Class 10 Maths Chapter 5 Exercise 5.4 Solutions 2026 – Algebraic Fractions Notes PDF

Unit 5: Algebraic Fractions | Exercise 5.4 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 5.4 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.

Where the LCM Finally Gets Used

Adding or subtracting algebraic fractions is the one operation in this chapter that absolutely requires a common denominator — exactly the LCM taught back in Exercise 5.2. Exercise 5.4 brings that skill back into play, combining it with careful numerator work to produce a single simplified fraction.

Key Concepts Covered in Exercise 5.4

Finding the LCM as the Common Denominator

Before adding or subtracting, factorize each denominator and find their LCM exactly as in Exercise 5.2. This LCM becomes the single denominator for the combined fraction.

Rewriting Each Fraction Over the Common Denominator

Each original fraction is multiplied (top and bottom) by whatever factor is missing from its denominator to reach the full LCM, without changing the fraction’s actual value.

Combining the Numerators

Once every fraction shares the same denominator, the numerators can be added or subtracted directly, keeping careful track of signs — especially when subtracting an entire numerator.

Simplifying the Result

After combining, the resulting numerator is simplified, and the whole fraction is checked for any further common factors with the denominator before being left as the final answer.

Step-by-Step Solved Examples

Q. No. 1: Simplify 1/x + 2/x².

LCM of x and x² is x²

Rewrite: 1/x = x/x², so x/x² + 2/x²

Combine numerators: (x + 2)/x²

Simplified: (x + 2)/x²  (with restriction x ≠ 0)

Q. No. 2: Simplify 3/(x+1) − 2/(x−1).

LCM of (x+1) and (x−1) is (x+1)(x−1)

Rewrite: 3(x−1)/[(x+1)(x−1)] − 2(x+1)/[(x+1)(x−1)]

Combine: [3(x−1) − 2(x+1)] / (x+1)(x−1)

Expand numerator: 3x−3−2x−2 = x−5

Simplified: (x−5) / (x+1)(x−1)  (with restrictions x ≠ −1, x ≠ 1)

Q. No. 3: Simplify 1/(x−2) + 1/(x+2).

LCM of (x−2) and (x+2) is (x−2)(x+2)

Rewrite: (x+2)/[(x−2)(x+2)] + (x−2)/[(x−2)(x+2)]

Combine: [(x+2) + (x−2)] / (x−2)(x+2)

Simplify numerator: x+2+x−2 = 2x

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

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 5.4 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 identifying the correct LCM to use as a common denominator
• Short Questions: Adding two fractions with simple monomial denominators, like Q. No. 1 above
• Long Questions: Subtracting fractions with binomial denominators requiring careful sign handling, like Q. No. 2 above

Where This Matters Beyond This Exercise

This exercise is where Exercises 5.1 through 5.3 all come together — factorization, HCF/LCM, and careful fraction arithmetic combine into a single multi-step process. Adding algebraic fractions is also a routine step in solving rational equations, a topic that frequently follows this chapter.

Common Mistakes Students Make in Exercise 5.4

• Forgetting to multiply the numerator by the same factor used to build up the denominator
• Losing a negative sign when subtracting an entire numerator, especially if it has more than one term
• Adding denominators directly instead of finding their LCM
• Not checking whether the final numerator and denominator share any further common factor

Why This Exercise Matters for the Board Exam

Because this exercise combines several earlier skills, it is one of the most heavily weighted long-question types in the chapter, and sign errors during subtraction are the single most common way marks are lost. Writing out each stage — LCM, rewritten fractions, combined numerator, simplified result — clearly tends to earn strong method marks.

Quick Links – Chapter 5: Algebraic Fractions

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 5.4 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. Why do I need the LCM to add algebraic fractions?

Just like numerical fractions, algebraic fractions can only be added or subtracted once they share the same denominator. The LCM is the smallest expression that both denominators divide into evenly, making it the most efficient common denominator to use.

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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