception

That the gradient of a line given the equation of the line is always just the coefficient of the x term.

Using graphing software to explore this could help.

This is a great opportunity to show how these areas of maths link together. Rearranging the equation of a straight line into different forms can be really useful.

Teacher tip

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This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
For the linear equation $$y=5x-7$$, you can call $$y$$ the __________ of the equation.

gradient

solution

Correct answer: subject

Q2.
Which of the below are correct rearrangements of the formula $$V=a\times{l}$$ ?

Correct answer: $$V=l\times{a}$$

$$l=a\times{V}$$

Correct answer: $${V\over{l}}=a$$

Correct answer: $${V\over{a}}=l$$

$${l\over{V}}=a$$

Q3.
Make $$y$$ the subject of the equation $$8y-3x=24.$$

$$8y=3x+24$$

$$y={3\over8}x+24$$

Correct answer: $$y={3\over8}x+3$$

$$y=3x+24-7y$$

Correct answer: $$y={{3x+24}\over8}$$

Q4.
Make $$e$$ the subject of $${{c+d}\over{e}}=f.$$

Correct answer: $${{c+d}\over{f}}=e$$

$$f(c+d)=e$$

$${{f}\over{c+d}}=e$$

$$e=cf+df$$

Q5.
Make $$d$$ the subject of $${{c-d}\over{e}}=f.$$

$${{c-f}\over{e}}=d$$

Correct answer: $$c-ef=d$$

$$ef-c=d$$

$$c+ef=d$$

Q6.
Make $$a$$ the subject of $${5\over{a+b}}=c.$$

$${5\over{c+b}}=a$$

$${5c\over{b}}=a$$

$${5c-{b}}=a$$

Correct answer: $${5\over{c}}-b=a$$

$${5\over{c}}+b=a$$

Assessment exit quiz

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6 Questions

Q1.
You can divide both sides of the formula $$s\times{t}=d$$ by $$t$$ to make $$s$$ the __________.

divisor

equation

Correct answer: subject

substitution

Q2.
$$s={d\over{t}}$$ can be rearranged as $$s\times{t}=d$$ and $$t={d\over{s}}$$. Which arrangement is the most useful if you know time and speed and wish to calculate distance?

$$s={d\over{t}}$$

Correct answer: $$s\times{t}=d$$

$$t={d\over{s}}$$

Q3.
Which of these arrangements of the formula for area of a circle is most useful if you know the area and wish to find the radius?

$$A={\pi}r^2$$

$${A\over{\pi}}=r^2$$

Correct answer: $$\sqrt{{A\over{\pi}}}=r$$

$${A\over{r^2}}=\pi$$

Q4.
Which rearrangement of the linear equation $$6x+7y=126$$ should you use if you know the $$x$$ coordinate and wish to find the $$y$$ coordinate?

$$6x+7y=126$$

$$x={{126-7y}\over6}$$

Correct answer: $$y={{126-6x}\over7}$$

$$7y=126-6x$$

Q5.
What is the gradient of the straight line with the linear equation $$5y-2x=30$$ ?

$$-2$$

Correct answer: $$2\over5$$

$$2$$

$$5\over2$$

$$5$$

Q6.
The gradient of a straight line is $$-{5\over3}$$ and the $$y$$-intercept is $$(0,20)$$. Give the equation of the line in the form $$ax+by=c.$$

$$5x+3y=20$$

$$3x+5y=20$$

Correct answer: $$5x+3y=60$$

$$5x-3y=60$$

$$3x+5y=60$$

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Maths

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Changing the subject to suit the context

Changing the subject to suit the context

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.For the linear equation $$y=5x-7$$, you can call $$y$$ the __________ of the equation.

Q2.Which of the below are correct rearrangements of the formula $$V=a\times{l}$$ ?

Q3.Make $$y$$ the subject of the equation $$8y-3x=24.$$

Q4.Make $$e$$ the subject of $${{c+d}\over{e}}=f.$$

Q5.Make $$d$$ the subject of $${{c-d}\over{e}}=f.$$

Q6.Make $$a$$ the subject of $${5\over{a+b}}=c.$$

Assessment exit quiz

6 Questions

Q1.You can divide both sides of the formula $$s\times{t}=d$$ by $$t$$ to make $$s$$ the __________.

Q2.$$s={d\over{t}}$$ can be rearranged as $$s\times{t}=d$$ and $$t={d\over{s}}$$. Which arrangement is the most useful if you know time and speed and wish to calculate distance?

Q3.Which of these arrangements of the formula for area of a circle is most useful if you know the area and wish to find the radius?

Q4.Which rearrangement of the linear equation $$6x+7y=126$$ should you use if you know the $$x$$ coordinate and wish to find the $$y$$ coordinate?

Q5.What is the gradient of the straight line with the linear equation $$5y-2x=30$$ ?

Q6.The gradient of a straight line is $$-{5\over3}$$ and the $$y$$-intercept is $$(0,20)$$. Give the equation of the line in the form $$ax+by=c.$$

Lesson appears in

UnitMaths / Expressions and formulae

Maths

Q1.
For the linear equation $$y=5x-7$$, you can call $$y$$ the __________ of the equation.

Q2.
Which of the below are correct rearrangements of the formula $$V=a\times{l}$$ ?

Q3.
Make $$y$$ the subject of the equation $$8y-3x=24.$$

Q4.
Make $$e$$ the subject of $${{c+d}\over{e}}=f.$$

Q5.
Make $$d$$ the subject of $${{c-d}\over{e}}=f.$$

Q6.
Make $$a$$ the subject of $${5\over{a+b}}=c.$$

Q1.
You can divide both sides of the formula $$s\times{t}=d$$ by $$t$$ to make $$s$$ the __________.

Q2.
$$s={d\over{t}}$$ can be rearranged as $$s\times{t}=d$$ and $$t={d\over{s}}$$. Which arrangement is the most useful if you know time and speed and wish to calculate distance?

Q3.
Which of these arrangements of the formula for area of a circle is most useful if you know the area and wish to find the radius?

Q4.
Which rearrangement of the linear equation $$6x+7y=126$$ should you use if you know the $$x$$ coordinate and wish to find the $$y$$ coordinate?

Q5.
What is the gradient of the straight line with the linear equation $$5y-2x=30$$ ?

Q6.
The gradient of a straight line is $$-{5\over3}$$ and the $$y$$-intercept is $$(0,20)$$. Give the equation of the line in the form $$ax+by=c.$$