Viral Maths — Ch04: Multiplication

📌 What This Chapter Covers

Multiplication is the method of finding the product of two or more numbers — this is the LARGEST chapter in Viral Maths with 26 named approaches.
The book advises daily practice: find numbers around you and multiply them verbally.
The approaches are organized into groups: the Repeat Family (11/99/101/1001), general break methods, Miya or consecutive-number tricks, the ×5 family, the fraction-shortcut family (25/125/0.5, etc.), Ice Cream (repeated digits), Double & Partition, and special-pattern methods (zero in the middle and numbers ending in 1).

⚡ QUICK RECALL

First check whether the multiplier is 11, 99, 101 or 1001; whether one number is 5/25/125/0.5/1.5/2.5/12.5; or whether the two numbers are consecutive or close. Choose the correct tab accordingly.

🗂️ Chapter Index (26 Types Grouped into 9 Families)

Tab	Types Covered	Family
2	Type 1, 2, 14, 15	×11, ×99/999/9999, ×101 (Chhoti Machine), ×1001 (Badi Machine)
3	Type 3, 21	Any-number×any-number break method, Table Approach
4	Type 4, 5, 6, 18	Bade Miya-Chote Miya (even×ends5, ending-75), Padosan (consecutive), Trishul (consecutive even/odd)
5	Type 7, 8	Even×5, Odd×5
6	Type 9,10,11,12,13,16,17,19	×25, ×0.5, ×125, ×1.25, ×12.5, ×1.5, ×15, ×2.5
7	Type 20	Ice Cream Approach (repeat-digit × single digit)
8	Type 22, 23, 24	Number×its double, Product Partition (a) and (b)
9	Type 25, 26	Triple-digit with 0 in middle, Two-digit numbers ending in 1
10	—	Master Table — all 26 types summarized

Type 1 — Multiplication with 11 (Space Method)

2-digit example: 11 × 63

Step 1: Leave a space between digits: 6 _ 3 Step 2: Add them: 6+3 = 9 Step 3: Place in middle: 693

3-digit example: 11 × 876

Step 1: 8 _ _ 6 (outer digits fixed) Step 2: Add adjacent pairs from right: 7+6=13, 8+7=15 Step 3: Place with carries: 8(15)(13)6 → carries roll left Step 4: Final answer: 9636

⚠ EXAM TRAP

Whenever the sum of adjacent digits is at least 10, immediately carry to the left before finalizing; otherwise the answer will be incorrect.

Type 2 — Multiplication with 99 / 999 / 9999

Example: 999 × 648

Step 1: Subtract 1 from 648: 647 Step 2: 999 − 647 = 352 Step 3: Combine: 647352

⚡ QUICK RECALL

n × 99...9 (k nines) = (n−1) | (10^k − n) — left part is n−1, right part is the complement.

Type 14 — Chhoti Photocopy Machine Approach (× 101)

2-digit number × 101 → just repeat the number

21 × 101 = 2121 35 × 101 = 3535

Type 15 — Badi Photocopy Machine Approach (× 1001)

3-digit number × 1001 → repeat the number

352 × 1001 = 352352 546 × 1001 = 546546

2-digit number × 1001 → repeat with a 0 in the middle

45 × 1001 = 45045 31 × 1001 = 31031

⚡ QUICK RECALL — "Photocopy" Family

×101 = Chhoti (small) machine, repeats a 2-digit number.
×1001 = Badi (big) Machine; it repeats a three-digit number, or a two-digit number padded with 0.

Type 3 — Any Number × Any Number (Place-Value Break)

Example: 39 × 17

Step 1: Break 39 as (30+9) Step 2: (30×17) + (9×17) = 510 + 153 Step 3: Answer = 663

Example: 251 × 12

Break 251 = 200+50+1 (200×12)+(50×12)+(1×12) = 2400+600+12 = 3012

Type 21 — Table Approach (Number 1–99 × Single Digit)

Example: 56 × 7

Step 1: Break 56 as (50+6) Step 2: 50×7 = 350 Step 3: 6×7 = 42 Step 4: Add: 350+42 = 392

⚡ QUICK RECALL

Types 3 and 21 use the same core idea. Type 21 is highlighted specifically for single-digit multipliers because this is the most common exam pattern.

Type 4 — Bade Miya-Chote Miya Approach (Even × Ends-in-5)

Example: 35 × 26

Step 1: Double the number ending in 5: 35×2 = 70 Step 2: Half the even number: 26/2 = 13 Step 3: Multiply results: 70×13 = 910

Type 18 — Bade Miya-Chote Miya Extended (× Number Ending in 75)

Base pattern: 75×4=300, 175×4=700, 275×4=1100, 375×4=1500...

Example: 28 × 175

Step 1: Divide 28 by 4: 7 Step 2: Multiply 175 by 4: 700 Step 3: Multiply results: 7×700 = 4900

⚠ EXAM TRAP

This method works only when the first number is exactly divisible by 4; otherwise a fraction appears and the approach becomes slower.

Type 5 — Padosan Approach (Consecutive Numbers)

Requires knowing squares 1–100 by heart

Example: 24 × 25

Method A: Square of smaller + smaller: 24²+24 = 576+24 = 600 Method B: Square of bigger − bigger: 25²−25 = 625−25 = 600

Type 6 — Trishul Approach (Consecutive Even/Odd Numbers)

Example: 12 × 14 (middle = 13)

12 is 1 less than 13, 14 is 1 more Answer = 13² − 1² = 169−1 = 168

Example: 47 × 53 (middle = 50)

47 is 3 less, 53 is 3 more than 50 Answer = 50² − 3² = 2500−9 = 2491

⚡ QUICK RECALL

Trishul = find the middle number, square it, subtract the square of the gap. Works for BOTH consecutive-even and consecutive-odd pairs, and even wider symmetric gaps.

Type 7 — Multiplication of Even Number with 5

Example: 56 × 5

Step 1: Half of 56 = 28 Step 2: Add a 0 at the end: 280

Example: 648 × 5

Half of 648 = 324 → 3240

Type 8 — Multiplication of Odd Number with 5

Example: 57 × 5

Step 1: Subtract 1: 57−1 = 56 (now even) Step 2: Half of 56: 28 Step 3: Add 5 at the end: 285

Example: 457 × 5

457−1=456 → half=228 → append 5 → 2285

⚠ EXAM TRAP

Even number×5 → append 0. Odd number×5 → append 5. Don't mix these up.

Type 9 — × 25 (= 100/4)

Example: 648 × 25

Divide by 4: 648/4 = 162 Add 00: 16200

Type 10 — × 0.5 (= 1/2)

Example: 246 × 0.5

Just halve it: 246/2 = 123

Type 11 — × 125 (= 1000/8)

Example: 128 × 125

Divide by 8: 128/8 = 16 Add 000: 16000

Type 12 — × 1.25 (= 10/8)

Example: 48 × 1.25

Divide by 8: 48/8 = 6 Add 0: 60

Type 13 — × 12.5 (= 100/8)

Example: 128 × 12.5

Divide by 8: 128/8 = 16 Add 00: 1600

⚠ EXAM TRAP

×1.25, ×12.5 and ×125 all use ÷8. Only the number of zeros differs: 1.25 → one 0, 12.5 → two 0s, and 125 → three 0s.

Type 16 — × 1.5 (Add Half of Itself)

Example: 42 × 1.5

Half of 42 = 21 42+21 = 63

Type 17 — × 15 (Add Half, Then ×10)

Example: 48 × 15

Step 1: Add half of itself: 48+24 = 72 Step 2: Append a 0: 720

Type 19 — × 2.5 (= 10/4)

Example: 36 × 2.5

Divide by 4: 36/4 = 9 Add 0: 90

Example: 248 × 2.5

248/4 = 62 → 620

⚡ QUICK RECALL — Whole Fraction-Shortcut Family

×0.5=÷2 | ×2.5=÷4+0 | ×25=÷4+00 | ×1.25=÷8+0 | ×12.5=÷8+00 | ×125=÷8+000 | ×1.5=+half | ×15=+half then ×10

Type 20 — Ice Cream Approach (Repeated-digit Number × Single Digit)

Use for: 22, 44, 55, 555, 666... × single digit

Example: 44 × 3

Step 1: Units product: 4×3 = 12 Step 2: One "4" left over → leave 1 space Step 3: Place sum of end digits (1+2=3) in between Answer: 1(3)2 = 132

Example: 666 × 8

Step 1: Units product: 6×8 = 48 Step 2: Two "6"s left → leave 2 spaces Step 3: Fill with sum (4+8=12), carry 1 Answer: 5328

⚠ EXAM TRAP

The number of gaps created in the middle matches the number of digit repetitions. Propagate carries carefully to the left.

Type 22 — Number × Its Own Double

Example: 14 × 28

Square of smaller: 14² = 196 Double it: 196×2 = 392

⚡ QUICK RECALL

n × 2n = 2n² — requires knowing squares 1-100 fluently (connects to Ch01 Important Products).

Type 23 — Product Partition Approach (a) — Clean 2-digit Split

Example: 1224 × 4

Step 1: Break into 12 (Part 1) and 24 (Part 2) Step 2: 12×4 = 48 Step 3: 24×4 = 96 Step 4: Since part 2 has exactly 2 digits, combine directly: 4896

Type 24 — Product Partition Approach (b) — With Carry

Example: 2568 × 2

Step 1: Break into 256 (Part 1) and 8 (Part 2) Step 2: 256×2 = 512 Step 3: 8×2 = 16 Step 4: Part 2 should be 1 digit only — use 6, carry the 1 to Part 1 Step 5: 512+1 = 513, combine with 6: 5136

⚠ EXAM TRAP

The result of the right partition must always contain the same number of digits as the original right part. If there is an extra digit, carry it to the LEFT as in column addition.

Type 25 — Triple-Digit × Triple-Digit with Zero in Middle

Pattern: a0b × c0d

Example: 503 × 408

Step 1: 5×4 = 20 (left block) Step 2: 5×8 + 4×3 = 40+12 = 52 (middle block) Step 3: 3×8 = 24 (right block) Step 4: Combine (with carries): 20|52|24 → 205224

⚡ QUICK RECALL

Left = a×c, Middle = a×d+b×c, Right = b×d. Form these three blocks and then adjust the carry from right to left.

Type 26 — Two-digit Numbers Ending in 1

Example: 51 × 41

Step 1: Units product: 1×1 = 1 Step 2: Sum of tens digits: 5+4 = 9 Step 3: Product of tens digits: 5×4 = 20 Combine: 20 | 9 | 1 → 2091

⚠ EXAM TRAP

This works only when the units digit of BOTH numbers is 1; it does not apply to 51×42.

📋 Master Table — All 26 Multiplication Types

#	Approach	Rule
1	× 11	Space method: add adjacent digits, place in middle
2	× 99/999/9999	(n−1) \| complement to power of 10
3	Any × Any	Break by place value, multiply each part, add
4	Bade Miya-Chote Miya	Even × ends-5: double the 5-ender, halve the even
5	Padosan (consecutive)	smaller²+smaller OR bigger²−bigger
6	Trishul (consecutive even/odd)	middle² − gap²
7	Even × 5	Half the number, append 0
8	Odd × 5	Subtract 1, half, append 5
9	× 25	÷4, append 00
10	× 0.5	÷2
11	× 125	÷8, append 000
12	× 1.25	÷8, append 0
13	× 12.5	÷8, append 00
14	Chhoti Machine (×101)	Repeat 2-digit number
15	Badi Machine (×1001)	Repeat 3-digit (or 2-digit with 0 pad)
16	× 1.5	Add half of itself
17	× 15	Add half of itself, append 0
18	Bade Miya (ends-75)	÷4 first number, ×4 second number, multiply
19	× 2.5	÷4, append 0
20	Ice Cream (repeat-digit×1digit)	units product, spaced digit-sum insert
21	Table Approach	Break tens+units, multiply single digit, add
22	Number × its double	2 × (smaller number)²
23	Product Partition (a)	Split clean, multiply each, combine
24	Product Partition (b)	Split with carry when right part overflows
25	Zero-middle triple×triple	a×c \| a×d+b×c \| b×d
26	Ends-in-1 (2-digit)	tens×tens \| tens sum \| 1

🔑 Approach Selection Flowchart

Multiplier is 11 → Type 1
Multiplier is 99/999/9999 → Type 2
Multiplier is 101 → Type 14 | 1001 → Type 15
One number even, other ends in 5 → Type 4 (or Type 18 if ends in 75)
Two consecutive numbers → Type 5
Two consecutive even OR odd numbers → Type 6 (Trishul)
Multiplier is 5 → Type 7/8 (even/odd)
Multiplier is 25/125/0.5/1.25/12.5/1.5/15/2.5 → Fraction-Shortcut family (Tab 6)
Number is a repeated digit (22,44,555...) × single digit → Type 20 (Ice Cream)
Number × its own double → Type 22
Big number × single digit, no special pattern → Type 23/24 (Product Partition)
Triple-digit × triple-digit, zero in middle → Type 25
Both numbers end in 1 → Type 26