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.
Instead of finding a value though, you will find an expression that the variable is equal to.

Common misconception

When rearranging multiplicative relationships, the values just 'swap'

Pupils should understand how to manipulate multiplicative relationships properly instead of relying on a 'trick'. This will be useful in other subject areas as well.

Keywords

Subject of an equation - 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.

There are opportunities to see the importance of changing the subject in a range of topic areas. For example when rearranging trigonometric ratios, or using geometric formula. There are also examples of linear relationships between x and y which can be linked to identifying the gradient of a line.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

Skip video

Worksheet

Download worksheet

Skip worksheet

Starter quiz

Download starter quiz

6 Questions

Q1.

If the side of an equilateral triangle is $$3n+1$$, write an expression for the perimeter.

Correct Answer: 3(3n+1), 9n + 3

Q2.

If the side of a regular pentagon is $$14y - a$$ write an expression for the perimeter.

Correct Answer: 5(14y - a), 70y - 5a

Q3.

Which of the following is an expression for the area of a square with side length $$3x$$

$$3x^2$$

$$(3x^2)$$

Correct answer: $$(3x)^2$$

Q4.

What is the value of $$x$$ for $$5(x + 7) = 30$$?

Correct Answer: -1

Q5.

If $$x$$ is a positive integer, what is the value of $$x$$ for $$x^2 - 4 = 0$$?

Correct Answer: 2

Q6.

What is the value of $$x$$ for $$2x - 3 = 7$$?

Correct Answer: 5

Exit quiz

Download exit quiz

6 Questions

Q1.

Make $$x$$ the subject of $$3y - x = 15$$

Correct answer: $$x = 3y - 15$$

$$x = 15 - 3y$$

$$x = 3y + 15$$

$$x = -3y - 15$$

Q2.

Make $$y$$ the subject of $$4x + 2y = 8$$

$$y = 2x + 4$$

$$y = -2x - 4$$

Correct answer: $$y = 4 - 2x$$

$$y = 2 - 4x$$

Q3.

Make $$z$$ the subject of $$\frac{z}{2} + 3x = 7$$

$$z = 7 - 3x$$

$$z = 4 - 3x$$

$$z = 14 - 3x$$

Correct answer: $$z = 14 - 6x$$

Q4.

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

$$a = \frac{b + 2}{3} - 4$$

Correct answer: $$a = \frac{b - 2}{3} + 4$$

$$a = \frac{b - 2}{3} - 4$$

$$a = \frac{b + 6}{3}$$

Q5.

Make $$m$$ the subject of $$\frac{4m + 5}{3} = n$$

$$m = 3n + 5$$

$$m = \frac{3n + 5}{4}$$

Correct answer: $$m = \frac{3n - 5}{4}$$

$$m = \frac{n - 5}{3}$$

Q6.

Make $$p$$ the subject of $$2p + \frac{q}{3} = 4$$

$$p = \frac{8 - q}{6}$$

$$p = 2 - \frac{q}{3}$$

$$p = \frac{4 - q}{3}$$

Correct answer: $$p = 2 - \frac{q}{6}$$