Class 7 | Ganita Prakash | Chapter 8
🍕 Working with Fractions
Multiplication · Division · Reciprocals · Problems
✖️ 8.1 — Multiplication of Fractions
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Multiplying Fractions:
Examples:
a/b × c/d = (a×c)/(b×d)
Examples:
- 2/3 × 4/5 = (2×4)/(3×5) = 8/15
- 3/4 × 8/9 = 24/36 = 2/3 (simplify!)
- 1/2 × 1/2 = 1/4 (half of a half = quarter!)
Fraction × Whole number:
2/3 × 6 = 2/3 × 6/1 = 12/3 = 4
Or shortcut: 2/3 × 6 = 2 × (6÷3) = 2 × 2 = 4
Simplify BEFORE multiplying (cancel common factors!):
3/4 × 8/9 → cancel: 3 and 9 (÷3), 4 and 8 (÷4) → 1/1 × 2/3 = 2/3
2/3 × 6 = 2/3 × 6/1 = 12/3 = 4
Or shortcut: 2/3 × 6 = 2 × (6÷3) = 2 × 2 = 4
Simplify BEFORE multiplying (cancel common factors!):
3/4 × 8/9 → cancel: 3 and 9 (÷3), 4 and 8 (÷4) → 1/1 × 2/3 = 2/3
🍕 Pizza thinking!
1/2 of 3/4 pizza = 3/8 pizza
"Of" means MULTIPLY: 1/2 × 3/4 = 3/8
1/2 of 3/4 pizza = 3/8 pizza
"Of" means MULTIPLY: 1/2 × 3/4 = 3/8
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➗ 8.2 — Division of Fractions
Dividing by a fraction = Multiplying by its reciprocal!
a/b ÷ c/d = a/b × d/c
(Flip the second fraction, then multiply!)
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Examples:
2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
5 ÷ 1/2 = 5 × 2 = 10
(How many halves in 5 wholes? 10 halves!)
1/2 ÷ 4 = 1/2 × 1/4 = 1/8
2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
5 ÷ 1/2 = 5 × 2 = 10
(How many halves in 5 wholes? 10 halves!)
1/2 ÷ 4 = 1/2 × 1/4 = 1/8
🔑 Reciprocal = Flip the fraction!
Reciprocal of 3/4 = 4/3
Reciprocal of 5 = 1/5
Reciprocal of 1/7 = 7
Any number × its reciprocal = 1 ✅
(3/4 × 4/3 = 12/12 = 1 ✅)
Reciprocal of 3/4 = 4/3
Reciprocal of 5 = 1/5
Reciprocal of 1/7 = 7
Any number × its reciprocal = 1 ✅
(3/4 × 4/3 = 12/12 = 1 ✅)
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🧩 8.3 — Problems with Fractions
Common Problem Types:
🍎 Part of a whole:
3/4 of 24 apples = 3/4 × 24 = 18 apples
🚶 Fraction of distance:
Walked 2/5 of 15 km = 2/5 × 15 = 6 km
💰 Fraction of money:
Spent 3/8 of ₹400 = 3/8 × 400 = ₹150
🍎 Part of a whole:
3/4 of 24 apples = 3/4 × 24 = 18 apples
🚶 Fraction of distance:
Walked 2/5 of 15 km = 2/5 × 15 = 6 km
💰 Fraction of money:
Spent 3/8 of ₹400 = 3/8 × 400 = ₹150
Read: identify what fraction of what
"Of" = multiply; "divided equally" = divide
Write the fraction equation
Simplify before multiplying
Check: answer should make sense!
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⚡ Quick Tips & Tricks
🧠 Mental Math Shortcuts!
- Half of a fraction: multiply by 1/2 → divide numerator by 2
- Double a fraction: multiply by 2 → multiply numerator by 2
- To compare fractions: cross-multiply! a/b vs c/d → compare ad vs bc
- Mixed number to improper: 2 3/4 → (2×4+3)/4 = 11/4
- Improper to mixed: 11/4 → 2 remainder 3 → 2 3/4
Adding/Subtracting Fractions — common denominator first!
1/3 + 1/4 → LCD = 12 → 4/12 + 3/12 = 7/12
3/5 – 1/3 → LCD = 15 → 9/15 – 5/15 = 4/15
1/3 + 1/4 → LCD = 12 → 4/12 + 3/12 = 7/12
3/5 – 1/3 → LCD = 15 → 9/15 – 5/15 = 4/15
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📝 Quick Cheatsheet
Multiply: top×top
bottom×bottom
a/b × c/d = ac/bd
bottom×bottom
a/b × c/d = ac/bd
Divide = Flip &
Multiply!
÷ c/d = × d/c
Multiply!
÷ c/d = × d/c
Reciprocal = flip
3/4 → 4/3
n × 1/n = 1
3/4 → 4/3
n × 1/n = 1
"of" = ×
Simplify first!
Then multiply
Simplify first!
Then multiply
| Operation | Rule | Example |
|---|---|---|
| Multiply | Numerator × numerator, denominator × denominator | 2/3 × 3/4 = 6/12 = 1/2 |
| Divide | Multiply by reciprocal of divisor | 2/3 ÷ 4/5 = 2/3 × 5/4 = 5/6 |
| Simplify | Divide top & bottom by HCF | 6/9 → 6÷3/9÷3 = 2/3 |
| "of" | Always multiply! | 1/2 of 20 = 10 |
🌟 Chapter 8 Complete! 🌟
Made with ❤️ by @edugrown
Made with ❤️ by @edugrown