Viral Maths — Ch11: Fraction

📌 What This Chapter Covers

Fraction chapter mein 6 types hain — addition/subtraction (like aur unlike denominators), fraction+whole number combos, multiplication, aur division (Shark Approach).
Butterfly Approach aur Shark Approach dono cross-multiplication based hain lekin different operations ke liye — inhe mix mat karo.

⚡ QUICK RECALL

Butterfly = Addition/Subtraction of unlike fractions (cross-multiply then ADD/SUBTRACT numerators). Shark = Division of fractions (cross-multiply differently, no addition involved).

🗂️ Chapter Index

Tab	Type	Operation
2	Type 1: Like Fractions	Add/Subtract (same denominator)
3	Type 2: Butterfly Approach	Add/Subtract (different denominators)
4	Type 3: Fraction + Whole	Addition
5	Type 4: Whole − Fraction	Subtraction
6	Type 5: Fraction × Fraction	Multiplication
7	Type 6: Shark Approach	Division (single or multiple fractions)
8	Master Table	All types summarized

Type 1 — Like Fractions (Same Denominator)

Example: 2/12 + 5/12

Step 1: Add numerators: 2+5 = 7 Step 2: Keep same denominator: 12 Answer: 7/12

⚡ QUICK RECALL

Jab denominators SAME hon, sirf numerators add/subtract karo — denominator touch mat karo.

Type 2 — Butterfly Approach (Unlike Fractions, Different Denominators)

Example: 3/11 + 5/9

Step 1: Cross-multiply: 3×9=27 and 5×11=55 Step 2: Add the results: 27+55 = 82 (numerator) Step 3: Multiply denominators: 11×9 = 99 (denominator) Answer: 82/99

⚠ EXAM TRAP

Subtraction ke liye bhi same cross-multiply hota hai, bas numerators ADD ki jagah SUBTRACT karo (bade se chhota).

⚡ QUICK RECALL — "Butterfly" Visual

Do fractions ke beech "X" pattern (butterfly wings) banao — diagonal cross-multiply karke jodo, phir denominators multiply karo.

Type 3 — Fraction Added with a Whole Number

Example: 6 + 5/6

Step 1: Keep 6 as the whole number Step 2: Attach the fraction as-is Answer: 6⅚ (mixed number)

⚡ QUICK RECALL

Whole number + fraction = seedha mixed number bana do, koi calculation nahi chahiye jab tak fraction already proper form mein ho.

Type 4 — Fraction Subtracted from a Whole Number

Example: 42 − 5/12

Step 1: Subtract 1 from the whole number: 42−1 = 41 Step 2: Find the difference between denominator and numerator: 12−5 = 7 Step 3: Combine: 41 and 7/12 Answer: 41 7/12

⚠ EXAM TRAP

Whole number se seedha 1 minus karna zaroori hai (kyunki 1 "borrow" hoti hai fraction ke liye) — aur new numerator (denominator−original numerator) se aata hai, original numerator se nahi.

Type 5 — Fraction Multiplication

Example: 23/71 × 11/20

Step 1: Multiply numerators: 23×11 = 253 Step 2: Multiply denominators: 71×20 = 1420 Answer: 253/1420

⚡ QUICK RECALL

Multiplication sabse simple hai: Num×Num over Den×Den — koi cross-multiply nahi chahiye (yeh Butterfly ya Shark se alag hai).

Type 6 — Shark Approach (Fraction ÷ Fraction)

Example: (23/71) ÷ (2/3) — one other fraction

Step 1: Main numerator × other's denominator: 23×3 = 69 Step 2: Main denominator × other's numerator: 71×2 = 142 Answer: 69/142

Example: (23/71) ÷ (2/3) ÷ (1/5) — two other fractions

Step 1: Main numerator × all others' denominators: 23×3×5 = 345 Step 2: Main denominator × all others' numerators: 71×2×1 = 142 Answer: 345/142

⚠ EXAM TRAP

"Main" fraction hamesha PEHLI fraction hoti hai chain mein — uska numerator baaki sabke denominators ko grab karta hai, uska denominator baaki sabke numerators ko grab karta hai.

⚡ QUICK RECALL

Shark Approach = repeated "flip-and-multiply" ek hi step mein — jitni bhi fractions divide ho rahi hon, sabka effect ek saath le lo.

📋 Master Table — All Fraction Types

Type	Operation	Core Rule
Like Fractions	Add/Subtract (same denom)	Operate on numerators only, keep denominator
Butterfly Approach	Add/Subtract (unlike denom)	Cross-multiply, add/subtract results, multiply denominators
Fraction + Whole	Addition	Combine directly as mixed number
Whole − Fraction	Subtraction	Whole−1, new numerator = denominator−original numerator
Fraction × Fraction	Multiplication	Num×Num over Den×Den
Shark Approach	Division	Main num×others' denoms / Main denom×others' nums