Class 6 Mathematics Chapter 7 Fractions

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I. Chapter Summary:

This chapter introduces the concept of fractions as parts of a whole. Students learn how to represent fractions, understand the numerator and denominator, and compare different fractions. The chapter explains equivalent fractions, simplest form, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers. Through visual models and examples, students build a strong foundation in working with fractions in real-life contexts.

II. Key Concepts Covered:

• Fraction Definition: Part of a whole expressed as numerator $denominator\frac{\text{numerator}}{\text{denominator}}denominator numerator​.$

• Numerator and Denominator: Numerator represents parts taken, denominator represents total parts.

• Types of Fractions: Proper, improper, and mixed fractions.

• Equivalent Fractions: Different fractions representing the same value.

• Simplest Form: Fraction reduced so numerator and denominator have no common factor except 1.

• Comparing Fractions: Using common denominators or cross multiplication.

• Addition and Subtraction: Performed on fractions with the same denominator.

• Multiplication of Fraction by Whole Number: Multiplying numerator by the whole number.

• Visual Representation: Using pie charts, bar models, and number lines.

III. Important Questions:

(A) Multiple Choice Questions (1 Mark):

1. What is the denominator in the fraction 35\frac{3}{5}53​?
   a) 3
   b) 5
   c) 8
   d) 15
   Answer: b) 5
   (PYQ 2022)

2. Which fraction is equivalent to 24\frac{2}{4}42​?
   a) 12\frac{1}{2}21​
   b) 28\frac{2}{8}82​
   c) 34\frac{3}{4}43​
   d) 13\frac{1}{3}31​
   Answer: a) 12\frac{1}{2}21​
   (PYQ 2021)

3. The sum of 15+25\frac{1}{5} + \frac{2}{5}51​+52​ is:
   a) 310\frac{3}{10}103​
   b) 35\frac{3}{5}53​
   c) 25\frac{2}{5}52​
   d) 11\frac{1}{1}11​
   Answer: b) 35\frac{3}{5}53​

4. A fraction where numerator is greater than denominator is called:
   a) Proper fraction
   b) Improper fraction
   c) Mixed fraction
   d) Equivalent fraction
   Answer: b) Improper fraction

(B) Short Answer Questions (2/3 Marks):

1. Define numerator and denominator with examples.

2. Write two equivalent fractions for 36\frac{3}{6}63​.

3. Simplify the fraction 812\frac{8}{12}128​.

4. Add 37+27\frac{3}{7} + \frac{2}{7}73​+72​.

(C) Long Answer Questions (5 Marks):

1. Explain how to compare 45\frac{4}{5}54​ and 35\frac{3}{5}53​ using visual models.

2. Subtract 58−38\frac{5}{8} – \frac{3}{8}85​−83​ and express your answer in simplest form.

3. Multiply 34\frac{3}{4}43​ by 6 and simplify your answer.

4. Write a note on types of fractions with examples.

(D) HOTS (Higher Order Thinking Skills) Questions:

1. If you have 34\frac{3}{4}43​ of a cake and you eat 12\frac{1}{2}21​ of what you have, how much cake did you eat?

2. Compare 56\frac{5}{6}65​ and 79\frac{7}{9}97​ without finding their decimal equivalents. Explain your method.

IV. Key Formulas/Concepts:

• Addition/Subtraction of fractions with like denominators:

  ad±bd=a±bd\frac{a}{d} \pm \frac{b}{d} = \frac{a \pm b}{d}da​±db​=da±b​

• Multiplication of fraction by whole number:

  n×ab=n×abn \times \frac{a}{b} = \frac{n \times a}{b}n×ba​=bn×a​

• Simplest form: Divide numerator and denominator by their GCD.

• Equivalent fractions: Multiply/divide numerator and denominator by the same number.

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

VII. Previous Year Questions (PYQs):

• 2022: MCQ on denominator (1 mark)

• 2021: Short answer on equivalent fractions (2 marks)

• 2020: Long answer on fraction addition (5 marks)

• 2019: HOTS on multiplication of fractions (3 marks)

VIII. Real-World Application Examples to Connect with Topics:

• Cooking recipes where ingredients are measured in fractions.

• Dividing property, money, or food into fractional parts.

• Time management using fractional parts of an hour.

• Sharing objects equally among people.

IX. Student Tips & Strategies for Success:

• Practice simplifying fractions regularly.

• Use visual aids like pie charts and number lines for better understanding.

• Memorize addition and multiplication rules for fractions with like denominators.

• Solve past papers and sample questions for exam readiness.

X. Career Guidance & Exploration:

• For Classes 9–10:

  • Strong grasp on fractions aids success in Science, Commerce, and Arts streams.

  • Competitive exams like NTSE and Olympiads emphasize fraction knowledge.

• For Classes 11–12:

  • Careers in Engineering, Medicine, and Economics require solid fraction skills.

  • Entrance exams like JEE, NEET, CUET test fraction concepts deeply.

XI. Important Notes:

• Always consult the official CBSE website for the latest syllabus updates.

• Conceptual clarity is more important than memorization for long-term success.

• Regular revision and practice are essential.