Class 10 Maths Chapter 5 Exercise 5.3 Solutions 2026 – Algebraic Fractions Notes PDF

Unit 5: Algebraic Fractions | Exercise 5.3 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 5.3 solutions for Algebraic Fractions have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

Multiplying and Dividing Without Finding a Common Denominator

Unlike addition and subtraction, multiplying or dividing fractions never requires a common denominator — this is true for both numbers and algebraic expressions. Exercise 5.3 applies the familiar numerical fraction rules to algebraic fractions, with factorization playing a bigger role than ever in simplifying the result.

Key Concepts Covered in Exercise 5.3

Multiplying Algebraic Fractions

To multiply two algebraic fractions, multiply the numerators together and the denominators together, then simplify by cancelling any common factors — ideally before multiplying everything out.

Dividing Algebraic Fractions

To divide by an algebraic fraction, multiply by its reciprocal instead (flip the second fraction upside down, then multiply). This turns every division problem back into a multiplication problem.

Factorizing Before Cancelling

The key skill in this exercise is factorizing every numerator and denominator first, then cancelling common factors across the whole expression — not just within a single fraction — before multiplying anything out.

Simplifying the Final Answer

After cancelling, the remaining factors are multiplied to give the final simplified expression, ideally left in factored form rather than expanded, unless a fully expanded answer is specifically requested.

Step-by-Step Solved Examples

Q. No. 1: Multiply (x/3) × (6/x²).

(x × 6) / (3 × x²) = 6x / 3x²

Cancel common factor 3x: 6x/3x² = 2/x

Simplified: 2/x  (with restriction x ≠ 0)

Q. No. 2: Multiply (x+2)/(x−1) × (x−1)/(x+3).

Write as one fraction: (x+2)(x−1) / (x−1)(x+3)

Cancel the common factor (x−1):

Simplified: (x+2)/(x+3)  (with restrictions x ≠ 1, x ≠ −3)

Q. No. 3: Divide (x²−4)/(x+1) ÷ (x+2)/(x+1).

Multiply by the reciprocal: (x²−4)/(x+1) × (x+1)/(x+2)

Factorize x²−4 = (x−2)(x+2):

(x−2)(x+2)(x+1) / (x+1)(x+2)

Cancel (x+1) and (x+2):

Simplified: x − 2  (with restrictions x ≠ −1, x ≠ −2)

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 5.3 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on what the reciprocal of a given algebraic fraction is
• Short Questions: Multiplying two simple algebraic fractions, like Q. No. 1 above
• Long Questions: Division problems requiring factorization before simplifying, like Q. No. 3 above

Where This Matters Beyond This Exercise

Multiplying and dividing algebraic fractions confidently is what makes the addition and subtraction exercise ahead manageable, since some of those problems also involve a multiplication step along the way. These same skills are used later in solving rational equations and in simplifying complex expressions in trigonometry and calculus.

Common Mistakes Students Make in Exercise 5.3

• Forgetting to flip the second fraction (find its reciprocal) when dividing
• Cancelling terms instead of factors, the same mistake carried over from Exercise 5.1
• Multiplying out numerators and denominators before checking for common factors, making cancellation harder
• Forgetting to state restrictions on the variable in the final answer

Why This Exercise Matters for the Board Exam

Multiplication and division questions are compact and formulaic, making them efficient marks once the reciprocal rule for division is memorized. Examiners often test whether students factorize before multiplying, since doing so is both faster and less error-prone than expanding everything first.

Quick Links – Chapter 5: Algebraic Fractions

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Download Exercise 5.3 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 5.3 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. Do I need a common denominator to multiply or divide algebraic fractions?

No — a common denominator is only needed for addition and subtraction. Multiplication and division work directly, with division simply requiring the second fraction to be flipped (its reciprocal used) first.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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