Rearranging Formulae
Rearranging formulae means changing the subject of a formula. The subject is the variable that is on its own.
In v = u + at, the subject is v.
If we rearrange to u = v - at, the subject is now u.
Using inverse operations
Rearranging formulae uses the same idea as solving equations. Whatever you do to one side, you must do to the other side.
Example 1: Make x the subject
Make x the subject of y = x + 5.
Subtract 5 from both sides:
y - 5 = x
x = y - 5
Example 2: Make x the subject
Make x the subject of y = 3x.
Divide both sides by 3:
x = y/3
Two-step rearranging
Undo addition or subtraction first, then undo multiplication or division.
Example 3: Make x the subject
Make x the subject of y = 2x + 7.
Subtract 7 from both sides:
y - 7 = 2x
Divide both sides by 2:
x = (y - 7)/2
Formulae with fractions
If the variable is in a fraction, multiply both sides first to remove the denominator.
Example 4: Make x the subject
Make x the subject of y = x/4.
Multiply both sides by 4:
4y = x
x = 4y
Formulae with brackets
Sometimes you need to expand brackets or divide by a whole bracket.
Example 5: Make x the subject
Make x the subject of y = a(x + b).
Divide both sides by a:
y/a = x + b
Subtract b:
x = y/a - b
Formulae where the subject appears twice
Higher GCSE questions may include the variable you want on both sides. Collect those terms together, then factorise.
Example 6: Subject appears twice
Make x the subject of ax + b = cx.
Move ax to the right side:
b = cx - ax
Factorise x:
b = x(c - a)
Divide by c - a:
x = b/(c - a)
A common mistake is dividing only one term instead of the whole side. For example, from y - 7 = 2x, the answer is x = (y - 7)/2, not y - 7/2.
Treat rearranging formulae like solving equations. Use one clear inverse operation at a time and keep the target variable in sight.
Video explanation
A short Worthing Maths Tutor video explanation for rearranging formulae can be embedded here later to improve student engagement and time on page.
Practice questions
- Make x the subject of y = x + 9.
- Make x the subject of y = 5x.
- Make x the subject of y = 3x - 4.
- Make x the subject of y = x/6.
- Make x the subject of y = a(x - 2).
Answers
- x = y - 9
- x = y/5
- x = (y + 4)/3
- x = 6y
- x = y/a + 2
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