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25 Dec 2025

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3 pages

Master 'Changing the Subject' - GCSE Maths Guide

Lucía

@luttior

Ever wondered how to flip a formula around to find... Show more

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# Changing the subject

• In the formula; y = 2x

y is known as the 'subject' of the formula
This is because you are being give y 'in the te

What Does "Subject" Mean?

Think of the subject of a formula as the star of the show - it's the variable that stands alone on one side of the equals sign. In y = 2x, y is the subject because everything else is working to define what y equals.

Changing the subject means rearranging the formula so a different variable becomes the star. It's like rewriting the same story from a different character's perspective.

To change the subject, you need to get your chosen variable completely on its own. Use inverse operations (opposite maths operations) to "undo" everything that's happening to your variable.

Quick Tip: Whatever you do to one side of the equation, you must do to the other side too - it's the golden rule of algebra!

Step-by-Step Rearranging

Let's see how this works with real examples. Starting with m = 7n + 5, if you want n as the subject, first subtract 5 from both sides to get m - 5 = 7n.

Next, divide both sides by 7, giving you n = $m - 5$ /7. You've successfully made n the subject by working backwards through the operations.

For more complex formulas like S = 3t + 5u, you can make either variable the subject. To get t alone, subtract 5u first, then divide by 3: t = $S - 5u$ /3.

The same formula can be rearranged for u by subtracting 3t and dividing by 5: u = $S - 3t$ /5. One formula, multiple arrangements!

Handling Brackets and Fractions

When brackets appear in formulas like a = 3 $b + c$ , deal with them strategically. Divide by the number outside the bracket first: a/3 = b + c, then continue rearranging normally.

Fractions need special attention too. In a = b/3 + 5, subtract 5 first to get a - 5 = b/3, then multiply both sides by 3 to find b = 3 $a - 5$ .

Remember to expand brackets when needed - 5 $2 + t$ = w becomes 10 + 5t = w before you continue rearranging. This makes the next steps much clearer.

Pro Tip: Always check your final answer by substituting some numbers back into both the original and rearranged formulas - they should give the same results!

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25 Dec 2025

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3 pages

Master 'Changing the Subject' - GCSE Maths Guide

Lucía

@luttior

Ever wondered how to flip a formula around to find different variables? Changing the subject of a formula is like rearranging puzzle pieces - you're simply moving terms around to solve for whichever variable you need.

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What Does "Subject" Mean?

Changing the subject means rearranging the formula so a different variable becomes the star. It's like rewriting the same story from a different character's perspective.

To change the subject, you need to get your chosen variable completely on its own. Use inverse operations (opposite maths operations) to "undo" everything that's happening to your variable.

Quick Tip: Whatever you do to one side of the equation, you must do to the other side too - it's the golden rule of algebra!

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Step-by-Step Rearranging

Let's see how this works with real examples. Starting with m = 7n + 5, if you want n as the subject, first subtract 5 from both sides to get m - 5 = 7n.

Next, divide both sides by 7, giving you n = $m - 5$ /7. You've successfully made n the subject by working backwards through the operations.

For more complex formulas like S = 3t + 5u, you can make either variable the subject. To get t alone, subtract 5u first, then divide by 3: t = $S - 5u$ /3.

The same formula can be rearranged for u by subtracting 3t and dividing by 5: u = $S - 3t$ /5. One formula, multiple arrangements!

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Handling Brackets and Fractions

When brackets appear in formulas like a = 3 $b + c$ , deal with them strategically. Divide by the number outside the bracket first: a/3 = b + c, then continue rearranging normally.

Fractions need special attention too. In a = b/3 + 5, subtract 5 first to get a - 5 = b/3, then multiply both sides by 3 to find b = 3 $a - 5$ .

Remember to expand brackets when needed - 5 $2 + t$ = w becomes 10 + 5t = w before you continue rearranging. This makes the next steps much clearer.

Pro Tip: Always check your final answer by substituting some numbers back into both the original and rearranged formulas - they should give the same results!