Change of Subject of a Formula Explained — Rules & Worked Examples (JAMB/WAEC Mathematics)

The subject of a formula is the single variable that stands alone on one side of an equation, and changing the subject means rearranging the formula so a different variable takes that place, using consistent, balanced operations on both sides.

This lesson covers the definition, the core rules to follow, and several worked practical examples for JAMB and WAEC Mathematics.

Quick takeaways

• The subject of a formula is the variable that stands alone on one side of the equals sign.
• Whatever operation you apply to one side of an equation, you must apply to the other side too, to keep it balanced.
• Fractions should be cleared by multiplying both sides by the denominator before isolating the target variable.
• Square roots and powers must be removed last, only after the term containing them has been fully isolated.
• Practicing a range of worked examples is the most reliable way to become comfortable with this skill, since formulas vary widely in structure.

Timestamps

• 0:00 Introduction
• 0:54 What is the Subject of a Formula?
• 1:20 Rules for Changing the Subject
• 2:41 Worked Example 1
• 5:33 Worked Example 2
• 7:53 Worked Example 3

What is the subject of a formula?

The subject of a formula is the variable that appears alone on one side of an equation, with every other term on the other side. For example, in v = u + at, v is the subject. Changing the subject means rearranging the equation so a different variable — such as u, a, or t — becomes the new subject instead, while the formula remains mathematically equivalent.

What rules should you follow when changing the subject of a formula?

1. Keep both sides balanced — any operation performed on one side must be performed identically on the other
2. Clear fractions early — multiply both sides by the denominator before isolating the target variable
3. Isolate the target variable’s term first — move every other term away before dealing with roots or powers
4. Remove roots and powers last — square both sides to clear a square root, or take a root to clear a power, only once that term is fully isolated
5. Watch your signs — moving a term across the equals sign changes its sign, and this is where most careless errors happen

Worked example 1: a simple linear formula

Make t the subject of v = u + at:

• Subtract u from both sides: v − u = at
• Divide both sides by a: t = (v − u)/a

Worked example 2: a formula with a fraction

Make x the subject of y = (x + 3)/2:

• Multiply both sides by 2: 2y = x + 3
• Subtract 3 from both sides: x = 2y − 3

Worked example 3: a formula with a square root

Make r the subject of A = πr²:

• Divide both sides by π: A/π = r²
• Take the square root of both sides: r = √(A/π)

Working through examples like these in order of increasing difficulty — starting with simple linear rearrangements, then fractions, then roots or powers — builds the skill progressively rather than jumping straight into the hardest cases.

Common mistakes students make with this topic

• Performing an operation on only one side of the equation
• Trying to remove a square root or power before the term containing it is fully isolated
• Losing track of a sign when moving a term across the equals sign
• Rushing through practice examples without working through each rearrangement step by step

Frequently asked questions

Q: What does it mean to change the subject of a formula? It means rearranging an equation so a different variable stands alone on one side, using balanced operations on both sides to keep the equation mathematically equivalent.

Q: What should you do first when a formula contains a fraction? Multiply both sides of the equation by the denominator to clear the fraction before proceeding with the usual steps to isolate the target variable.

Q: When should you remove a square root from an equation? Only after the term containing the square root has been fully isolated on one side — squaring both sides too early can complicate the rest of the rearrangement.

Q: Why is practicing multiple worked examples important for this topic? Because formulas vary widely in structure (linear, fractional, involving roots or powers), and practicing a range of examples builds the flexibility needed to handle whatever structure appears in an exam question.

This is one topic from our full JAMB & WAEC Maths course — see everything covered →