Class 6 Maths Fractions Notes

Class 6 Maths – Chapter: Fractions

1. Introduction

• A fraction represents a part of a whole.
• Form:$\frac{numerator}{denominator}$denominatornumerator​
  • Numerator: Number of parts considered
  • Denominator: Total equal parts of the whole

Example:

• $\frac{3}{4}$43​ → 3 parts out of 4

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2. Types of Fractions

1. Proper fraction: Numerator < Denominator (e.g., 3/5)
2. Improper fraction: Numerator ≥ Denominator (e.g., 7/4)
3. Mixed fraction: Whole number + Proper fraction (e.g., 2 1/3)
4. Equivalent fractions: Fractions that are equal (e.g., 1/2 = 2/4)

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3. Basic Operations with Fractions

a) Addition

• Same denominator: Add numerators
  $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$52​+51​=53​
• Different denominators: Find LCM first
  $\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$21​+31​=63​+62​=65​

b) Subtraction

• Same denominator: Subtract numerators
• Different denominators: Find LCM

c) Multiplication

• Multiply numerators and denominators
  $\frac{2}{3} × \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$32​×43​=126​=21​

d) Division

• Multiply by reciprocal
  $\frac{2}{3} ÷ \frac{4}{5} = \frac{2}{3} × \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$32​÷54​=32​×45​=1210​=65​

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4. Conversion

• Improper fraction → Mixed fraction
  Divide numerator by denominator → quotient = whole number, remainder = numerator
• Mixed fraction → Improper fraction
  $\text{Whole number × denominator + numerator}$Whole number × denominator + numerator

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5. Examples

1. Add fractions:
   $\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$72​+73​=75​
2. Subtract fractions:
   $\frac{5}{6} – \frac{1}{2} = \frac{5}{6} – \frac{3}{6} = \frac{2}{6} = \frac{1}{3}$65​−21​=65​−63​=62​=31​
3. Multiply fractions:
   $\frac{3}{4} × \frac{2}{5} = \frac{6}{20} = \frac{3}{10}$43​×52​=206​=103​
4. Divide fractions:
   $\frac{7}{8} ÷ \frac{1}{4} = \frac{7}{8} × \frac{4}{1} = \frac{28}{8} = 3 ½$87​÷41​=87​×14​=828​=3½

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6. Practice Questions (50 Mixed)

Part A – MCQs – 15 Questions

1. Which is a proper fraction? 7/5, 2/3, 9/4, 12/7
2. 3/4 + 1/4 = ?
3. 5/6 – 1/3 = ?
4. 2/3 × 3/5 = ?
5. 7/8 ÷ 7/4 = ?
6. Convert 9/4 into mixed fraction
7. Convert 2 1/2 into improper fraction
8. Equivalent fraction of 3/5
9. 1/2 + 2/3 = ?
10. 5/7 – 2/7 = ?
11. Multiply 4/5 × 5/6 = ?
12. Divide 3/8 ÷ 3/4 = ?
13. Which fraction is improper? 2/3, 9/5, 3/7, 1/2
14. 7/10 + 2/5 = ?
15. 8/9 – 1/3 = ?

Part B – Fill in the Blanks – 10 Questions

16. Numerator is the __________ of a fraction
17. Denominator is the __________ of a fraction
18. 3/4 + 2/4 = __________
19. 5/6 – 1/2 = __________
20. 2/3 × 3/4 = __________
21. 3/5 ÷ 6/7 = __________
22. Convert 11/3 into mixed fraction = __________
23. Convert 1 2/5 into improper fraction = __________
24. Equivalent fraction of 2/3 = __________
25. 7/8 + 1/4 = __________

Part C – True/False – 5 Questions

26. 5/5 is a proper fraction (False)
27. 7/4 is an improper fraction (True)
28. Mixed fraction = Whole + proper fraction (True)
29. 2/3 × 3/2 = 1 (True)
30. Denominator can be 0 (False)

Part D – Match the Following – 5 Questions

Column A	Column B
31. Proper fraction	a) ≥ 1
32. Improper fraction	b) < 1
33. Mixed fraction	c) Whole + fraction
34. Reciprocal	d) Flip numerator & denominator
35. Equivalent fraction	e) Same value

Part E – Short Answer / Problem Solving – 15 Questions

36. Add 2/5 + 3/10
37. Subtract 7/8 – 1/4
38. Multiply 3/7 × 14/3
39. Divide 5/6 ÷ 2/3
40. Convert 17/5 into mixed fraction
41. Convert 3 3/4 into improper fraction
42. Add 2/3 + 3/4
43. Subtract 9/10 – 1/2
44. Multiply 7/8 × 4/7
45. Divide 3/5 ÷ 6/10
46. Find reciprocal of 5/6
47. Find 3 equivalent fractions of 4/9
48. Simplify 12/16
49. Add 5/12 + 7/18
50. Subtract 11/15 – 2/5

Answers – Class 6 Maths: Fractions

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Part A – MCQs (Answers)

1. 2/3 → Proper fraction
2. 3/4 + 1/4 = 4/4 = 1
3. 5/6 – 1/3 = 5/6 – 2/6 = 3/6 = 1/2
4. 2/3 × 3/5 = 6/15 = 2/5
5. 7/8 ÷ 7/4 = 7/8 × 4/7 = 4/8 = 1/2
6. 9/4 = 2 1/4 → Mixed fraction
7. 2 1/2 = 5/2 → Improper fraction
8. 3/5 = 6/10 → Equivalent fraction
9. 1/2 + 2/3 = 3/6 + 4/6 = 7/6 = 1 1/6
10. 5/7 – 2/7 = 3/7
11. 4/5 × 5/6 = 20/30 = 2/3
12. 3/8 ÷ 3/4 = 3/8 × 4/3 = 12/24 = 1/2
13. 9/5 → Improper fraction
14. 7/10 + 2/5 = 7/10 + 4/10 = 11/10 = 1 1/10
15. 8/9 – 1/3 = 8/9 – 3/9 = 5/9

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Part B – Fill in the Blanks (Answers)

16. Number of parts considered
17. Total equal parts of the whole
18. 5/4 or 1 1/4
19. 5/6 – 3/6 = 2/6 = 1/3
20. 2/3 × 3/4 = 6/12 = 1/2
21. 3/5 ÷ 6/7 = 3/5 × 7/6 = 21/30 = 7/10
22. 11/3 = 3 2/3
23. 1 2/5 = (1×5 + 2)/5 = 7/5
24. Equivalent fraction of 2/3 = 4/6, 6/9, 8/12
25. 7/8 + 1/4 = 7/8 + 2/8 = 9/8 = 1 1/8

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Part C – True/False (Answers)

26. False
27. True
28. True
29. True
30. False

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Part D – Match the Following (Answers)

Column A	Column B
31. Proper fraction	b) < 1
32. Improper fraction	a) ≥ 1
33. Mixed fraction	c) Whole + fraction
34. Reciprocal	d) Flip numerator & denominator
35. Equivalent fraction	e) Same value

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Part E – Short Answer / Problem Solving (Answers)

36. 2/5 + 3/10 = 4/10 + 3/10 = 7/10
37. 7/8 – 1/4 = 7/8 – 2/8 = 5/8
38. 3/7 × 14/3 = 42/21 = 2
39. 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 1 1/4
40. 17/5 = 3 2/5
41. 3 3/4 = (3×4 + 3)/4 = 15/4
42. 2/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1 5/12
43. 9/10 – 1/2 = 9/10 – 5/10 = 4/10 = 2/5
44. 7/8 × 4/7 = 28/56 = 1/2
45. 3/5 ÷ 6/10 = 3/5 × 10/6 = 30/30 = 1
46. Reciprocal of 5/6 = 6/5
47. Three equivalent fractions of 4/9 = 8/18, 12/27, 16/36
48. Simplify 12/16 = 3/4
49. 5/12 + 7/18 = 15/36 + 14/36 = 29/36
50. 11/15 – 2/5 = 11/15 – 6/15 = 5/15 = 1/3