🔟➕ Viral Maths — Chapter 11: Fraction

by Navneet Tiwari (Adda247)  ·  6 Types incl. Butterfly & Shark Approach · Bank / SSC / Railway / BPSC / BSSC

📌 What This Chapter Covers
  • The Fractions chapter has six types: addition and subtraction with like or unlike denominators, fraction-plus-whole-number combinations, multiplication, and division using the Shark Approach.
  • The Butterfly and Shark approaches are both based on cross multiplication but apply to different operations. Do not mix them.
⚡ 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
TabTypeOperation
2Type 1: Like FractionsAdd/Subtract (same denominator)
3Type 2: Butterfly ApproachAdd/Subtract (different denominators)
4Type 3: Fraction + WholeAddition
5Type 4: Whole − FractionSubtraction
6Type 5: Fraction × FractionMultiplication
7Type 6: Shark ApproachDivision (single or multiple fractions)
8Master TableAll 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
When the denominators are the SAME, add or subtract only the numerators and leave the denominator unchanged.
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 uses the same cross multiplication, but SUBTRACT the numerators instead of adding them, taking the smaller from the larger.
⚡ QUICK RECALL — "Butterfly" Visual
Form an X pattern, or butterfly wings, between the two fractions. Cross-multiply diagonally and add the results, then multiply the denominators.
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 = write it directly as a mixed number. No calculation is required as long as the fraction is already in proper form.
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
Subtract 1 directly from the whole number because 1 is borrowed for the fraction. The new numerator is denominator − original numerator, not the original numerator itself.
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 is the simplest: Num×Num over Den×Den. No cross multiplication is needed; this differs from the Butterfly and Shark approaches.
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
The “main” fraction is always the FIRST fraction in the chain. Its numerator takes all the remaining denominators, while its denominator takes all the remaining numerators.
⚡ QUICK RECALL
The Shark Approach performs repeated flip-and-multiply in one step. Combine the effect of all fractions being divided at once.
📋 Master Table — All Fraction Types
TypeOperationCore Rule
Like FractionsAdd/Subtract (same denom)Operate on numerators only, keep denominator
Butterfly ApproachAdd/Subtract (unlike denom)Cross-multiply, add/subtract results, multiply denominators
Fraction + WholeAdditionCombine directly as mixed number
Whole − FractionSubtractionWhole−1, new numerator = denominator−original numerator
Fraction × FractionMultiplicationNum×Num over Den×Den
Shark ApproachDivisionMain num×others' denoms / Main denom×others' nums