Formulas where Subject Appears Once (Edexcel GCSE Maths)
Revision Note
Written by: Mark Curtis
Reviewed by: Dan Finlay
Simple Rearranging
What are formulas?
A formula is a rule, definition or relationship between different quantities, written in shorthand using letters (variables)
They include an equals sign
Some examples you should be familiar with are:
The equation of a straight line
The area of a trapezium
Pythagoras' theorem
How do I rearrange formulas?
The letter (variable) that is on its own on one side is called the subject
y is the subject of y = mx + c
To make a different letter the subject, we need to rearrange the formula
This is also called changing the subject
The method is as follows:
First, remove any fractions
Multiply both sides by the lowest common denominator
Then use inverse (opposite) operations to get the variable on its own
This is similar to solving equations
For example, make the subject of
First remove fractions
Multiply both sides by 2
Then get on its own
Subtract 6 from both sides
Divide both sides by 5
There may be more than one correct way to write an answer
The following are acceptable alternative forms
Should I expand brackets?
Expand brackets if it releases the variable you want from inside the brackets
If not, you can leave them in
To make the subject of
is inside the brackets, so expand
Rearrange
To make the subject of
is not inside the brackets, so you do not need to expand
Instead, divide both sides by the bracket
What if I get fractions in fractions?
Some rearrangements can lead to fractions in fractions
Either rewrite with a divide sign, , then use the method of dividing two fractions
Or multiply top and bottom by the the lowest common denominator of the two fractions and cancel
becomes
What if I end up dividing by a negative?
Remember that (minus below) is the same as (minus above) and the same as (minus outside)
Though be careful, as is
becomes (minus below)
This is the same as (minus above) or (minus outside)
brackets are required for minus above
brackets are assumed for minus outside
You can also expand the brackets
Examiner Tips and Tricks
Mark schemes will accept different forms of the same answer, as long as they are correct and fully simplified
Worked Example
Make the subject of the following.
(a)
Get 5x on its own by subtracting 4m from both sides
Get x on its own by dividing both sides by 5
(b)
Remove fractions by multiplying both sides by the denominator, x
Get x on its own by dividing both sides by 3t
(c)
Remove fractions by multiplying both sides by the denominator, 2g
x is inside the brackets
Expand the brackets to release the x term
One way to get x on its own is by subtracting 9 then dividing by -36
Or you can first add 36x to both sides, to create positive 36x on the left
Now get x on its own by subtracting 2gA then dividing by 36
Other accepted forms of the answer are
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