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
- The equation of a straight line
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
- First, remove any fractions
- For example, make the subject of
- First remove fractions
- Multiply both sides by 2
- Multiply both sides by 2
- Then get on its own
- Subtract 6 from both sides
- Divide both sides by 5
- Subtract 6 from both sides
- There may be more than one correct way to write an answer
- The following are acceptable alternative forms
- The following are acceptable alternative forms
- First remove fractions
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
- is inside the brackets, so expand
- 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
- This is the same as (minus above) or (minus outside)
Exam Tip
- 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
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
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