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Class 7 Mathematics Chapter 8 Working With Fractions

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I. Chapter Summary:

This chapter deals with the fundamental concepts of fractions including their operations such as addition, subtraction, multiplication, and division. It explains how to simplify fractions, convert improper fractions to mixed numbers and vice versa, and compare fractions. The chapter also covers practical applications of fractions in solving real-life problems, helping students develop a strong conceptual understanding and arithmetic skills related to fractions.

II. Key Concepts Covered:

• Fractions: Proper, improper, and mixed fractions explained with examples.

• Equivalent Fractions: Understanding and finding fractions equal in value.

• Simplification of Fractions: Techniques to reduce fractions to their simplest form.

• Operations on Fractions:

  • Addition and subtraction with like and unlike denominators.

  • Multiplication and division of fractions.

• Conversion: Converting mixed numbers to improper fractions and vice versa.

• Comparison of Fractions: Using common denominators or cross-multiplication to compare.

• Word Problems: Application of fraction operations in practical scenarios.

III. Important Questions:

(A) Multiple Choice Questions (1 Mark):

1. Which of the following is an improper fraction?
   a) 3/4
   b) 7/5
   c) 1/3
   d) 2/7
   Answer: b) 7/5
   (PYQ 2021)

2. The sum of 2/5 and 3/5 is:
   a) 5/10
   b) 1
   c) 1/2
   d) 5/5
   Answer: b) 1
   (PYQ 2020)

3. The reciprocal of 7/9 is:
   a) 9/7
   b) 7/9
   c) -9/7
   d) None
   Answer: a) 9/7
   (PYQ 2019)

4. Convert the mixed number 2 3/4 into an improper fraction:
   a) 11/4
   b) 8/3
   c) 7/4
   d) 10/4
   Answer: a) 11/4
   (PYQ 2018)

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

1. Simplify the fraction 24/36.

2. Add 3/7 and 2/5 and simplify the answer.

3. Subtract 5/6 from 1 1/2 and express the result as a mixed number.

4. Multiply 4/9 by 3/5 and simplify.

(C) Long Answer Questions (5 Marks):

1. Explain the steps to add fractions with different denominators and solve: 5/8 + 2/3.

2. Divide 7/12 by 3/4 and express the answer in simplest form.

3. Solve the word problem: A recipe needs 2 1/2 cups of flour, but only 1 3/4 cups are available. How much more flour is needed?

4. Explain how to convert an improper fraction into a mixed number with examples.

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

1. If the sum of two fractions is 1 and one of the fractions is 3/7, find the other fraction.

2. Show that the product of a fraction and its reciprocal is always 1.

IV. Key Formulas/Concepts:

• Addition/Subtraction: ab±cd=ad±bcbd\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}ba​±dc​=bdad±bc​

• Multiplication: ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}ba​×dc​=bdac​

• Division: ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}ba​÷dc​=ba​×cd​

• Conversion of mixed to improper: abc=ac+bca \frac{b}{c} = \frac{ac + b}{c}acb​=cac+b​

• Simplification: Divide numerator and denominator by their GCD (Greatest Common Divisor).

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):

• 1 Mark: Basic concepts and definitions (2018, 2019)

• 2/3 Marks: Operations and simplifications (2020, 2021)

• 5 Marks: Word problems and detailed explanation of operations (2019, 2022)

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

• Cooking and baking measurements often use fractions for ingredient quantities.

• Construction and craft projects use fractions to measure lengths and quantities.

• Financial calculations such as interest rates and discounts use fractional values.

• Splitting resources or time among people often involves fractions.

IX. Student Tips & Strategies for Success (Class-Specific):

• Practice converting between mixed numbers and improper fractions regularly.

• Always simplify your answers to the lowest terms for clarity.

• Use visual aids like fraction strips or pie charts to understand fraction concepts better.

• Solve as many word problems as possible to apply fractions in real contexts.

X. Career Guidance & Exploration (Class-Specific):

• For Classes 9–10:

  • Strengthens numeracy skills necessary for commerce, science, and engineering streams.

  • Essential foundation for competitive exams like NTSE and Olympiads.

• For Classes 11–12:

  • Applied in higher mathematics, physics, chemistry, and statistics.

  • Important for careers in finance, engineering, and data sciences.

XI. Important Notes:

• Refer to official CBSE and NCERT sources for latest syllabus updates.

• Consistent revision and solving practice problems are crucial for mastery.

• Conceptual understanding of fractions helps in advanced topics and exams.