Previous knowledge

Before learning this topic, students should:

be able to add negative numbers
have knowledge of inverse operators ie the inverse of addition is subtraction and the inverse of multiplication is division
be able to solve simple equations

We rearrange the items in a formula so that a different variable becomes the subject. Knowledge of solving equations and inverse operations is a necessary tool in order to change the subject. If not too familiar with inverse operators, please experiment with this function machine game.

Example 1
A = bh
Let's ÷ h on both sides
b = A ⁄ h

If we know the area and the height, we have just rearranged the formula for the area to find the base.

Example 2

v = u + at is an equation used in physics. We can rearrange the equation to find a.

v = u+at

Let's - u on both sides

v - u = at
Let's ÷t on both sides

a = (v-u) ⁄ t

Example 3
Rearrange the equation so that k is the subject
p = k ⁄ j

Let's x j on both sides

k = pj

Example 4
Rearrange the equation so that j is the subject
k = pj

Let's ÷ p on both sides

j = k ⁄ p

in order to get x on its own we apply the inverse operator to both sides- square root

in order to get x on its own we apply the inverse operator ie square root both sides

Diagnostic questions

Before we move on, let's see how much we have understood.

Question 1

Question 2

If you did not get these answers all correct, please go through again the examples above.

Explore tasks

Apply inverse operators to both sides to change the subject of the equation

basic , advanced

Independent tasks

Work through the bronze, silver and gold tasks.

Activity 1

Finally, try out the exam questions

Activity 2

Misconceptions

Students should be aware of the traps when rearranging equations:

switching the letters e.g m = p + 4 mistakenly becomes p = m + 4
when dividing both sides by a value, students may forget to firstly include brackets e.g 2m = p + 4 → 2m = (p+4) → m = (p+4)⁄2
when rearranging the equation, students should remember to use inverse operators e.g the inverse operator of addition is subtraction and the inverse operator of multiplication is division.