Changing the Subject of a Formula — Class 9

Changing the Subject of a Formula – Class 9 Worksheet Practice

Changing the subject of a formula means rearranging a mathematical formula so that a different letter is isolated on one side of the equation. This is an important algebra skill because formulas are used throughout mathematics and science. A student may be given a formula with one quantity as the subject, but a problem can ask for another quantity. Instead of memorising many versions of the same formula, students can learn a reliable rearrangement method.

What does “subject of the formula” mean?

The subject is the variable written alone on one side of an equation. For example, in v = u + at, the subject is v. If a question asks you to make t the subject, subtract u from both sides and then divide by a: t = (v − u) / a. The key rule is that any operation performed on one side must also be performed on the other side.

Key rules for changing the subject

• Addition: move an added term by subtracting it from both sides.
• Subtraction: move a subtracted term by adding it to both sides.
• Multiplication: remove a factor by dividing both sides.
• Division: remove a denominator by multiplying both sides.
• Squares: use the square root when the required variable is squared.
• Square roots: square both sides when appropriate.
• Fractions: clear denominators carefully before isolating the required variable.

Important formulas and examples

Linear formula: If y = ax + b, make x the subject: x = (y − b)/a.

Speed formula: From v = d/t, making t the subject gives t = d/v, while making d the subject gives d = vt.

Area of a triangle: From A = ½bh, making h the subject gives h = 2A/b, and making b the subject gives b = 2A/h.

Rectangle: From A = lw, making w the subject gives w = A/l.

Perimeter: From P = 2(l+w), making w the subject gives w = P/2 − l.

Square relationship: If A = x², then x = √A for a non-negative length.

How to use this online worksheet

Start by selecting the number of questions, question type, difficulty and timer. Press Start New Test to generate a fresh worksheet. Each question has an answer box and its own Check Answer button. The answer remains hidden until the question has been checked. A correct response is highlighted in green and an incorrect response in red. After checking, the student can reveal the correct answer. The progress bar updates as questions are checked, and the final result displays the score.

Why regular practice matters

Changing the subject becomes easier when students repeatedly apply inverse operations rather than relying on memorised patterns. Mixed practice is especially useful because it forces the learner to decide which operation should be performed first. This worksheet includes linear, fraction, square/root, reciprocal, geometry, multi-step and word-formula styles so that students practise the same core skill in different contexts. The shuffle feature creates a new order for every test and the generator can create up to 1,000 questions in one worksheet.

Tips for students

Write one algebraic step at a time. Keep the required subject clearly in mind. If a variable is multiplied by a number, divide both sides. If it is divided by a number, multiply both sides. When brackets are involved, simplify carefully. For squared variables, remember that taking a square root may introduce a positive/negative mathematical possibility; for school-level length questions, the positive value is normally selected. Always substitute your result back into the original formula when you have time. This is one of the best ways to catch sign or division errors.

For teachers and parents

This free online worksheet can be used for homework, classroom warm-ups, revision, remedial practice and quick assessments. The difficulty selector helps create appropriately challenging sets, while the timer can add exam-style practice. The PDF button provides a printable copy of the currently displayed questions. Because the page is responsive, students can practise on phones, tablets, laptops or desktop computers without installing an app.

Frequently Asked Questions

Can I make 1,000 questions? Yes. The worksheet generator supports up to 1,000 questions in a single test.

Can questions be shuffled? Yes. Start a new test or use Shuffle Worksheet to create a new randomized order.

Can I see an answer before checking? No. The answer is deliberately hidden until the question has been checked.

Does it work on mobile? Yes. The interface uses responsive layouts and large touch-friendly controls.

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