Vardaan
Class 7 Maths • Chapter 02

Fractions and Decimals

Vardaan Learning Institute • Detailed Notes with Practice Questions

🍕 1. Types of Fractions

FRACTIONS Proper Fraction Numerator < Denominator e.g. 3/5, 2/7 Improper Fraction Numerator ≥ Denominator e.g. 7/3, 5/2 Mixed Number Whole + Proper fraction e.g. 2¼, 3½ Like Fractions Same denominator: 1/7, 3/7, 5/7 Unlike Fractions Diff denominators: 1/3, 2/5 Equivalent Fractions Same value: 1/2 = 2/4 = 3/6

✖️ 2. Multiplication of Fractions

Fraction × Fraction = (Numerator₁ × Numerator₂) / (Denominator₁ × Denominator₂)
Examples:
• 3
5 × 4
7 = 12
35

• Fraction × Whole number: 2
3 × 6 = 2 × 6
3 = 12
3 = 4

• Mixed numbers: First convert to improper, then multiply.
2½ × 3⅓ = 5
2 × 10
3 = 50
6 = 81
3
⚡ Shortcut: Cross-Cancellation Before multiplying, cancel common factors diagonally to simplify.
E.g. 4
9 × 3
8 → cancel 4 and 8 by 4, cancel 3 and 9 by 3 → 1
3 × 1
2 = 1/6
Reciprocal: The reciprocal of a
b is b
a.     Reciprocal of 5 = 1
5.     Fraction × its reciprocal = 1

➗ 3. Division of Fractions

a/b ÷ c/d = a/b × d/c (multiply by the reciprocal of the divisor)
Examples:
• 3
4 ÷ 5
8 = 3
4 × 8
5 = 24
20 = 6
5 = 11
5

• Whole ÷ Fraction: 5 ÷ 1
3 = 5 × 3 = 15 (Think: how many ⅓s fit in 5?)

• Fraction ÷ Whole: 3
7 ÷ 4 = 3
7 × 1
4 = 3
28

💧 4. Decimals — Multiplication

Type Method Example
Decimal × 10 Move decimal 1 place right 2.36 × 10 = 23.6
Decimal × 100 Move decimal 2 places right 2.36 × 100 = 236
Decimal × 1000 Move decimal 3 places right 2.36 × 1000 = 2360
Decimal × Decimal Multiply as whole numbers; count total decimal places; put them in the answer 0.3 × 0.4: 3×4=12; 2 dec places → 0.12

💧 5. Decimals — Division

Type Method Example
Decimal ÷ 10 Move decimal 1 place LEFT 36.5 ÷ 10 = 3.65
Decimal ÷ 100 Move decimal 2 places LEFT 36.5 ÷ 100 = 0.365
Decimal ÷ Whole Divide normally, keep decimal position 4.8 ÷ 4 = 1.2
Decimal ÷ Decimal Multiply both by 10/100 to make divisor a whole number, then divide 2.4 ÷ 0.4 = 24 ÷ 4 = 6
✏️ Practice Questions — Fractions & Decimals (30 Questions)

Section A — Direct Computation Easy

Q1. 3/5 × 10/9 = ?
Q2. 1/4 ÷ 1/8 = ?
Q3. 2.5 × 0.4 = ?
Q4. 7.2 ÷ 0.9 = ?
Q5. 3²/₃ × 2¼ = ?
Q6. 5 ÷ 2/3 = ?
Q7. 0.07 × 100 = ?
Q8. 1.4 ÷ 14 = ?
Q9. Reciprocal of 7/11 = ?
Q10. 4/5 × 5/4 = ?

Section B — Mixed Operations Medium

Q11. 3/7 of 49 apples = ?
Q12. Fill: 5/8 ÷ __ = 5
Q13. 1³/₄ ÷ 1/4 = ?
Q14. 0.24 ÷ 0.06 = ?
Q15. Arrange in ascending order: 5/6, 3/4, 7/8
Q16. 2/3 × 3/4 × 4/5 = ?
Q17. 1⅓ × 1½ × 1⅗ = ?
Q18. By how much does 8.3 exceed 6.79?
Q19. Convert 7/4 to mixed number, then multiply by 1.25
Q20. Cost of 2.5 m of cloth at ₹35.50/m = ?

Section C — Word Problems Medium

  1. Q21. Ramesh drank ¾ of a bottle of water. Each bottle holds 1.2 L. How much did he drink?
  2. Q22. A car travels 48.6 km in 0.9 hours. Find its speed in km/h.
  3. Q23. A ribbon is 12⅔ m long. Each piece requires ⅔ m. How many pieces can be cut?
  4. Q24. A recipe uses 2¾ cups of flour for 12 cookies. How much flour for 20 cookies?

Section D — Challenge Hard

  1. Q25. What should be multiplied to 3/7 to get 6/35?
  2. Q26. Find: (4/5 × 3/8) ÷ (9/10 ÷ 3/4)
  3. Q27. The product of two fractions is 36/77. One fraction is 9/7. Find the other.
  4. Q28. A tank is 3/5 full. After using 12 litres, it is ¼ full. What is the total capacity of the tank?
  5. Q29. A piece of wire is 73.5 cm. It is cut into equal pieces of 0.35 cm each. How many pieces?
  6. Q30. Find the value of x: (x × 2/3) ÷ (3/4 × 8/9) = 5/6
✅ Key Answers: Q1: 2/3 | Q2: 2 | Q3: 1.0 | Q4: 8 | Q5: 8¼ | Q6: 7.5 | Q7: 7 | Q8: 0.1 | Q9: 11/7 | Q10: 1 | Q20: ₹88.75 | Q22: 54 km/h | Q23: 19 pieces

📝 Quick Revision

  1. Proper: Numerator < Denominator. Improper: Num ≥ Den. Mixed: Whole + Proper
  2. Multiply fractions: Num × Num / Den × Den. Always simplify the result
  3. Reciprocal: flip the fraction. Any number × its reciprocal = 1
  4. Divide fractions: multiply by reciprocal of divisor (KCF: Keep Change Flip)
  5. For decimals × powers of 10: shift decimal RIGHT. For ÷ powers of 10: shift decimal LEFT
  6. Decimal × Decimal: count TOTAL decimal places → place them in the answer